FLUID MECHANICS & MACHINERY NOTES WITH QUESTION BANK AND TWO MARK QUESTION ANSWERS

R.M.K COLLEGE OF ENGINEERING AND TECHNOLOGY RSM NAGAR, PUDUVOYAL-601206

DEPARTMENT OF MECHANICAL ENGINEERING

CE6451 – FLUID MECHANICS & MACHINERY

III SEM MECHANICAL ENGINEERING Regulation 2013

QUESTION BANK PREPARED BY R.ASHOK KUMAR M.E (CAD)

R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015

UNIT - I - FLUID PROPERTIES AND FLOW CHARACTERISTICS Part - A 1.1) What is a fluid? How are fluids classified? 1.2) Define fluid. Give examples. 1.3) How fluids are classified?

[AU, Nov / Dec - 2010] [AU, Nov / Dec - 2008, May / June - 2012]

1.4) Distinguish between solid and fluid.

[AU, May / June - 2006]

1.5) Differentiate between solids and liquids.

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1.6) Discuss the importance of ideal fluid.

[AU, April / May - 2011]

1.7) What is a real fluid?


1.8) Define Newtonian and Non – Newtonian fluids.

[AU, Nov / Dec - 2008]

1.9) What are Non – Newtonian fluids? Give example.

[AU, Nov / Dec - 2009]

1.10) Differentiate between Newtonian and Non – Newtonian fluids. [AU, Nov / Dec - 2007] 1.11) What is the difference between an ideal and a real fluid? 1.12) Differentiate between liquids and gases. 1.13) Define Pascal’s law.

[AU, Nov / Dec – 2005, 2008]

1.14) Define the term density. 1.15) Define mass density and weight density.

[AU, Nov / Dec - 2007]

1.16) Distinguish between the mass density and weight density. [AU, May / June - 2009] 1.17) Define the term specific volume and express its units.


1.18) Define specific weight. 1.19) Define specific weight and density. 1.20) Define density and specific gravity of a fluid.

[AU, May / June - 2012] [AU, Nov / Dec - 2012]

1.21) Define the term specific gravity. 1.22) What is specific weight and specific gravity of a fluid?


1.23) What is specific gravity? How is it related to density?


1.24) What do you mean by the term viscosity? 1.25) What is viscosity? What is the cause of it in liquids and in gases? [AU, Nov / Dec - 2005] 1.26) Define Viscosity and give its unit.

[AU, Nov / Dec - 2003]

1.27) Define Newton’s law of viscosity.

[AU, Nov / Dec - 2012]

CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 2


1.28) State the Newton's law of viscosity. [AU, April / May, Nov / Dec - 2005, May / June - 2007] 1.29) Define Newton’s law of viscosity and write the relationship between shear stress and velocity gradient?

[AU, Nov / Dec - 2006]

1.30) What is viscosity and give its units?


1.31) Define coefficient of viscosity.


1.32) Define coefficient of volume of expansion.

[AU, Nov / Dec - 2012]

1.33) Define relative or specific viscosity.

[AU, May / June - 2013]

1.34) Define kinematic viscosity.

[AU, Nov / Dec - 2009]

1.35) Define kinematic and dynamic viscosity.

[AU, May / June - 2006]

1.36) What is the importance of kinematic viscosity?

[AU, Nov / Dec - 2014]

1.37) Mention the significance of kinematic viscosity.

[AU, Nov / Dec - 2011]

1.38) What is dynamic viscosity? What are its units? 1.39) Define dynamic viscosity.

[AU, Nov / Dec - 2008, May / June - 2012]

1.40) Define the terms kinematic viscosity and give its dimensions. [AU, May / June - 2009] 1.41) What is kinematic viscosity? State its units?

[AU, May / June - 2014]

1.42) Differentiate between kinematic viscosity of liquids and gases with respect to pressure.

[AU, Nov / Dec - 2013]

1.43) Write the units and dimensions for kinematic and dynamic viscosity. [AU, Nov / Dec - 2005] 1.44) What are the units and dimensions for kinematic and dynamic viscosity of a fluid? [AU, Nov / Dec - 2006, 2012] 1.45) Differentiate between kinematic and dynamic viscosity. [AU, May / June - 2007, Nov / Dec – 2008, 2011] 1.46) How does the dynamic viscosity of liquids and gases vary with temperature? [AU, Nov / Dec - 2007, April / May - 2008] 1.47) What are the variations of viscosity with temperature for fluids? [AU, Nov / Dec - 2009] 1.48) What is the effect of temperature on viscosity of water and that of air? 1.49) Why is it necessary in winter to use lighter oil for automobiles than in summer? To what property does the term lighter refer?

[AU, Nov / Dec - 2010]



1.50) Define the term pressure. What are its units?

[AU, Nov / Dec - 2005]

1.51) Give the dimensions of the following physical quantities [AU, April / May - 2003] a)

Pressure

b)

surface tension

c)

Dynamic viscosity

d)

kinematic viscosity

1.52) Define eddy viscosity. How it differs from molecular viscosity? [AU, Nov / Dec - 2010] 1.53) Define surface tension.

[AU, May / June - 2006]

1.54) Define surface tension and expression its unit.


1.55) Define capillarity.

[ AU, Nov / Dec - 2005, May / June - 2006]

1.56) What is the difference between cohesion and adhesion? 1.57) Define the term vapour pressure. 1.58) What is meant by vapour pressure of a fluid? 1.59) Brief on the significance of vapour pressure.

[AU, April / May - 2010] [AU, Nov / Dec - 2014]

1.60) What are the types of pressure measuring devices? 1.61) What do you understand by terms: i)

Isothermal process ii)

adiabatic process

1.62) What do you mean by capillarity?

[AU, Nov / Dec - 2009]

1.63) Explain the phenomenon of capillarity. 1.64) Define surface tension. 1.65) What is compressibility of fluid? 1.66) Define compressibility of the fluid. [AU, Nov / Dec – 2008, May / June - 2009] 1.67) Define compressibility and viscosity of a fluid.


1.68) Define coefficient of compressibility. What is its value for ideal gases? [AU, Nov / Dec - 2010] 1.69) List the components of total head in a steady, in compressible irrotational flow. [AU, Nov / Dec - 2009] 1.70) Define the bulk modulus of fluid.

[AU, Nov / Dec - 2008]

1.71) Define - compressibility and bulk modulus.

[AU, Nov / Dec – 2011]

1.72) Write short notes on thyxotropic fluid.



1.73) What is Thyxotrphic fluid?

[AU, Nov / Dec - 2003]

1.74) One poise’s equal to __________Pa.s. 1.75) State the empirical pressure density relation for a liquid. [AU, Nov / Dec - 2014] 1.76) Give the types of fluid flow. 1.77) Define steady flow and give an example. 1.78) Define unsteady flow and give an example. 1.79) Differentiate between the steady and unsteady flow.

[AU, May / June - 2006]

1.80) When is the flow regarded as unsteady? Give an example for unsteady flow. [AU, April / May - 2003] 1.81) Define uniform flow and give an example. 1.82) Define non uniform flow and give an example. 1.83) Differentiate between steady flow and uniform flow.

[AU, Nov / Dec - 2007]

1.84) Define laminar and turbulent flow and give an example. 1.85) Differentiate between laminar and turbulent flow. [AU, Nov / Dec – 2005, 2008, April / May - 2015] 1.86) Distinguish between Laminar and Turbulent flow.


1.87) State the criteria for laminar flow.

[AU, Nov / Dec - 2008]

1.88) State the characteristics of laminar flow.


1.89) What are the characteristics of laminar flow?

[AU, May / June - 2014]

1.90) Mention the general characteristics of laminar flow.

[AU, May / June - 2013]

1.91) Define - Incompressible fluid.

[AU, Nov / Dec - 2014]

1.92) Define compressible and incompressible flow and give an example. 1.93) Define rotational and irrotational flow and give an example. 1.94) Distinguish between rotation and circularity in fluid flow. [AU, April / May - 2005] 1.95) Define stream line. What do stream lines indicate?

[AU, Nov / Dec - 2007]

1.96) Define streamline and path line in fluid flow.

[AU, Nov / Dec - 2005]

1.97) What is stream line and path line in fluid flow? 1.98) What is a streamline? 1.99) Define streak line. 1.100) Define stream function.

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[AU, April / May – 2010, May / June - 2012]



1.101) Define control volume.


1.102) What is the use of control volume?


1.103) What is meant by continuum?

[AU, Nov / Dec - 2008]

1.104) Define continuity equation. 1.105) Write down the equation of continuity.

[AU, Nov / Dec –2008, 2009, 2012]

1.106) State the continuity equation in one dimensional form? [AU, May / June - 2012] 1.107) State the general continuity equation for a 3 - D incompressible fluid flow. [AU, May / June - 2007, Nov / Dec - 2012] 1.108) State the continuity equation for the case of a general 3-D flow. [AU, Nov / Dec - 2007] 1.109) State the equation of continuity in 3 dimensional incompressible flow. [AU, Nov / Dec - 2005] 1.110) State the assumptions made in deriving continuity equation. [AU, Nov / Dec - 2011] 1.111) Define Euler's equation of motion. 1.112) Write the Euler's equation.


1.113) What is Euler’s equation of motion?

[AU, Nov / Dec - 2008]

1.114) Define Bernoulli's equation. 1.115) Write the Bernoulli’s equation in terms of head. Explain each term. [AU, Nov / Dec - 2007] 1.116) What are the basic assumptions made is deriving Bernoulli’s theorem? [AU, Nov / Dec – 2005, 2012] 1.117) List the assumptions which are made while deriving Bernoulli’s equation. [AU, May / June - 2012] 1.118) State at least two assumptions of Bernoulli’s equation. [AU, May / June - 2009] 1.119) What are the three major assumptions made in the derivation of the Bernoulli’s equation?


1.120) State the assumptions used in the derivation of the Bernoulli's equation. [AU, Nov / Dec - 2014] 1.121) State Bernoulli’s theorem as applicable to fluid flow.

[AU, Nov / Dec - 2003]



1.122) Give the assumptions made in deriving Bernoulli’s equation. [AU, Nov / Dec - 2012] 1.123) What are the applications of Bernoulli’s theorem?


1.124) Give the application of Bernoulli’s equation. 1.125) List the types of flow measuring devices fitted in a pipe flow, which uses the principle of Bernoulli’s equation.

[AU, May / June - 2012]

1.126) Mention the uses of manometer.

[AU, Nov / Dec - 2009]

1.127) State the use of venturimeter.

[AU, May / June - 2006]

1.128) Define momentum principle. 1.129) Define impulse momentum equation. 1.130) Write the impulse momentum equation.

[AU, May / June - 2007]

1.131) What do you understand by impulse momentum equation? [AU, May / June - 2013] 1.132) State the momentum equation. When can it applied.

[AU, May / June - 2009]

1.133) State the usefulness of momentum equation as applicable to fluid flow phenomenon.

[AU, May / June – 2007, Nov / Dec - 2012]

1.134) Define discharge (or) rate of flow. 1.135) Discuss the momentum flux.


1.136) Find the continuity equation, when the fluid is incompressible and densities are equal. 1.137) What is the moment of momentum equation?

[AU, May / June - 2014]

1.138) Explain classification of fluids based on viscosity. 1.139) State and prove Euler's equation of motion. Obtain Bernoulli's equation from Euler's equation. 1.140) State and prove Bernoulli's equation. What are the limitations of the Bernoulli's equation? 1.141) State the momentum equation. How will you apply momentum equation for determining the force exerted by a flowing liquid on a pipe bend? 1.142) Give the equation of continuity. Obtain an expression for continuity equation for a three - dimensional flow. 1.143) Calculate the density of one litre petrol of specific gravity 0.7? [AU, April / May - 2011] CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 7


1.144) If a liquid has a viscosity of 0.051 poise and kinematic viscosity of 0.14 stokes, calculate its specific gravity.


1.145) Calculate the mass density and specific volume of one litre of a liquid which weighs 7 N.


1.146) A soap bubble is formed when the inside pressure is 5 N/m2above the atmospheric pressure. If surface tension in the soap bubble is 0.0125 N/m, find the diameter of the bubble formed.


1.147) Determine the gauge pressure inside a soap bubble of diameter 0.25 cm and 6 cm at 22°C.

[AU, Nov / Dec - 2014]

1.148) The converging pipe with inlet and outlet diameters of 200 mm and 150 mm carries the oil whose specific gravity is 0.8. The velocity of oil at the entry is 2.5 m/s, find the velocity at the exit of the pipe and oil flow rate in kg/sec. [AU, April / May - 2010] 1.149) Find the height through which the water rises by the capillary action in a 2mm bore if the surface tension at the prevailing temperature is0.075 g/cm. [AU, April / May - 2003] 1.150) Find the height of a mountain where the atmospheric pressure is 730mm of Hg at normal conditions.

[AU, Nov / Dec - 2009]

1.151) Suppose the small air bubbles in a glass of tap water may be on the order of50 μ m in diameter. What is the pressure inside these bubbles?

[AU, Nov / Dec - 2010]

1.152) An open tank contains water up to depth of 2.85m and above it an oil of specific gravity 0.92 for the depth of 2.1m. Calculate the pressures at the interface of two liquids and at the bottom of the tank.


1.153) Two horizontal plates are placed 12.5mm apart, the space between them is being filled with oil of viscosity 14 poise. Calculate the shear stress in the oil if the upper plate is moved with the velocity of 2.5m/s. Define specific weight. [AU, May / June - 2012] 1.154) Calculate the height of capillary rise for water in a glass tube of diameter 1mm. [AU, May / June - 2012] PART - B 1.155) What are the various classification of fluids? Discuss 1.156) State and prove Pascal's law.

[AU, Nov / Dec - 2012]

[AU, May / June, Nov / Dec - 2007]



1.157) What is Hydrostatic law? Derive an expression to show the same. [AU, Nov / Dec - 2009] 1.158) Explain the properties of hydraulic fluid.

[AU, Nov / Dec - 2009]

1.159) Discuss the equation of continuity. Obtain an expression for continuity equation in three dimensional forms.


1.160) Explain in detail the Newton's law of viscosity. Briefly classify the fluids based on the density and viscosity. Give the limitations of applicability of Newton's law of viscosity.


1.161) Classify the fluids according to the nature of variation of viscosity. Give examples


1.162) State the effect of temperature and pressure on viscosity. [AU, May / June - 2009] 1.163) Explain the term specific gravity, density, compressibility and vapour pressure. [AU, May / June - 2009] 1.164) Explain the terms Specific weight, Density, Absolute pressure and Gauge pressure.


1.165) Define Surface tension and also compressibility of a fluid? [AU, Nov / Dec - 2006] 1.166) Explain the practical significance of the following liquid properties: surface tension, capillarity and vapour pressure.


1.167) Explain the phenomenon surface tension and capillarity. [AU, April / May - 2011] 1.168) Derive an expression for the capillary rise of a liquid having surface tension σ and contact angle θ between two vertical parallel plates at a distance W apart. If the plates are of glass, what will be the capillary rise of water? Assume σ = 0.773N / m, θ= 0° Take W=l mm.

[AU, May / June - 2014]

1.169) What is compressibility of fluids? Give the relationship between compressibility and bulk modulus

[AU, Nov / Dec - 2009]

1.170) Prove that the relationship between surface tension and pressure inside the droplet of liquid in excess of outside pressure is given by P = 4σ/d. [AU, April / May –2010, 2011, Nov / Dec - 2008] 1.171) Explain the following CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 9


 Capillarity  Surface tension  Compressibility  Kinematic viscosity

[AU, May / June - 2012]

1.172) Derive the energy equation and state the assumptions made while deriving the equation.

[AU, Nov / Dec - 2010]

1.173) Derive Euler's equation of motion.

[AU, May / June - 2014]

1.174) Derive from the first principles, the Euler’s equation of motion for a steady flow along a stream line. Hence derive Bernoulli’ equation. State the various assumptions involved in the above derivation.

[AU, May / June - 2009]

1.175) Derive from basic principle the Euler’s equation of motion in 2D flow in X-Y coordinate system and reduce the equation to get Bernoulli’s equation for unidirectional stream lined flow.


1.176) State Euler’s equation of motion, in the differential form. Derive Bernoulli’s equation from the above for the cases of an ideal fluid flow. [AU, May / June - 2007, Nov / Dec - 2012] 1.177) State the law of conservation of man and derive the equation of continuity in Cartesian coordinates for an incompressible fluid. Would it alter if the flow were unsteady, highly viscous and compressible?


1.178) Derive the equation of continuity for one dimensional flow. [AU, Nov / Dec - 2008, April / May - 2010] 1.179) Derive the continuity equation for 3 dimensional flow in Cartesian coordinates. [AU, May / June - 2006] 1.180) Derive the general form of continuity equation in Cartesian coordinates. [AU, Nov / Dec - 2012] 1.181) Derive the continuity equation of differential form. Discuss weathers equation is valid for a steady flow or unsteady flow, viscous or in viscid flow, compressible or incompressible flow. 1.182) Derive continuity equation from basic principles.


1.183) Derive Bernoulli’s equation along with assumptions made. [AU, May / June - 2007]



1.184) State Bernoulli’s theorem for steady flow of an in compressible fluid. [AU, Nov / Dec – 2004, 2005, April / May – 2010, May / June - 2013] 1.185) State Bernoulli’s theorem for steady flow of an in compressible fluid. Derive an expression for Bernoulli equation and state the assumptions made. [AU, May / June - 2009] 1.186) State the assumptions in the derivation of Bernoulli’s equation. [AU, May / June, Nov / Dec - 2007] 1.187) Derive an expression for Bernoulli’s equation for a fluid flow. [AU, Nov / Dec – 2004, 2005, April / May - 2010] 1.188) Derive Bernoulli’s equation from the first principles? State the assumptions made while deriving Bernoulli’s equation.

[AU, May / June - 2012]

1.189) Derive from basic principle the Euler’s equation of motion in Cartesian co – ordinates system and deduce the equation to Bernoulli’s theorem steady irrotational flow.


1.190) Derive the Euler’s equation of motion and deduce the expression to Bernoulli’s equation.

[AU, Nov / Dec - 2012]

1.191) Develop the Euler equation of motion and then derive the one dimensional form of Bernoulli’s equation.

[AU, Nov / Dec - 2011]

1.192) Show that for a perfect gas the bulk modulus of elasticity equals its pressure for  An isothermal process  γ times the pressure for an isentropic process [AU, April / May - 2003] 1.193) State and derive impulse momentum equation.


1.194) Derive momentum equation for a steady flow.

[AU, May / June - 2012]

1.195) Derive the linear momentum equation using the control volume approach and determine the force exerted by the fluid flowing through a pipe bend. [AU, Nov / Dec - 2011] 1.196) With a neat sketch, explain briefly an orifice meter and obtain an expression for the discharge through it.

[AU, Nov / Dec - 2012]

1.197) Draw the sectional view of Pitot’s tube and write its concept to measure velocity of fluid flow?




PROBLEMS 1.198) A soap bubble is 60mm in diameter. If the surface tension of the soap film is 0.012 N/m. Find the excess pressure inside the bubble and also derive the expression used in this problem.

[AU, Nov / Dec - 2009]

1.199) A spherical water droplet of 5 mm in diameter splits up in the air into 16 smaller droplets of equal size. Find the work involved in splitting up the droplet. The surface tension of water may be assumed as 0.072 N/m

[AU, Nov / Dec - 2012]

1.200) A liquid weighs 7.25N per litre. Calculate the specific weight, density and specific gravity of the liquid. 1.201) One litre of crude oil weighs 9.6N. Calculate its specific weight, density and specific gravity.

[AU, Nov / Dec - 2008]

1.202) Determine the viscosity of a liquid having a kinematic viscosity 6 stokes and specific gravity 1.9.

[AU, Nov / Dec - 2008, April / May - 2010]

1.203) Determine the mass density; specific volume and specific weight of liquid whose specific gravity 0.85.


1.204) If the volume of a balloon is to reach a sphere of 8m diameter at an altitude where the pressure is 0.2 bar and temperature -40°C. Determine the mass hydrogen to be charged into the balloon and volume and diameter at ground level. Where the pressure is 1bar and temperature is 25°C.

[AU, Nov / Dec - 2009]

1.205) A pipe of 30 cm diameter carrying 0.25 m3/s water. The pipe is bent by 135° from the horizontal anti-clockwise. The pressure of water flowing through the pipe is 400 kN. Find the magnitude and direction of the resultant force on the bend. [AU, Nov / Dec - 2011] 1.206) A liquid has a specific gravity of 0.72. Find its density and specific weight. Find also the weight per litre of the liquid. 1.207) A 1.9mm diameter tube is inserted into an unknown liquid whose density is 960kg/m3, and it is observed that the liquid raise 5mm in the tube, making a contact angle of 15°. Determine the surface tension of the liquid.


1.208) A hollow cylinder of 150 mm OD with its weight equal to the buoyant forces is to be kept floating vertically in a liquid with a surface tension of 0.45 N/m2. The contact angle is 60º. Determine the additional force required due to surface tension. [AU, Nov / Dec - 2014] CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 12


1.209) A 0.3m diameter pipe carrying oil at 1.5m/s velocity suddenly expands to 0.6m diameter pipe. Determine the discharge and velocity in 0.6m diameter pipe. [AU, May / June - 2012] 1.210) Explain surface tension. Water at 20°C (σ = 0.0.73N/m, γ = 9.8kN/m3 and angle of contact = 0°) rises through a tube due to capillary action. Find the tube diameter requires, if the capillary rise is less than 1mm.

[AU, Nov / Dec - 2010]

1.211) A Newtonian fluid is filled in the clearance between a shaft and a concentric sleeve. The sleeve attains a speed of 50cm/s, when a force of 40N is applied to the sleeve parallel to the shaft. Determine the speed of the shaft, if a force of 200N is applied.

[AU, Nov / Dec - 2006]

1.212) An oil film thickness 10mm is used for lubrication between the square parallel plate of size 0.9 m * 0.9 m, in which the upper plate moves at 2m/s requires a force of 100 N to maintain this speed. Determine the  Dynamic viscosity of the oil in poise and  Kinematic viscosity of the oil in stokes. The specific gravity of the oil is 0.95.

[AU, Nov / Dec – 2003]

1.213) The space between two square flat parallel plates is filled with oil. Each side of the plate is 60cm. The thickness of the oil film is 12.5mm. The upper plate, which moves at 2.5 meter per sec, requires a force of 98.1N to maintain the speed. Determine the  Dynamic viscosity of the oil in poise and  Kinematic viscosity of the oil in stokes. The specific gravity of the oil is 0.95.

[AU, Nov / Dec - 2012]

1.214) What is the bulk modulus of elasticity of a liquid which is compressed in a cylinder from a volume of 0.0125m3 at 80N/cm2 pressure to a volume of 0.0124m3 at pressure 150N/cm2

[AU, Nov / Dec - 2004]

1.215) Determine the bulk modulus of elasticity of elasticity of a liquid, if the pressure of the liquid is increased from 7MN/m2 to 13MN/m2, the volume of liquid decreases by 0.15%.

[AU, May / June - 2009]

1.216) The measuring instruments fitted inside an airplane indicate the pressure 1.032 *105Pa, temperature T0 = 288 K and density ρ0 = 1.285 kg/m3 at takeoff. If a standard temperature lapse rate of 0.0065° K/m is assumed, at what elevation is the plane CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 13


when a pressure of 0.53*105 recorded? Neglect the variations of acceleration due gravity with the altitude and take airport elevation as 600m. 1.217) A person must breathe a constant mass rate of air to maintain his metabolic process. If he inhales 20 times per minute at the airport level of 600m, what would you except his breathing rate at the calculated altitude of the plane? [AU, May / June - 2009] 1.218) Two points (1) and (2) which are at the same level in the body of water in a whirlpool are at radial distances of 1.2m and 0.6m respectively from the axis of rotation. The pressure and then velocity of water at point (1) and 15KPa (gauge) and 2 m/s respectively. What are the pressure and velocity at point (2)? What is the difference in water surface elevations above points (1) and (2)? What are the radial distances of a point on the water surface which is at same level (1) and (2)? [AU, April / May - 2015] 1.219) The space between two square parallel plates is filled with oil. Each side of the plate is 75 cm. The thickness of oil film is 10 mm. The upper plate which moves at 3 m/s requires a force of 100 N to maintain the speed. Determine the  Dynamic viscosity of the oil  Kinematic viscosity of the oil, if the specific gravity of the oil is 0.9. 1.220) A rectangular plate of size 25cm* 50cm and weighing at 245.3 N slides down at 30° inclined surface with uniform velocity of 2m/s. If the uniform 2mm gap between the plates is inclined surface filled with oil. Determine the viscosity of the oil. [AU, April / May – 2004, Nov / Dec - 2012] 1.221) A space between two parallel plates 5mm apart, is filled with crude oil of specific gravity 0.9. A force of 2N is require to drag the upper plate at a constant velocity of 0.8m/s. the lower plate is stationary. The area of upper plate is 0.09m2. Determine the dynamic viscosity in poise and kinematic viscosity of oil in strokes. [AU, May / June - 2009] 1.222) The space between two large flat and parallel walls 25mm apart is filled with liquid of absolute viscosity 0.7 Pa.sec. Within this space a thin flat plate 250mm * 250mm is towed at a velocity of 150mm/s at a distance of 6mm from one wall, the plate and its movement being parallel to the walls. Assuming linear variations of



velocity between the plates and the walls, determine the force exerted by the liquid on the plate.

[AU, May / June - 2012]

1.223) A jet issuing at a velocity of 25 m/s is directed at 35° to the horizontal. Calculate the height cleared by the jet at 28 m from the discharge location? Also determine the maximum height the jet will clear and the corresponding horizontal location. [AU, Nov / Dec - 2011] 1.224) Determine the velocity of a jet directed at 35º to the horizontal to clear 8 m height at a distance of 22 m. Also determine the maximum height this jet will clear and the total horizontal travel. What will be the horizontal distance at which the jet will be again at 8 m height?

[AU, Nov / Dec - 2014]

1.225) A flat plate of area 0.125m2 is pulled at 0.25 m/sec with respect to another parallel plate 1mm distant from it, the space between the plates containing water of viscosity 0.001Ns/ m2. Find the force necessary to maintain this velocity. Find also the power required. 1.226) The velocity distribution for flow over a plate is given by u = 2y – y2 where u is the velocity in m/sec at a distance y meters above the plate. Determine the velocity gradient and shear stress at the boundary and 0.15m from it. Dynamic viscosity of the fluid is 0.9Ns/m2


1.227) The velocity distribution over a plate is given by u = (3/4) * y – y2 where u is velocity in m/s and at depth y in m above the plate. Determine the shear stress at a distance of 0.3m from the top of plate. Assume dynamic viscosity of the fluid is taken as 0.95 Ns/m2


1.228) The velocity distribution over a plate is given by a relation,

2 𝑢 = 𝑦( −𝑦) 3 1.229) Where y is the vertical distance above the plate in meters. Assuming a

viscosity of 0.9Pa.s, find the shear stress at y = 0 and y = 0.15m. [AU, Nov / Dec - 2012] 1.230) If the velocity distribution of a fluid over a plate is given by 𝑢 = 𝑎𝑦 2 + 𝑏𝑦 + 𝑐 with the vertex 0.2m from the plate, where the velocity is 1.2 m/s. calculate the velocity gradients and shear stresses at a distance of 0m, 0.1m and 0.2m from the plate, if the viscosity of the fluid is 0.85Ns/m2.




1.231) Lateral stability of a long shaft 150 mm in diameter is obtained by means of a 250 mm stationary bearing having an internal diameter of 150.25 mm. If the space between bearing and shaft is filled with a lubricant having a viscosity 0.245 N s/m2, what power will be required to overcome the viscous resistance when the shaft is rotated at a constant rate of 180 rpm?

[AU, Nov / Dec - 2010]

1.232) Find the kinematic viscosity of water whose specific gravity is 0.95 and viscosity is0.0011Ns/m2. 1.233) The dynamic viscosity of oil, used for lubrication between a shaft and sleeve is6poise. The shaft is of diameter 0.4m and rotates at 190 rpm. Calculate the power lost in the bearing for a sleeve length of 90mm. The thickness of the oil film is 1.5mm.


1.234) A 200 mm diameter shaft slides through a sleeve, 200.5 mm in diameter and 400 mm long, at a velocity of 30 cm/s. The viscosity of the oil filling the annular space is m = 0.1125 NS/ m2. Find resistance to the motion.

[A.U. Nov / Dec - 2008]

1.235) A 0.5m shaft rotates in a sleeve under lubrication with viscosity 5 Poise at 200rpm. Calculate the power lost for a length of 100mm if the thickness of the oil is 1mm.

[AU, Nov / Dec - 2009]

1.236) A 15 cm diameter vertical cylinder rotates concentrically inside another cylinder of diameter 15.10 cm. Both cylinders are 25 cm high. The space between the cylinders is filled with a liquid whose viscosity is unknown. If a torque of 12.0 Nm is required to rotate the inner cylinder at 100 rpm, determine the viscosity of the fluid.

[AU, May / June - 2013]

1.237) Oil flows through a pipe 150mm in diameter and 650mm in length with a velocity of 0.5m/s. If the kinematic viscosity of oil is 18.7 * 10-4 m2/s, find the power lost in overcoming friction. Take the specific gravity of oil as 0.9. [AU, April / May - 2015] 1.238) A400 mm diameter shaft is rotating at 200 r.p.m. in a bearing of length 120 mm. If the thickness of film is 1.5 mm and the dynamic viscosity of the oil is 0.7 N.s/m2, determine (i) Torque required to overcome friction in bearing (ii) Power utilized to overcoming viscous friction. Assume linear velocity profile. [AU, May / June - 2014]



1.239) The viscosity of a fluid is to be measured by a viscometer constructed of two 80cm long concentric cylinders. The outer diameter of the inner cylinder is 16 cm, and the gap between the two cylinders is 0.12 cm. The inner cylinder is rotated at 210 rpm, and the torque is measured to be 0.8 N m. Determine the viscosity of the fluid.

[AU, Nov / Dec - 2014]

1.240) Calculate the gauge pressure and absolute pressure within (i) a droplet of water 0.4cm in diameter (ii) a jet of water 0.4cm in diameter. Assume the surface tension of water as 0.03N/m and the atmospheric pressure as 101.3kN/m2. 1.241) What do you mean by surface tension? If the pressure difference between the inside and outside of air bubble of diameter, 0.01 mm is 29.2kPa, what will be the surface tension at air water interface? Derive an expression for the surface tension in the air bubble and from it, deduce the result for the given conditions. [AU, Nov / Dec - 2005] 1.242) Determine the viscous drag torque and power absorbed on one surface of a collar bearing of 0.2 m ID and 0.3 m OD with an oil film thickness of 1 mm and a viscosity of 30 centi poise if it rotates at 500 rpm.

[AU, Nov / Dec - 2014]

1.243) A 1.9-mm - diameter tube is inserted into an unknown liquid whose density is 960 kg/ m3, and it is observed that the liquid rises 5 mm in the tube, making a contact angle of 15°. Determine the surface tension of the liquid. [AU, April / May - 2008] 1.244) At the depth of 2km in ocean the pressure is 82401kN/m2. Assume the specific weigth at the surface as 10055 N/m3 and the average bulk modulus of elasticity is 2.354 * 109 N/m2 for the pressure range. Determine the change in specific volume between the surface and 2km depth and also determine the specific weight at the depth?

[AU, April / May – 2004, Nov / Dec - 2012]

1.245) At the depth of 8km from the surface of the ocean, the pressure is stated to be 82MN/m2. Determine the mass density, weight density and specific volume of water at this depth. Take density at the surface ρ = 1025kg/m3 and bulk modulus K = 2350MPa for indicated pressure range.

[AU, May / June - 2009]

1.246) Eight kilometers below the surface of ocean pressure is 81.75MPa. Determine the density of sea water at this depth if the density at the surface is 1025 kg/m3 and the average bulk modulus of elasticity is 2.34GPa.

[AU, May / June - 2012]



1.247) A cylinder of radius 0.65 m filled partially with a fluid and axially rotated at 18 rad/s is empty up to 0.3 m radius. The pressure at the extreme edge at the bottom was 0.3 bar gauge. Determine the density of the fluid.

[AU, Nov / Dec - 2014]

1.248) A liquid is compressed in a cylinder having a volume of 0.012 m3 at a pressure of 690 N/cm2. What should be the new pressure in order to make its volume 0.0119 m3? Assume bulk modulus of elasticity (K) for the liquid = 6.9 x 104 N/cm2. [AU, May / June - 2013] 1.249) Calculate the capillary rise in glass tube of 3 mm diameter when immersed in mercury; take the surface tension and the angle of contact of mercury as 0.52 N/m and 130° respectively. Also determine the minimum size of the glass tube, if it is immersed in water, given that the surface tension of water is 0.0725 N/m and capillary rise in the tube is not to exceed 0.5mm.

[AU, Nov / Dec - 2003]

1.250) The capillary rise in a glass tube is not to exceed 0.2mm of water. Determine its minimum size, given that the surface tension for water in contact with air = 0.0725N/m.


1.251) Calculate the capillary effect in millimeters in a glass tube of 4mm diameter when immersed in(i) water and (ii) mercury. The temperature of the liquid is 20°C and the values of surface tension of water and mercury at 20 °C in contact with air are 0.0735 N/m and 0.51 N/m respectively. The contact angle for water u = 0 ° and for mercury u = 130°. Take specific weight of water at 20°C as equal to 9780 N/m3. [AU, Nov / Dec - 2007] 1.252) Derive an expression for the capillary rise at a liquid in a capillary tube of radius r having surface tension σ and contact angle θ . If the plates are of glass, what will be the capillary rise of water having σ = 0.073 N/m, θ = 0°? Take r = 1mm. [AU, Nov / Dec - 2011] 1.253) A pipe containing water at 180kN/m2 pressure is connected to differential gauge to another pipe 1.6m lower than the first pipe and containing water at high pressure. If the difference in height of 2 mercury columns of the gauge is equal to 90mm, what is the pressure in the lower pipe?

[AU, Nov / Dec - 2008]



1.254) Determine the minimum size of glass tubing that can be used to measure water level. If the capillary rise in the tube is not exceed 2.5mm. Assume surface tension of water in contact with air as 0.0746 N/m.

[AU, Nov / Dec – 2004, 2012]

1.255) Calculate the capillary effect in millimeters in a glass tube of 4 mm diameter, when immersed in (i) water and (ii) mercury. The temperature of the liquid is 20°C and the values of surface tension of water and mercury at 20 °C in contact with air are 0.0735 N/m and 0.51 N/m respectively. The contact angle for water u = 0 and for mercury u = 130°. Take specific weight of water at 20°C as equal to 9790N/ m3. [AU, Nov / Dec – 2005, 2007] 1.256) A Capillary tube having inside diameter 6 mm is dipped in CCl4at 20o C. Find the rise of CCl4 in the tube if surface tension is 2.67 N/m and Specific gravity is 1.594 and contact angle u is 60° and specific weight of water at 20° C is 9981 N/m3. [AU, Nov / Dec - 2008] 1.257) Two pipes A & B are connected to a U – tube manometer containing mercury of density 13,600kg/m3. Pipe A carries a liquid of density 1250kg/m3 and a liquid of density 800kg/m3 flows through a pipe B, The center of pipe A is 80mm above the pipe B. The difference of mercury level manometer is 200mm and the mercury surface on pipe A side is 100mm below the center. Find the difference of pressure between the two connected points of the pipes.

[AU, Nov / Dec - 2010]

1.258) A crude oil of viscosity 0.9 poise and relative density 0.9 is flowing through a horizontal circular pipe of diameter 120 mm and length 12 m. Calculate the difference of pressure at the two ends of the pipe, if 785 N of the oils collected in a tank in 25 seconds.

[AU, May / June - 2014]

1.259) A simple U tube manometer containing mercury is connected to a pipe in which a fluid of specific gravity 0.8 and having vacuum pressure is flowing. The other end of the manometer is open to atmosphere. Find the vacuum pressure in the pipe, if the difference of mercury level in the two limbs is 40cm and the height of the fluid in the left from the center pipe is 15cm below. Draw the sketch for the above problem. [AU, April / May - 2011, May / June - 2012] 1.260) A U-tube is made of two capillaries of diameter 1.0 mm and 1.5 mm respectively. The tube is kept vertically and partially filled with water of surface tension 0.0736 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 19


N/m and zero contact angles. Calculate the difference in the levels of the mercury caused by the capillary.

[AU, Nov / Dec - 2010]

1.261) Define the terms gauge pressure and absolute pressure. A U tube containing mercury has its right limb open to atmosphere. The left limb is full of water and is connected to a pipe containing water under pressure, the centre of which is in the level with the free surface of mercury. If the difference in the levels of mercury in the limbs id 5.1cm, calculate the water pressure in the pipe. [AU, Nov / Dec - 2012] 1.262) The barometric pressure at sea level is 760 mm of mercury while that on a mountain top is

735 mm. If the density of air is assumed constant at 1.2 kg/m3,

what is the elevation of the mountain top?

[AU, Nov / Dec - 2007]

1.263) The barometric pressure at the top and bottom of a mountain are 734mm and 760mm of mercury respectively. Assuming that the average density of air = 1.15kg/m3, calculate the height of the mountain.

[AU, Nov / Dec - 2009]

1.264) The maximum blood pressure in the upper arm of a healthy person is about 120 mmHg. If a vertical tube open to the atmosphere is connected to the vein in the arm of the person, determine how high the blood will rise in the tube. Take the density of the blood to be 1050 kg/ m3.


1.265) When a pressure of 20.7 MN/m2 is applied to 100 litres of a liquid, its volume decreases by one litre. Find the bulk modulus of the liquid and identify this liquid. [AU, Nov / Dec - 2007] 1.266) The water level in a tank is 20 m above the ground. A hose is connected to the bottom of the tank, and the nozzle at the end of the hose is pointed straight up. The tank is at sea level, and the water surface is open to the atmosphere. In the line leading from the tank to the nozzle is a pump, which increases the pressure of water. If the water jet rises to a height of 27 m from the ground, determine the minimum pressure rise supplied by the pump to the water line.

[AU, Nov / Dec - 2014]

1.267) Determine the minimum size of the glass tubing that can be used to measure water level. If the capillary rise in the tube is not to exceed 2.5mm. Assume surface tension of water in contact with air as 0.0746 N/m


1.268) A cylinder of 0.6m3 in volume contains air at 50oC and 0.3N/mm2 absolute pressure. The air is compressed to 0.3m3. Find the (i) pressure inside the cylinder



assuming isothermal process and (ii) pressure and temperature assuming adiabatic process. Take k = 1.4. 1.269) A 30cm diameter pipe, conveying water, branches into two pipes of diameters 20cm and 15cm respectively. If the average velocity in the 30cm diameter pipe is 2.5m/sec, find the discharge in this pipe. Also determine the velocity in the 15cm diameter pipe if the average velocity in the 20cm diameter pipe is 2m/sec. [AU, Nov / Dec - 2008, April / May - 2010] 1.270) Water flows through a pipe AB 1.2m diameter at 3m/second then passes through a pipe BC 1.5m diameter. At C, the pipe branches. Branch CD is 0.8m in diameter and carries one - third of the flow in AB. The flow velocity in branch CE is 2.5m/sec. Find the volume rate of flow in AB, the velocity in BC, the velocity in CD and the diameter of CE. 1.271) Water is flowing through a pipe having diameters 20cm and 10cm at sections 1 and 2 respectively. The rate of flow, through the pipe is 35litre/sec. The section 1 is 6m above datum and section 2 is 4m above datum. If the pressure at section 1 is 39.24N/cm2, find the intensity of pressure at section 2.

[AU, Nov / Dec - 2008]

1.272) A pipe 200m long slopes down at 1 in 100 and tapers from 600mm diameter at the higher end to 300mm diameter at the lower end and carries 100 litres/sec of oil having specific gravity 0.8. If the pressure gauge at the higher end reads 60kN/m2, determine the velocities at the two ends and also the pressure at the lower end. Neglect all losses


1.273) Water is flowing through a taper pipe of length 100m having diameters 600mm at the upper end and 300mm at the lower end, at the rate of 50 litres/ sec. The pipe has a slope of 1 in 30. Find the pressure at the lower end if the pressure at the higher level is 19.62 N/cm2. 1.274) Water flows at the rate of 200 litres per second upwards through a tapered vertical pipe. The diameter at the bottom is 240 mm and at the top 200 mm and the length is 5 m. The pressure at the bottom is 8 bar, and the pressure at the topside is 7.3 bar. Determine the head loss through the pipe. Express it as a function of exit velocity head.

[AU, Nov / Dec - 2014]

1.275) A pipe of diameter 400mm carries water at a velocity of 25m/sec. The pressures at the points A and B are given as 29.43N/cm2 and 22.563 N/cm2 respectively, while CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 21


the datum head at A and B are 28m and 30m. Find the loss of head between A and B. 1.276) A drainage pipe is tapered in a section running with full of water. The pipe diameters at the inlet and exit are 1000 mm and 50 mm respectively. The water surface is 2 m above the center of the inlet and exit is 3 m above the free surface of the water. The pressure at the exit is250 mm of Hg vacuum. The friction loss between the inlet and exit of the pipe is 1/10 of the velocity head at the exit. Determine the discharge through the pipe.


1.277) A pipeline 60 cm in diameter bifurcates at a Y-junction into two branches 40 cm and 30 cm in diameter. If the rate of flow in the main pipe is 1.5 m3/s, and the mean velocity of flow in the 30 cm pipe is 7.5 m/s, determine the rate of flow in the 40 cm pipe.

[AU, Nov / Dec - 2010]

1.278) A pipeline of 175 mm diameter branches into two pipes which delivers the water at atmospheric pressure. The diameter of the branch 1 which is at 35° counterclockwise to the pipe axis is 75mm. and the velocity at outlet is 15 m/s. The branch 2 is at 15° with the pipe center line in the clockwise direction has a diameter of 100 mm. The outlet velocity is 15 m/s. The pipes lie in a horizontal plane. Determine the magnitude and direction of the forces on the pipes.

[AU, Nov / Dec - 2011]

1.279) A pipeline conveys 10 lit/s of water from an overhead tank to a building. The pipe is 2km long and 15cm diameter, the friction factor is 0.03. It is planned to increase the discharge by 30% by installing another pipeline in parallel with this over half the length. Find the suitable diameter of pipe to be installed. Is there any upper limit on discharge augmentation by this arrangement?

[AU, Nov / Dec - 2012]

1.280) The water is flowing through a taper pipe of length 100 m having diameters 600 mm at the upper end and 300 mm at the lower end, at the rate of 50 litres/s. The pipe has a slope of 1 in 30. Find the pressure at the lower end if the pressure at the higher level is 19.62 N/cm2.

[AU, May / June - 2013]

1.281) A 45° reducing bend is connected in a pipe line, the diameters at the inlet and outlet of the bend being 600mm and 300mm respectively. Find the force exerted by water on the bend if the intensity of pressure at the inlet to the bend is 8.829N/cm2 and rate of flow of water is600 litre / sec.



1.282) Gasoline (specific gravity = 0.8) is flowing upwards through a vertical pipe line which tapers from300mm to 150mm diameter. A gasoline mercury differential manometer is connected between 300 mm and 150 mm pipe sections to measure the rate of flow. The distance between the manometer tappings is 1meter and the gauge heading is 500 mm of mercury. Find the(i) differential gauge reading in terms of gasoline head (ii) rate of flow. Assume frictional and other losses are negligible. [AU, May / June – 2007, 2014, Nov / Dec - 2012] 1.283) Water enters a reducing pipe horizontally and comes out vertically in the downward direction. If the inlet velocity is 5 m/s and pressure is 80 kPa (gauge) and the diameters at the entrance and exit sections are 30 cm and 20 cm respectively, calculate the components of the reaction acting on the pipe. [AU, May / June – 2007, Nov / Dec - 2012] 1.284) A horizontal pipe has an abrupt expansion from 10 cm to 16 cm. The water velocity in the smaller section is 12 m/s, and the flow is turbulent. The pressure in the smaller section is 300 kPa. Determine the downstream pressure, and estimate the error that would have occurred if Bernoulli’s equation had been used. [AU, Nov / Dec - 2011] 1.285) Air flows through a pipe at a rate of 20 L/s. The pipe consists of two sections of diameters20 cm and 10 cm with a smooth reducing section that connects them. The pressure difference between the two pipe sections is measured by a water manometer. Neglecting frictional effects, determine the differential height of water between the two pipe sections. Take the air density to be 1.20 kg/m3. [AU, April / May - 2008] air 200 L/s

20 cm

h

1.286) A horizontal venturimeter with inlet diameter 200 mm and throat diameter 100 mm is employed to measure the flow of water. The reading of the differential



manometer connected to the inlet is 180 mm of mercury. If Cd = 0.98, determine the rate of flow.


1.287) A horizontal venturimeter of specification 200mm * 100mm is used to measure the discharge of an oil of specific gravity 0.8. A mercury manometer is used for the purpose. If the discharge is 100 litres per second and the coefficient of discharge of meter is 0.98, find the manometer deflection.

[AU, May / June - 2007]

1.288) Determine the pressure difference between inlet and throat of a vertical venturimeter of size 150 mm x 75 mm carrying oil of S = 0.8 at flow rate of 40 lps. The throat is 150 mm above the inlet. 1.289) A pipe of 300 mm diameter inclined at 30° to the horizontal is carrying gasoline (specific gravity = 0.82). A venturimeter is fitted in the pipe to find out the flow rate whose throat diameter is 150 mm. The throat is 1.2 m from the entrance along its length.

The pressure gauges fitted to the venturimeter read 140 kN/m2and

80kN/m2respectively. Find out the co-efficient of discharge of venturimeter if the flow is 0.20 m3/s.


1.290) A venturimeter of throat diameter 0.085m is fitted in a 0.17m diameter vertical pipe in which liquid a relative density 0.85 flows downwards. Pressure gauges ate fitted at the inlet and to the throat sections. The throat being 0.9m below the inlet. Taking the coefficient of the meter as 0.95 find the discharge when the pressure gauges read the same and also when the inlet gauge reads 15000N/m2 higher than the throat gauge.


1.291) A Venturimeter having inlet and throat diameters 30 cm and 15 cm is fitted in a horizontal diesel pipe line (Sp. Gr. = 0.92) to measure the discharge through the pipe. The venturimeter is connected to a mercury manometer. It was found that the discharge is 8 litres /sec. Find the reading of mercury manometer head in cm. Take Cd =0.96.

[AU, Nov / Dec - 2011]

1.292) A venturimeter is inclined at 60° to the vertical and its 150 mm diameter throat is 1.2 m from the entrance along its length. It is fitted to a pipe of diameter 300 mm. The pipe conveys gasoline of S = 0.82 and flowing at 0.215 m3/s upwards. Pressure gauges inserted at entrance and throat show the pressures of 0.141 N/mm2and 0.077 N/mm2respectively. Determine the co-efficient of discharge of the venturimeter. Also determine the reading in mm of differential mercury column, if instead of CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 24


pressure gauges the entrance and the throat of the venturimeter are connected to the limbs of a U tube mercury manometer.


1.293) A horizontal venturimeter with inlet and throat diameter 300mm and 100mm respectively is used to measure the flow of water. The pressure intensity at inlet is 130 kN/m2 while the vacuum pressure head at throat is 350 mm of mercury. Assuming 3% head lost between the inlet and throat. Find the value of coefficient of discharge for venturimeter and also determine the rate of flow. [AU, Nov / Dec – 2004, 2005, April / May - 2010] 1.294) A vertical venturimeter carries a liquid of relative density 0.8 and has inlet throat diameters of 150mm and 75mm. The pressure connection at the throat is 150mm above the inlet. If the actual rate of flow is 40litres/sec and C d = 0.96, find the pressure difference between inlet and throat in N/m2.

[AU, May / June - 2006]

1.295) A 300 mm x 150 mm venturimeter is provided in a vertical pipeline carrying oil of relative density 0.9, the flow being upwards. The differential U tube mercury manometer shows a gauge deflection of 250 mm. Calculate the discharge of oil, if the co-efficient of meter is 0.98.

[AU, Nov / Dec - 2007]

1.296) In a vertical pipe conveying oil of specific gravity 0.8, two pressure gauges have been installed at A and B, where the diameters are 160mm a 80mm respectively. A is 2m above B. The pressure gauge readings have shown that the pressure at B is greater than at A by 0.981 N/cm2. Neglecting all losses, calculate the flow rate. If the gauges at A and B are replaced by tubes filled with the same liquid and connected to a U – tube containing mercury, calculate the difference in the level of mercury in the two limbs of the U – tube.

[AU, May / June - 2012]

1.297) Determine the flow rate of oil of S = 0.9 through an orifice meter of size 15 cm diameter fitted in a pipe of 30 cm diameter. The mercury deflection of U tube differential manometer connected on the two sides of the orifice is 50 cm. Assume Cd of orifice meter as 0.64. 1.298) A submarine moves horizontally in sea and has its axis 15 m below the surface of water. A pitot static tube properly placed just in front of the submarine along its axis and is connected to the two limbs of a U - tube containing mercury. The difference of mercury level is found to be170 mm. Find the speed of submarine knowing that the sp. gr of sea water is 1.026. CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 25


1.299) A submarine fitted with a Pitot tube move horizontally in sea. Its axis is 20m below surface of water. The Pitot tube placed in front of the submarine along its axis is connected to a differential mercury manometer showing the deflection of 20cm. Determine the speed of the submarine.


1.300) A pitot-static probe is used to measure the velocity of an aircraft flying at 3000 m. If the differential pressure reading is 3 kPa, determine the velocity of the aircraft. [AU, April / May - 2008] 1.301) A 15 cm diameter vertical pipe is connected to 10 cm diameter vertical pipe with a reducing socket. The pipe carries a flow of 1001/s. At point 1 in 15 cm pipe gauge pressure is 250 kPa. At point 2 in the 10 cm pipe located 1.0 m below point 1 the gauge pressure is 175 kPa.  Find whether the flow is upwards / downwards.  Head loss between the two points. 1.302) Water enters a reducing pipe horizontally and comes out vertically in the downward direction. If the inlet velocity is 5 m/sec and pressure is 80 kPa (gauge) and the diameters at the entrance and exit sections are 300 mm and 200 mm respectively. Calculate the components of the reaction acting on the pipe.



UNIT - II - FLOW THROUGH CIRCULAR CONDUCTS PART - A 2.1) How are fluid flows classified?

[AU, May / June - 2012]

2.2) Distinguish between Laminar and Turbulent flow.

[AU, Nov / Dec - 2006]

2.3) Write down Hagen Poiseuille’s equation for viscous flow through a pipe. 2.4) Write down Hagen Poiseuille’s equation for laminar flow. [AU, April / May - 2005, Nov / Dec - 2012] 2.5) Write the Hagen – Poiseuille’s Equation and enumerate its importance. [AU, April / May - 2011] 2.6) State Hagen – Poiseuille’s formula for flow through circular tubes. [AU, May / June - 2012] 2.7) Write down the Darcy - Weisbach’s equation for friction loss through a pipe [AU, Nov / Dec - 2009, April / May - 2011] 2.8) What is the relationship between Darcy Friction factor, Fanning Friction Factor and Friction coefficient?

[AU, May / June - 2012]

2.9) Mention the types of minor losses.


2.10) List the minor losses in flow through pipe. [AU, April / May - 2005, May / June - 2007] 2.11) What are minor losses? Under what circumstances will they be negligible? [AU, May / June - 2012] 2.12) Distinguish between the major loss and minor losses with reference to flow through pipes.

[AU, May / June - 2009]

2.13) List the causes of minor energy losses in flow through pipes. [AU, Nov / Dec - 2009] 2.14) What are the losses experienced by a fluid when it is passing through a pipe? 2.15) What is a minor loss in pipe flows? Under what conditions does a minor loss become a major loss? 2.16) What do you understand by minor energy losses in pipes? [AU, Nov / Dec - 2008] 2.17) List out the various minor losses in a pipeline



2.18) What are ‘major’ and ‘minor losses’ of flow through pipes? [AU, May / June 2007, Nov / Dec - 2007, 2012, April / May - 2010] 2.19) List the minor and major losses during the flow of liquid through a pipe. [AU, April / May - 2008] 2.20) Enlist the various minor losses involved in a pipe flow system. [AU, Nov / Dec - 2008] 2.21) Write the expression for calculating the loss due to sudden expansion of the pipe. [AU, April / May - 2015] 2.22) What factors account in energy loss in laminar flow.

[AU, May / June - 2012]

2.23) Differentiate between pipes in series and pipes in parallel. [AU, Nov / Dec - 2006] 2.24) What is Darcy's equation? Identify various terms in the equation. [AU, April / May - 2011] 2.25) What is the relation between Dracy friction factor, Fanning friction factor and friction coefficient?

[AU, Nov / Dec - 2010]

2.26) When is the pipe termed to be hydraulically rough?

[AU, Nov / Dec - 2009]

2.27) What is the physical significance of Reynold's number? [AU, May / June, Nov / Dec - 2007] 2.28) Define Reynolds Number.

[AU, Nov / Dec - 2012]

2.29) Write the Navier's Stoke equations for unsteady 3 - dimensional, viscous, incompressible and irrotational flow.


2.30) Define Moody’s diagram 2.31) What are the uses of Moody’s diagram? 2.32) Mention the use of Moody diagram. 2.33) State the importance of Moody's chart.

[AU, Nov / Dec - 2008, 2012] [AU, April / May - 2015] [AU, Nov / Dec - 2014]

2.34) Write down the formulae for loss of head due to (i) sudden enlargement in pipe diameter (ii) sudden contraction in pipe diameter and (iii) Pipe fittings. 2.35) Define (i) relative roughness and (ii) absolute roughness of a pipe inner surface. 2.36) How does surface roughness affect the pressure drop in a pipe if the flow is turbulent?

[AU, Nov / Dec - 2013]



2.37) A piping system involves two pipes of different diameters (but of identical length, material, and roughness) connected in parallel. How would you compare the flow rates and pressure drops in these two pipes?

[AU, Nov / Dec - 2013]

2.38) What do you mean by flow through parallel pipes?

[AU, May / June - 2013]

2.39) What is equivalent pipe? 2.40) What is the use of Dupuit’s equations? 2.41) What is the condition for maximum power transmission through a pipe line? 2.42) Give the expression for power transmission through pipes? [AU, Nov / Dec - 2008] 2.43) Write down the formula for friction factor of pipe having viscous flow. 2.44) Define boundary layer and boundary layer thickness. [AU, Nov / Dec – 2007, 2012] 2.45) Define boundary layer thickness.

[AU, May / June - 2006, Nov / Dec - 2009]

2.46) What is boundary layer? Give its sketch of a boundary layer region over a flat plate.


2.47) What is boundary layer? Why is it significant?

[AU, Nov / Dec - 2009]

2.48) Define boundary layer and give its significance.


2.49) What is boundary layer and write its types of thickness? [AU, Nov / Dec – 2005, 2006] 2.50) What do you understand by the term boundary layer? 2.51) Define the following (i)

[AU, Nov / Dec - 2008]

laminar boundary layer (ii) turbulent boundary layer

(iii) laminar sub layer. 2.52) What is a laminar sub layer?

[AU, Nov / Dec - 2010]

2.53) Define momentum thickness and energy thickness. [AU, May / June – 2007, 2012] 2.54) Define the term boundary layer.

[AU, May / June - 2009]

2.55) Define the terms boundary layer, boundary thickness.

[AU, Nov / Dec - 2008]

2.56) What is boundary layer separation?

[AU, Nov / Dec - 2012]

2.57) Give the classification of boundary layer flow based on the Reynolds number. [AU, April / May - 2015] 2.58) Define the following: (i)

Displacement thickness (ii) Momentum thickness



(iii)Energy

thickness.

2.59) What do you mean by displacement thickness and momentum thickness? [AU, Nov / Dec - 2008] 2.60) What do you understand by hydraulic diameter?

[AU, Nov / Dec - 2011]

2.61) What is hydraulic gradient line?

[AU, May / June - 2009]

2.62) Define hydraulic gradient line and energy gradient line. 2.63) Brief on HGL.


2.64) Differentiate between Hydraulic gradient line and total energy line. [AU, Nov / Dec - 2003, April / May - 2005, 2010, May / June–2007, 2009] 2.65) What is T.E.L?

[AU, Nov / Dec - 2009]

2.66) Distinguish between hydraulic and energy gradients.

[AU, Nov / Dec - 2011]

2.67) Differentiate hydraulic gradient line and energy gradient line. [AU, May / June - 2014] 2.68) Differentiate between hydraulic grade line and energy grade line. [AU, Nov / Dec - 2014] 2.69) What are stream lines, streak lines and path lines in fluid flow? [AU, Nov / Dec –2006, 2009] 2.70) What do you mean by Prandtl’s mixing length? 2.71) Draw the typical boundary layer profile over a flat plate. 2.72) Define flow net.

[AU, Nov / Dec - 2008]

2.73) What is flow net and state its use?


2.74) Define lift. 2.75) Define the terms: drag and lift.

[AU, Nov / Dec - 2005] [AU, Nov / Dec – 2007, May / June - 2009]

2.76) Define drag and lift co-efficient. 2.77) Give the expression for Drag coefficient and Lift coefficient. [AU, April / May - 2011] 2.78) What is meant by laminar flow instability?

[AU, Nov / Dec - 2014]

2.79) Considering laminar flow through a circular pipe, draw the shear stress and velocity distribution across the pipe section.

[AU, Nov / Dec - 2010]

2.80) Considering laminar flow through a circular pipe, obtain an expression for the velocity distribution.

[AU, Nov / Dec - 2012]



2.81) A circular and a square pipe are of equal sectional area. For the same flow rate, determine which section will lead to a higher value of Reynolds number. [AU, Nov / Dec - 2011] 2.82) A 20cm diameter pipe 30km long transport oil from a tanker to the shore at 0.01m3/s. Find the Reynolds number to classify the flow. Take the viscosity μ = 0.1 Nm/s2 and density ρ = 900 kg/m3 for oil.


2.83) Find the loss of head when a pipe of diameter 200 mm is suddenly enlarged to a diameter 0f 400 mm. Rate of flow of water through the pipe is 250 litres/s. [AU, April / May - 2010] PART - B 2.84) What are the various types of fluid flows? Discuss

[AU, Nov / Dec - 2010]

2.85) Define minor losses. How they are different from major losses? [AU, May / June - 2009] 2.86) Discuss on various minor losses in pipe flow.

[AU, Nov / Dec - 2013]

2.87) Discuss on minor losses in pipe flow.

[AU, Nov / Dec - 2014]

2.88) Which has a greater minor loss co-efficient during pipe flow: gradual expansion or gradual contraction? Why?


2.89) Derive Chezy’s formula for loss of head due to friction in pipes. [AU, Nov / Dec - 2012] 2.90) What is the hydraulic gradient line? How does it differ from the total energy line? Under what conditions do both lines coincide with the free surface of a liquid? [AU, April / May - 2008] 2.91) Write notes on the following:  Concept of boundary layer.  Hydraulic gradient  Moody diagram. 2.92) Briefly explain Moody’s diagram regarding pipe friction [AU, May / June - 2014] 2.93) Describe the Moody's chart.

[AU, Nov / Dec - 2014]

2.94) For a flow of viscous fluid flowing through a circular pipe under laminar flow conditions, show that the velocity distribution is a parabola. And also show that the average velocity is half of the maximum velocity.

[AU, May / June - 2013]



2.95) For flow of viscous fluids through an annulus derive the following expressions:  Discharge through the annulus.  Shear stress distribution.

[AU, May / June – 2007, 2012]

2.96) For a laminar flow through a pipe line, show that the average velocity is half of the maximum velocity. 2.97) Prove that the Hagen-Poiseuille’s equation for the pressure difference between two sections 1 and 2 in a pipe is given by with usual notations. 2.98) Derive Hagen – Poiseuille’s equation and state its assumptions made. [AU, Nov / Dec - 2005] 2.99) Derive Hagen – Poiseuille’s equation

[AU, Nov / Dec - 2008]

2.100) Obtain the expression for Hagen – Poiseuille’s flow. Deduce the condition of maximum velocity.

[AU, Nov / Dec - 2007]

2.101) Give a proof a Hagen – Poiseuille’s equation for a fully – developed laminar flow in a pipe and hence show that Darcy friction coefficient is equal to 16/R e, where Re is Reynold’s number.

[AU, May / June - 2012]

2.102) Derive an expression for head loss through pipes due to friction. [AU, April / May - 2010] 2.103) Explain Reynold’s experiment to demonstrate the difference between laminar flow and turbulent flow through a pipe line. 2.104) Derive Darcy - Weisbach formula for calculating loss of head due to friction in a pipe.

[AU, Nov / Dec - 2011]

2.105) Derive Darcy - Weisbach formula for head loss due to friction in flow through pipes.

[AU, Nov / Dec - 2005]

2.106) Obtain expression for Darcy – Weisbach friction factor f for flow in pipe. [AU, May / June - 2012] 2.107) Explain the losses of energy in flow through pipes.

[AU, Nov / Dec - 2009]

2.108) Derive an expression for Darcy – Weisbach formula to determine the head loss due to friction. Give an expression for relation between friction factor ‘f’ and Reynolds’s number ‘Re’ for laminar and turbulent flow.


2.109) Prove that the head lost due to friction is equal to one third of the total head at inlet for maximum power transmission through pipes.

[AU, Nov / Dec - 2008]



2.110) Show that for laminar flow, the frictional loss of head is given by hf= 8 fLQ2/gπ2D5

[AU, Nov / Dec - 2009]

2.111) Derive Euler’s equation of motion for flow along a stream line. What are the assumptions involved.

[AU, Nov / Dec - 2009]

2.112) A uniform circular tube of bore radius R1 has a fixed co axial cylindrical solid core of radius R2. An incompressible viscous fluid flows through the annular passage under a pressure gradient (-∂p/∂x). Determine the radius at which shear stress in the stream is zero, given that the flow is laminar and under steady state condition. [AU, May / June - 2009] 2.113) If the diameter of the pipe is doubled, what effect does this have on the flow rate for a given head loss for laminar flow and turbulent flow. [AU, April / May - 2011] 2.114) Derive an expression for the variation of jet radius r with distance y downwards for a jet directed downwards. The initial radius is R and the head of fluid is H. [AU, Nov / Dec - 2011] 2.115) Distinguish between pipes connected in series and parallel. [AU, Nov / Dec - 2005] 2.116) Discuss on hydraulic and energy gradient.

[AU, Nov / Dec - 2014]

2.117) Determine the equivalent pipe corresponding to 3 pipes in series with lengths and diameters l1, l2, l3, d1, d2, d3 respectively.

[AU, Nov / Dec - 2009]

2.118) For sudden expansion in a pipe flow, work out the optimum ratio between the diameter of before expansion and the diameter of the pipe after expansion so that the pressure rise is maximum.

[AU, May / June - 2012]

2.119) Obtain the condition for maximum power transmission through a pipe line. 2.120) Explain stream lines, path lines and flow net.

[AU, Nov / Dec - 2012]

2.121) What are the uses and limitations of flow net?

[AU, May / June - 2009]

2.122) Briefly explain about boundary layer separation.

[AU, Nov / Dec - 2008]

2.123) Explain on boundary layer separation and its control. 2.124) Considering a flow over a flat plate, explain briefly the development of hydrodynamic boundary layer.

[AU, Nov / Dec - 2010]

2.125) Discuss in detail about boundary layer thickness and separation of boundary layer.




2.126) What is boundary layer and write its types of thickness? [AU, April / May - 2003] 2.127) Explain in detail  Drag and lift coefficients  Boundary layer thickness  Boundary layer separation  Navier’s – strokes equation.

[AU, May / June - 2012]

2.128) In a water reservoir flow is through a circular hole of diameter D at the side wall at a vertical distance H from the free surface. The flow rate through an actual hole with a sharp-edged entrance (kL = 0.5) will be considerably less than the flow rate calculated assuming frictionless flow. Obtain a relation for the equivalent diameter of the sharp-edged hole for use in frictionless flow relations. [AU, Nov / Dec - 2011] 2.129) Define : Boundary layer thickness(δ); Displacement thickness(δ *); Momentum thickness(θ) and energy thickness(δ**).


2.130) Briefly explain the following terms  Displacement thickness  Momentum thickness  Energy thickness

[AU, May / June - 2014]

2.131) Find the displacement thickness momentum thickness and energy thickness for the velocity distribution in the boundary layer given by (u/v) = (y/δ), where ‘u’is the velocity at a distance ‘y’ from the plate and u=U at y=δ, where δ = boundary layer thickness. Also calculate (δ*/θ).


2.132) Explain the concept of boundary layer in pipes for both laminar and turbulent flows with neat sketches.

[AU, Nov / Dec - 2013]

2.133) What is hydraulic gradient line? How does it differ from the total energy line? Under what conditions do both lines coincide with surface of the liquid? [AU, April / May - 2008] 2.134) Derive an expression for the velocity distribution for viscous flow through a circular pipe.

[AU, May / June - 2007]



2.135) Write a brief note on velocity potential function and stream function. [AU, May / June - 2009] 2.136) Derive an expression for the velocity distribution for viscous flow through a circular pipe. Also sketch the distribution of velocity cross a section of the pipe. [AU, Nov / Dec - 2011] PROBLEMS 2.137) A 20 cm diameter pipe 30 km long transports oil from a tanker to the shore at 0.01m3/s. Find the Reynold’s number to classify the flow. Take viscosity and density for oil. 2.138) A pipe line 20cm in diameter, 70m long, conveys oil of specific gravity 0.95 and viscosity 0.23 N.s/m2. If the velocity of oil is 1.38m/s, find the difference in pressure between the two ends of the pipe.

[AU, May / June - 2012]

2.139) Oil of absolute viscosity 1.5 poise and density 848.3kg/m3 flows through a 300mm pipe. If the head loss in 3000 m, the length of pipe is 200m, assuming laminar flow, find (i)

the average velocity,

(ii)

Reynolds’s number and

(iii) Friction factor.

[AU, May / June - 2012]

2.140) An oil of specific gravity 0.7 is flowing through the pipe diameter 30cm at the rate of 500litres/sec. Find the head lost due to friction and power required to maintain the flow for a length of 1000m. Take γ = 0.29 stokes. [AU, Nov / Dec – 2008, May / June - 2009] 2.141) A pipe line 10km, long delivers a power of 50kW at its outlet ends. The pressure at inlet is 5000kN/m2 and pressure drop per km of pipeline is 50kN/m2. Find the size of the pipe and efficiency of transmission. Take 4f = 0.02. [AU, Nov / Dec - 2005] 2.142) A lubricating oil flows in a 10 cm diameter pipe at 1 m/s. Determine whether the flow is laminar or turbulent. 2.143) An oil of specific gravity 0.80 and kinematic viscosity 15 x 10 6m2/s flows in a smooth pipe of 12 cm diameter at a rate of 150 lit/min. Determine whether the flow is laminar or turbulent. Also, calculate the velocity at the centre line and the velocity



at a radius of 4 cm. What is head loss for a length of 10 m? What will be the entry length? Also determine the wall shear.

[AU, Nov / Dec - 2014]

2.144) For the lubricating oil 2 μ = 0.1Ns /m and ρ = 930 kg/m3. Calculate also transition and turbulent velocities.


2.145) Oil of ,mass density 800kg/m3 and dynamic viscosity 0.02 poise flows through 50mm diameter pipe of length 500m at the rate of 0.19 liters/ sec. Determine  Reynolds number of flow  Center line of velocity  Pressure gradient  Loss of pressure in 500m length  Wall shear stress  Power required to maintain the flow.

[AU, May / June - 2012]

2.146) In fully developed laminar flow in a circular pipe, the velocity at R/2 (midway between the wall surface and the center line) is measured to be 6m/s. Determine the velocity at the center of the pipe.


2.147) A pipe 85m long conveys a discharge of 25litres per second. If the loss of head is 10.5m. Find the diameter of the pipe take friction factor as 0.0075. [AU, Nov / Dec - 2009] 2.148) A smooth pipe carries 0.30m3/s of water discharge with a head loss of 3m per 100m length of pipe. If the water temperature is 20°C, determine diameter of the pipe.

[AU, May / June - 2012]

2.149) Water is flowing through a pipe of 250 mm diameter and 60 m long at a rate of 0.3 m3/sec. Find the head loss due to friction. Assume kinematic viscosity of water 0.012 stokes. 2.150) Consider turbulent flow (f = 0.184 Re-0.2) of a fluid through a square channel with smooth surfaces. Now the mean velocity of the fluid is doubled. Determine the change in the head loss of the fluid. Assume the flow regime remains unchanged. What will be the head loss for fully turbulent flow in a rough pipe? [AU, Nov / Dec - 2013] 2.151) A pipe of 12cm diameter is carrying an oil (μ = 2.2 Pa.s and ρ = 1250 kg/m3) with a velocity of 4.5 m/s. Determine the shear stress at the wall surface of the pipe,



head loss if the length of the pipe is 25 m and the power lost. [AU, Nov / Dec - 2011] 2.152) Find the head loss due to friction in a pipe of diameter 30cm and length 50cm, through which water is flowing at a velocity of 3m/s using Darcy’s formula. [AU, Nov / Dec - 2008] 2.153) For a turbulent flow in a pipe of diameter 300 mm, find the discharge when the center-line velocity is 2.0 m/s and the velocity at a point 100 mm from the center as measured by pitot-tube is 1.6 m/s.


2.154) A laminar flow is taking place in a pipe of diameter 20cm. The maximum velocity is 1.5m/s. Find the mean velocity and radius at which this occurs. Also calculate the velocity at 4cm from the wall pipe.

[AU, May / June - 2009]

2.155) Water is flowing through a rough pipe of diameter 60 cm at the rate of 600litres/second. The wall roughness is 3 mm. Find the power loss for 1 km length of pipe. 2.156) Water flows in a 150 mm diameter pipe and at a sudden enlargement, the loss of head is found to be one-half of the velocity head in 150 mm diameter pipe. Determine the diameter of the enlarged portion. 2.157) A 150mm diameter pipe reduces in diameter abruptly to 100mm diameter. If the pipe carries water at 30 liters per second, calculate the pressure loss across the contraction. The coefficient of contraction as 0.6.

[AU, Nov / Dec - 2012]

2.158) A pipe line carrying oil of specific gravity 0.85, changes in diameter from 350mm at position 1 to 550mm diameter to a position 2, which is at 6m at a higher level. If the pressure at position 1 and 2 are taken as 20N/cm2 and 15N/cm2 respectively and discharge through the pipe is 0.2m3/s. Determine the loss of head. [AU, May / June - 2007] 2.159) A pipe line carrying oil of specific gravity 0.87, changes in diameter from 200mm at position A to 500mm diameter to a position B, which is at 4m at a higher level. If the pressure at position A and B are taken as 9.81N/cm2 and 5.886N/cm2 respectively and discharge through the pipe is 200 litres/s. Determine the loss of head and direction of flow.

[AU, Nov / Dec - 2008]

2.160) A 30cm diameter pipe of length 30cm is connected in series to a 20 cm diameter pipe of length 20cm to convey discharge. Determine the equivalent length of pipe CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 37


diameter 25cm, assuming that the friction factor remains the same and the minor losses are negligible.


2.161) A pipe of 0.6m diameter is 1.5 km long. In order of augment the discharge, another line of the same diameter is introduced parallel to the first in the second half of the length. Neglecting minor losses. Find the increase in discharge, if friction factor f= 0.04. The head at inlet is 40m.

[AU, Nov / Dec – 2004, 2005, 2012]

2.162) A pipe of 10 cm in diameter and 1000 m long is used to pump oil of viscosity 8.5 poise and specific gravity 0.92 at the rate of1200 lit./min. The first 30 m of the pipe is laid along the ground sloping upwards at 10° to the horizontal and remaining pipe is laid on the ground sloping upwards 15° to the horizontal. State whether the flow is laminar or turbulent? Determine the pressure required to be developed by the pump and the power required for the driving motor if the pump efficiency is 60%. Assume suitable data for friction factor, if required.

[AU, Nov / Dec - 2010]

2.163) Oil with a density of 900 kg/m3and kinematic viscosity of 6.2 × 10-4m2/s is being discharged by a 6 mm diameter, 40 m long horizontal pipe from a storage tank open to the atmosphere. The height of the liquid level above the center of the pipe is 3 m. Neglecting the minor losses, determine the flow rate of oil through the pipe. [AU, Nov / Dec - 2011] 2.164) Oil at 27°C (ρ = 900 kg/m3 and µ = 40 centi poise) is flowing steadily in a 1.25cm diameter 40m long During the flow, the pressure at the pipe inlet and exit is measured to be 8.25 bar and 0.95 bar, respectively. Determine the flow rate of oil through the pipe assuming the pipe is

[AU, Nov / Dec - 2014]

 Horizontal,  Inclined 20º upward, and  Inclined 20º downward. 2.165) The velocity of water in a pipe 200mm diameter is 5m/s. The length of the pipe is 500m. Find the loss of head due to friction, if f = 0.008.

[AU, Nov / Dec - 2005]

2.166) A 200mm diameter (f = 0.032) 175m long discharges a 65mm diameter water jet into the atmosphere at a point which is 75m below the water surface at intake. The entrance to the pipe is reentrant with ke = 0.92 and the nozzle loss coefficient is 0.06. Find the flow rate and the pressure head at the base of the nozzle. [AU, April / May - 2011] CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 38


2.167) A pipe line 2000m long is used for power transmission 110kW is to be transmitted through a pipe in which water is having a pressure of 5000kN/m2 at inlet is flowing. If the pressure drop over a length of a pipe is 1000kN/m2 and coefficient of friction is 0.0065, find the diameter of the pipe and efficiency of transmission. [AU, May / June - 2012] 2.168) A horizontal pipe of 400 mm diameter is suddenly contracted to a diameter of 200 mm. The pressure intensities in the large and small pipe are given as 15 N/cm2 and 10 N/cm2 respectively. Find the loss of head due to contraction, if C c = 0.62, determine also the rate of flow of water. 2.169) A horizontal pipe line 40 m long is connected to a water tank at one end and discharges freely into the atmosphere at the other end. For the first 25 m of its length from the tank, the pipe is 150 mm diameter and its diameter is suddenly enlarged to 300 mm. The height of water level in the tank is 8 m above the centre of the pipe. Considering all losses of head which occur, determine the rate of flow. Take f = 0.01 for both sections of the pipe.

[AU, May / June - 2013]

2.170) A 15cm diameter vertical pipe is connected to 10cm diameter vertical pipe with a reducing socket. The pipe carries a flow of 100 l/s. At a point 1 in 15cm pipe gauge pressure is 250kPa. At point 2 in the 10cm pipe located 1m below point 1 the gauge pressure is 175kPa.  Find weather the flow is upwards /downwards  Head loss between the two points

[AU, Nov / Dec - 2008]

2.171) The rate of flow of water through a horizontal pipe is 0.25 m3/sec. The diameter of the pipe, which is 20 cm, is suddenly enlarged to 40 cm. The pressure intensity in the smaller pipe is 11.7 N/cm2. Determine the loss of head due to sudden enlargement and pressure intensity in the larger pipe, power loss due to enlargement. [AU, May / June - 2009] 2.172) In a city water supply systems, water is flowing through a pipe line 30cm in diameter. The pipe diameter is suddenly reduced to 20cm. estimate the discharge through the pipe if the difference across the sudden contraction is 5kPa. [AU, April / May - 2015] 2.173) A 45° reducing bend is connected to a pipe line. The inlet and outlet diameters of the bend being 600mm and 300mm respectively. Find the force exerted by water CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 39


on the bend, if the intensity of pressure at inlet to bend is 8.829N/cm2 and the rate of flow of water is 600 liters/s.

[AU, Nov / Dec - 2007]

2.174) Horizontal pipe carrying water is gradually tapering. At one section the diameter is 150mm and the flow velocity is 1.5m/s. If the drop pressure is 1.104bar is reduced section, determine the diameter of that section. If the drop is 5kN/m2, what will be the diameter – Neglect the losses?

[AU, Nov / Dec - 2009]

2.175) The rate of flow of water through a horizontal pipe is 0.3m3/sec. The diameter of the pipe, which is 25cm, is suddenly enlarged to 50 cm. The pressure intensity in the smaller pipe is 14N/cm2. Determine the loss of head due to sudden enlargement, pressure intensity in the larger pipe power lost due to enlargement. [AU, Nov / Dec - 2003] 2.176) Water at 15°C ( ρ =999.1 kg/m3andμ = 1.138 x 10-3kg/m. s) is flowing steadily in a30-m-long and 4 cm diameter horizontal pipe made of stainless steel at a rate of 8 L/s. Determine (i) the pressure drop, (ii) the head loss, and (iii) the pumping power requirement to overcome this pressure drop. Assume friction factor for the pipe as 0.015.


2.177) The discharge of water through a horizontal pipe is 0.25m3/s. The diameter of above pipe which is 200mm suddenly enlarges to 400mm at a point. If the pressure of water in the smaller diameter of pipe is 120kN/m2, determine loss of head due to sudden enlargement; pressure of water in the larger pipe and the power lost due to sudden enlargement.

[AU, May / June - 2009]

2.178) A pipe of varying sections has a sectional area of 3000, 6000 and 1250 mm2 at point A, B and C situated 16 m, 10 m and 2 m above the datum. If the beginning of the pipe is connected to a tank which is filled with water to a height of 26 m above the datum, find the discharge, velocity and pressure head at A, B and C. Neglect all losses. Take atmospheric pressure as 10 m of water. 2.179) An existing 300mm diameter pipeline of 3200m length connects two reservoirs having 13m difference in their water levels. Calculate the discharge Q1. If a parallel pipe 300mm in diameter is attached to the last 1600m length of the above existing pipe line, find the new discharge Q2. What is the change in discharge? Express it as a % of Q1. Assume friction factor f = 0.14 in Darcy – Weisbach formula. [AU, May / June - 2009] CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 40


2.180) Two reservoirs with a difference in water surface elevation of 15 m are connected by a pipe line ABCD that consists of three pipes AB, BC and CD joined in series. Pipe AB is 10 cm in diameter, 20 m long and has f = 0.02. Pipe BC is of 16 cm diameter, 25 m long and has f = 0.018. Pipe CD is of 12 cm diameter, 15 m long and has f = 0.02. The junctions with the reservoirs and between the pipes are abrupt. (a) Calculate the discharge (b) What difference in reservoir elevation is necessary to have a discharge of 20 litres/sec? Include all minor losses. 2.181) Two tanks of fluid ( ρ = 998 kg/m3 and µ = 0.001 kg/ms.) at 20°C are connected by a capillary tube 4 mm in diameter and 3.5 m long. The surface of tank 1 is 30 cm higher than the surface of tank 2. Estimate the flow rate in m3/h. Is the flow laminar? For what tube diameter will Reynolds number be 500? [AU, Nov / Dec - 2013] 2.182) Three pipes of 400mm, 350mm and 300mm diameter connected in series between two reservoirs. With difference in level of 12m. Friction factor is 0.024, 0.021 and 0.019 respectively. The lengths are 200m, 300m and 250m. Determine flow rate neglecting the minor losses.

[AU, Nov / Dec - 2009]

2.183) Three pipes of diameters 300 mm, 200 mm and 400 mm and lengths450 m, 255 m and 315 m respectively are connected in series. The difference in water surface levels in two tanks is 18 m. Determine the rate of flow of water if coefficients of friction are 0.0075, 0.0078and 0.0072 respectively considering: the minor losses and by neglecting minor losses.

[AU, Nov / Dec - 2011]

2.184) Three pipes of diameters 300 mm, 200 mm and 400 mm and lengths 300 m, 170 m and 210 m respectively are connected in series. The difference in water surface levels in two tanks is 12 m. Determine the rate of flow of water if coefficients of friction are 0.005, 0.0052 and 0.0048 respectively considering: the minor losses and by neglecting minor losses

[AU, May / June– 2012]

2.185) Three pipes connected in series to make a compound pipe. The diameters and lengths of pipes are respectively, 0.4m, 0.2m, 0.3m and 400m, 200m, 300m. The ends of the compound pipe are connected to 2 reservoirs whose difference in water levels is 16m. The friction factor for all the pipes is same and equal to 0.02. The coefficient of contraction is 0.6. Find the discharge through the compound pipe if,



minor losses are negligible. Also find the discharge if minor losses are included. [AU, Nov / Dec - 2010] 2.186) A compound piping system consists of 1800 m of 0.5 m, 1200 m of 0.4 m and 600 m of 0.3 m new cast-iron pipes connected in series. Convert the system to (i) an equivalent length of0.4 m diameter pipe and (ii) an equivalent size of pipe of 3600 m length.


2.187) A 100m long pipe line of 300mm in diameter contains two 90º elbows and two gate valves (wide open). Calculate the equivalent pipe length and total loss of head when the flow rate is 0.5m3/s, f = 0.005, and the pipe has a sharp entry and exit. [AU, April / May - 2015] 2.188) A pipe line of 600 mm diameter is 1.5 km long. To increase the discharge, another line of the same diameter is introduced parallel to the first in the second half of the length. If f = 0.01 and head at inlet is 30 m, calculate the increase in discharge. 2.189) A pipe line of 0.6m diameter is 1.5Km long. To increase the discharge, another line of same diameter is introduced in parallel to the first in second half of the length. Neglecting the minor losses, find the increase in discharge if 4f = 0.04. The head at inlet is 30cm.


2.190) A pipe line of 0.6m diameter is 1.5Km long. To increase the discharge, another line of same diameter is introduced in parallel to the first in second half of the length. Neglecting the minor losses, find the increase in discharge if Darcy’s friction factor 0.04. The head at inlet is 300mm.


2.191) Two pipes of 15cm and 30cm diameters are laid in parallel to pass a total discharge of 100 litres per second. Each pipe is 250m long. Determine discharge through each pipe. Now these pipes are connected in series to connect two tanks 500m apart, to carry same total discharge. Determine water level difference between the tanks. Neglect the minor losses in both cases, f=0.02 fn both pipes. [AU, May / June - 2007] 2.192) Two pipes of diameter 40 cm and 20 cm are each 300 m long. When the pipes are connected in series and discharge through the pipe line is0.10 m3/sec, find the loss of head incurred. What would be the loss of head in the system to pass the same total discharge when the pipes are connected in parallel? Take f = 0.0075 for each pipe.

[AU, May / June – 2007, 2012, Nov / Dec - 2010]



2.193) A main pipe divides into two parallel pipes, which again forms one pipe. The length and diameter for the first parallel pipe are 2000m and 1m respectively, while the length and diameter of second parallel pipe are 200m and 0.8m respectively. Find the rate of flow in each parallel pipe, if total flow in the main is 3m3/s. The coefficient of friction for each parallel pipe is same and equal to 0.005. [AU, May / June - 2007] 2.194) The main pipe is divided into two parallel pipes which again forms one pipe, the first parallel pipe has length of 1000 m and diameter of 0.8 m. The second parallel pipe has length of 1000 m and diameter of 0.6 m. The coefficient friction for each parallel pipe is 0.005. If the total rate of flow in the main pipe is 2 m3 /sec, find the rate of flow in each parallel pipe.

[AU, May / June - 2014]

2.195) For a town water supply, a main pipe line of diameter 0.4 m is required. As pipes more than 0.35m diameter are not readily available, two parallel pipes of same diameter are used for water supply. If the total discharge in the parallel pipes is same as in the single main pipe, find the diameter of parallel pipe. Assume co-efficient of discharge to be the same for all the pipes.


2.196) Two pipes of identical length and material are connected in parallel. The diameter of pipe A is twice the diameter of pipe B. Assuming the friction factor to be the same in both cases and disregarding minor losses, determine the ratio of the flow rates in the two pipes.


2.197) A pipe line 30cm in diameter and 3.2m long is used to pump up 50Kg per second of oil whose density is 950 Kg/m3 and whose kinematic viscosity is 2.1 strokes, the center of the pipe line at the upper end is 40m above than the lower end. The discharge at the upper end is atmospheric. Find the pressure at the lower end and draw the hydraulic gradient and total energy line.


2.198) Two water reservoirs A and B are connected to each other through a 50 m long, 2.5 cm diameter cast iron pipe with a sharp-edged entrance. The pipe also involves a swing check valve and a fully open gate valve. The water level in both reservoirs is the same, but reservoir A is pressurized by compressed air while reservoir B is open to the atmosphere. If the initial flow rate through the pipe is 1.5 l/s, determine the absolute air pressure on top of reservoir A. Take the water temperature to be 25°C.

[AU, Nov / Dec - 2011]



2.199) When water is being pumped is a pumping plant through a 600mm diameter main, the friction head was observed as 27m. In order to reduce the power consumption, it is proposed to lay another main of appropriate diameter along the side of existing one, so that the two pipes will work in parallel for the entire length and reduce the friction head to 9.6m only. Find the diameter of the new main if with the exception of diameter; it is similar to the existing one in all aspects. [AU, Nov / Dec - 2007] 2.200) Kerosene (SG = 0.810) at a temperature of 22ºC flows in a 75-mm diameter smooth brass pipeline at a rate of 0.90 lit/s. Find the friction head loss per meter, For the same head loss, what would be the flow rate if the temperature of the kerosene were raised to 40°C?

[AU, Nov / Dec - 2014]

2.201) Determine the  Pressure gradient  The shear stress at the two horizontal parallel plates and  Discharge per meter width for the laminar flow of oil with maximum velocity 2m/s between two horizontal parallel fixed plates which are 10cm apart. Given μ = 2.4525 Ns/m2


2.202) In fully developed laminar flow in a circular pipe, the velocity at R/2 (midway between the wall surface and the centerline) is measured to be 6 m/s. Determine the velocity at the center of the pipe.


2.203) A smooth two –dimensional flat plate is exposed to a wind velocity of 100 km/h. If laminar boundary layer exists up to a value of Rexequal to 3 x 105, find the maximum distance up to which laminar boundary layer exists and find its maximum thickness. Assume kinematic viscosity of air as 1.49 x 10-5m2/sec. [AU, April / May - 2003] 2.204) Air is flowing over a flat plate with a velocity of 5 m/s. The length of the plate is 2.5 m and width 1 m. The kinematic viscosity of air is given as 0.15 x 10 -4m2/s. Find the (i)

boundary layer thickness at the end of plate

(ii)

shear stress at 20 cm from the leading edge

(iii)

shear stress at 175 cm from the leading edge

(iv)

Drag force on one side of the plate.



(v)

Take the velocity profile

𝑢 𝑈

=

3 2

𝑦

1

𝛿

2

( )−

𝑦 3

( ) over a plate as and the 𝛿

density of air1.24 kg/m3. 2.205) A plate of 600mm length and 400mm wide is immersed in a fluid of specific gravity 0.9 and kinematic viscosity of = 10-4 m2/s. The fluid is moving with velocity of 6m/s. Determine  Boundary layer thickness  Shear stress at the end of the plate  Drag force on one side of the plate.

[AU, Nov / Dec - 2012]

2.206) Water at 20° C enters a pipe with a uniform velocity (U) of 3m/s. What is the distance at which the transition (x) occurs from a laminar to a turbulent boundary layer? If the thickness of this initial laminar boundary layer is given by 4.91√(vx/U) what is its thickness at the point of transition?(v – kinematic viscosity). [AU, April / May - 2011] 2.207) A flat plate 1.5 m x 1.5 m moves at 50 km/h in stationary air of density 1.15 kg/m3. If the co-efficient of drag and lift are 0.15 and 0.75 respectively, determine the (i) Lift force (ii) Drag force (iii) The resultant force and (iv) The power required to set the plate in motion.

[AU, Nov / Dec - 2007]

2.208) A jet plane which weighs 29430 N and has the wing area of 20m2 flies at the velocity of 250km/hr. When the engine delivers 7357.5kW. 65% of power is used to overcome the drag resistance of the wing. Calculate the coefficient of lift and coefficient of drag for the wing. Take density of air = 1.21 kg/m3 [AU, May / June - 2009] 2.209) For the velocity profile in laminar boundary layer as u/U = 3/2 (y/δ)-1/2(y/δ)3. Find the thickness of the boundary layer and shear stress, 1.8m from the leading edge of a plate. The plate is 2.5 m long and 1.5 m wide is placed in water, which is moving with a velocity of 15 cm/sec. Find the drag on one side of the plate if the viscosity of water is 0.01 poise.

[AU, Nov / Dec - 2003]



2.210) Consider flow of oil through a pipe of 0.3m diameter. The velocity distribution is parabolic with maximum velocity of 3 m/s at the pipe centre. Estimate the shear stress at the pipe wall and within the fluid 50mm from the pipe wall. The viscosity of the oil is 1.7Pa.s.

[AU, Nov / Dec - 2012]

2.211) The velocity distribution in the boundary layer is given by u/U = y/δ, where u is the velocity at the distance y from the plate u = U at y = δ, δ being boundary layer thickness. Find the displacement thickness, momentum thickness and energy thickness.


2.212) If the velocity distribution in a laminar boundary layer over a flat plate is given by 𝑢/𝑈∞ = sin(𝜋/2 𝑦 /𝛿), calculate the value of 𝛿, 𝛿 ∗ , 𝜃 and shear stress. [AU, April / May - 2015] 2.213) Water at 20°C flow through a 160mm diameter pipe with roughness of 0.016 mm. If the mean velocity is 6 m/s, what is the nominal thickness of the viscous sublayer? What will be the viscous sub -layer if the velocity is increased to 7.2 m/s? [AU, Nov / Dec - 2014] 2.214) The flow rate in a 260mm diameter pipe is 220 litres/sec. The flow is turbulent, and the centerline velocity is 4.85m/s. Plot the velocity profile, and determine the head loss per meter of pipe.


2.215) An oil of viscosity 0.9Pa.s and density 900kg/m3 flows through a pipe of 100mm diameter. The rate of pressure drop for every meter length of pipe is 25kPa. Find the oil flow arte, drag force per meter length, pumping power required to maintain the flow over a distance of 1km, velocity and shear stress at 15, from the pipe wall. [AU, Nov / Dec - 2010] 2.216) Consider the flow of a fluid with viscosity m through a circular pipe. The velocity profile in the pipe is given as where is the maximum flow velocity, which occurs at the centerline; r is the radial distance from the centerline; is the flow velocity at any position r; and R is the Reynold's number. Develop a relation for the drag force exerted on the pipe wall by the fluid in the flow direction per unit length of the pipe.




u(r) = umax(1-rn / Rn ) R umax

r o

2.217) Velocity components in flow are given by U = 4x, V = -4y. Determine the stream and potential functions. Plot these functions for φ 60, 120, 180, and 240 and Ф 0, 60, 120, 180, +60, +120, +180. Check for continuity.

[AU, Nov / Dec - 2009]

2.218) A fluid of specific gravity 0.9 flows along a surface with a velocity profile given by v = 4y - 8y3m/s, where y is in m. What is the velocity gradient at the boundary? If the kinematic viscosity is 0.36S, what is the shear stress at the boundary? [A.U. Nov / Dec - 2008] 2.219) In a two dimensional incompressible flow the fluid velocities are given by u = x – ay and v = - y – 4x. Show that the velocity potential exists and determine its form. Find also the stream function.

[AU, May / June - 2009]

2.220) A smooth flat plate with a sharp leading edge is placed along a free stream of water flowing at 3m/s. Calculate the distance from the leading edge and the boundary thickness where the transition from laminar to turbulent- flow may commence. Assume the density of water as 1000 kg/m3 and viscosity as 1centipoise. [AU, April / May - 2011] 2.221) A smooth two dimensional flat plate is exposed to a wind velocity of 100 km/hr. If laminar boundary layer exists up to a value of RN = 3 x105, find the maximum distance up to which laminar boundary layer persists and find its maximum thickness. Assume kinematic viscosity of air as 1.49x10-5 m2/s. [AU, Nov / Dec - 2008] 2.222) A power transmission pipe 10 cm diameter and 500 m long is fitted with a nozzle at the exit, the inlet is from a river with water level 60 m above the discharge nozzle. Assume f = 0.02, calculate the maximum power which can be transmitted and the diameter of nozzle required.

[AU, Nov / Dec - 2008]



UNIT - III - DIMENSIONAL ANALYSIS PART - A 3.1) What do you understand by fundamental units and derived units? [AU, April / May - 2010] 3.2) Differentiate between fundamental units and derived units. Give examples. [AU, Nov / Dec - 2011] 3.3) Define dimensional analysis. 3.4) What do you mean by dimensional analysis?

[AU, Nov / Dec - 2009]

3.5) Brief on dimensional variables with examples.

[AU, Nov / Dec - 2014]

3.6) Brief on Intuitive method. Give some examples.

[AU, Nov / Dec - 2014]

3.7) Define dimensional homogeneity. 3.8) What is dimensional homogeneity and write any one sample equation? [AU, Nov / Dec - 2006] 3.9) Explain the term dimensional homogeneity.

[AU, Nov / Dec - 2011]

3.10) Give the methods of dimensional analysis. 3.11) State a few applications, usefulness of ‘dimensional analysis’. [AU, May / June - 2007] 3.12) What is a dimensionally homogenous equation? Give example. [AU, Nov / Dec - 2003] 3.13) Cite examples for dimensionally homogeneous and non-homogeneous equations. [AU, Nov / Dec - 2010] 3.14) Check whether the following equation is dimensionally homogeneous. Q =Cd .a √(2 gh) .


3.15) Define Rayleigh's method. 3.16) Give the Rayleigh method to determine dimensionless groups. [AU, Nov / Dec - 2011] 3.17) State any two choices of selecting repeating variables in Buckingham π theorem. [AU, April / May - 2011] 3.18) State Buckingham’s π theorem. [AU, Nov / Dec – 2008, 2012, April / May - 2015] 3.19) What is Buckingham's π theorem?



3.20) The excess pressure Δp inside a bubble is known to be a function of the surface tension and the radius. By dimensional reasoning determine how the excess pressure. Will vary if we double the surface tension and the radius. [AU, Nov / Dec - 2013] 3.21) Distinguish between Rayleigh's method and Buckingham's π- theorem. [AU, April / May - 2011] 3.22) Under what circumstances, will Buckingham’s π theorem yield incorrect number of dimensionless group? 3.23) State a few applications / usefulness of dimensional analysis. 3.24) Define Euler's number.

[AU, May / June - 2009]

3.25) List out any four rules to select repeating variable. 3.26) Define similitude. 3.27) Give the three types of similarities. 3.28) What are the types of similarities?

[AU, Nov / Dec - 2012]

3.29) Define geometric similarity. 3.30) Define kinematic similarity. 3.31) What is meant by kinematic similarity?

[AU, Nov / Dec - 2014]

3.32) Define dynamic similarity. 3.33) What is meant by dynamic similarity?

[AU, Nov / Dec - 2008]

3.34) What is dynamic similarity?

[AU, Nov / Dec - 2009]

3.35) What is similarity in model study?


3.36) What is scale effect in physical model study? [AU, Nov / Dec – 2005, 2006, May / June– 2012] 3.37) If two systems (model and prototype) are dynamically similar, is it implied that they are also kinematically and geometrically similar?

[AU, May / June - 2012]

3.38) Distinguish between a control and differential control volume. [AU, April / May - 2011] 3.39) Mention the circumstances which necessitate the use of distorted models. [AU, Nov / Dec - 2010] 3.40) Give the types of forces in a moving fluid. 3.41) Give the dimensions of power and specific weight.

[AU, Nov / Dec - 2009]

3.42) Define inertia force. CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 49


3.43) Define viscous force. 3.44) Define gravity and pressure force. 3.45) Define surface tension force. 3.46) Define dimensionless numbers. 3.47) Give the types of dimensionless numbers. 3.48) Give the dimensions of the following physical quantities: surface tension and dynamic viscosity.

[AU, May / June - 2013]

3.49) Write the dimensions of surface tension and vapour pressure in MLT system. [AU, April / May - 2015] 3.50) Define Reynold’s number. What its significance? 3.51) Define Reynold’s number and state its significance?

[AU, Nov / Dec - 2010] [AU, April / May - 2015]

3.52) Define Reynold’s number and Froude’s numbers. [AU, Nov / Dec – 2007, 2011] 3.53) Define the Froude's dimensionless number.

[AU, May / June - 2014]

3.54) Define Froude's number. [AU, Nov / Dec – 2005, 2009, 2008, April / May – 2010, May / June - 2012] 3.55) State Froude's model law.

[AU, May / June - 2013]

3.56) Define Euler number and Mach number.

[AU, May / June - 2007]

3.57) Define Reynold’s number and Mach number.

[AU, Nov / Dec - 2012]

3.58) Define Mach number.

[AU, May / June - 2009]

3.59) What is Mach number? Mention its field of use.


3.60) Define Mach's number and mention its field of use. 3.61) Define -Mach number and state its application.

[AU, Nov / Dec - 2014]

3.62) Write down the dimensionless number for pressure.

[AU, Nov / Dec - 2011]

3.63) What are the similitudes that should exist between the model and its prototype? [AU, April / May - 2015] PART - B 3.64) Discuss on Buckingham's π theorem. 3.65) What is repeating variables? How are these selected?

[AU, Nov / Dec - 2014] [AU, May / June - 2007]

3.66) Discuss on the applications of dimensionless parameters. [AU, Nov / Dec - 2014] 3.67) State the similarity laws used in model analysis.


3.68) State and explain the various laws of similarities between model and its prototype.



3.69) What is meant by geometric, kinematic and dynamic similarities? [AU, May / June – 2007, 2014] 3.70) What is meant by geometric, kinematic and dynamic similarities? Are these similarities truly attainable? If not, why?

[AU, May / June - 2009]

3.71) Explain the different types of similarities exist between a proto type and its model. [AU, Nov / Dec - 2003] 3.72) What is distorted model and also give suitable example? [AU, April / May - 2004] 3.73) What are distorted models? State merits and demerits.

[AU, May / June - 2014]

3.74) Define dimensional homogeneity and also give example for homogenous equation.


3.75) Classify Models with scale ratios.

[AU, Nov / Dec - 2009]

3.76) Derive on the basis of dimensional analysis suitable parameters to present the thrust developed by a propeller. Assume that the thrust P depends upon the angular velocity ω , speed of advance V, diameter D, dynamic viscosity μ, mass density ρ , elasticity of the fluid medium which can be denoted by the speed of sound in the [AU, Nov / Dec – 2011, 2012]

medium C.

3.77) Check the following equations are dimensionally homogenous  Drag force = ½ ( Cd ρU2A) where Cd is coefficient of drag which is constant  F = γQ ( U1 – U2) / g – ( P1A1 – P2A2)  Total energy per unit mass = v2/2 + gz + P/ρ  Q = δ / 15Cd tan(θ/2) √(2g) * (H)5/2where Cd is coefficient of discharge constant

[AU, April / May - 2004, 2010, Nov / Dec - 2005]

3.78) Define and explain Reynold’s number, Froude’s number, Euler’s number and Mach’s number.

[AU, Nov / Dec - 2003]

3.79) What are the significance and the role of the following parameters?  Reynolds number  Froude number  Mach number  Weber number.




3.80) Define the following dimensionless numbers and state their significance for fluid flow problems.

[AU, May / June - 2014]

 Reynolds number  Mach number 3.81) Explain the Reynolds model law and state its applications. 3.82) Use dimensionless analysis to arrange the following groups into dimensionless parameters; ∆p, V, γ, g and f, ρ, L, V use MLT system.


3.83) Use dimensional analysis and the MLT system to arrange the following into a dimensionless number: L, ρ , µ and a.

[AU, Nov / Dec - 2013]

3.84) Consider force F acting on the propeller of an aircraft, which depends upon the variable U, ρ, μ, D and N. Derive the non – dimensional functional form F/(ρU2D2) = f ((UDρ/μ),(ND/U))

[AU, Nov / Dec - 2003]

3.85) The frictional torque T of a disc diameter D rotating at a speed N in a fluid of viscosity μ and density ρ in a turbulent flow is given by T = D5 N2 ρ Ф[μ/D2Nρ]. Prove this by Buckingham’s π theorem. [AU, Nov / Dec - 2003] 3.86) Resistance R, to the motion of a completely submerged body is given by R = ρv2l2φ(VL/γ), where ρ and γ are the mass density and kinematic viscosity of the fluid; v– velocity of flow; l – length of the body. If the resistance of a one – eighth scale air - ship model when tested in water at 12m/s is 22N, what will be the resistance of the air –ship at the corresponding aped, in air? Assume kinematic viscosity of air is 13times that of water and density of water is 810 times of air. [AU, Nov / Dec - 2007, April / May - 2010] 3.87) The resisting force R to a supersonic plane during flight can be considered as dependent upon the length of the aircraft l, velocity V, air viscosity m, air density and bulk modulus of air K. Express the functional relationship between these variables and the resisting force. 3.88) The resisting force F of a plane during flight can be considered as dependent upon the length of aircraft (l), velocity (v), air viscosity (μ), air density (ρ) and bulk modulus of air (K). Express the functional relationship between these variables using dimensional analysis. Explain the physical significance of the dimensionless groups arrived.

[AU, Nov / Dec - 2010]



3.89) Derive an expression for the shear stress at the pipe wall when an incompressible fluid flows through a pipe under pressure. Use dimensional analysis with the following significant parameters: pipe diameter D, flow velocity V, and viscosity µ and density ρ of the fluid.

[AU, Nov / Dec - 2013]

3.90) The resistance R, to the motion of a completely submerged body depends upon the length of the body (L), velocity of flow (V), mass density of fluid (ρ), kinematic viscosity (γ). Prove by dimensional analysis that R = ρV2L2φ(VL/γ)

[AU, May / June - 2009]

3.91) Obtain a relation using dimensional analysis, for the resistance to uniform motion of a partially submerged body in a viscous compressible fluid. [AU, Nov / Dec - 2014] 3.92) Using Buckingham π method of dimensional analysis obtain an expression for the drag force R on a partially submerged body moving with a relative velocity V in a fluid; the other variables being the linear dimension L, height of surface roughness K, Fluid density ρ and the gravitational acceleration g.


3.93) The power developed by hydraulic machines is found to depend on the head h, flow rate Q, density ρ, speed N, runner diameter D, and acceleration due to gravity g. Obtain suitable dimensionless parameters to correlate experimental results. [AU, Nov / Dec – 2011, 2014] 3.94) Show that the power P developed in a water turbine can be expressed as:

Where, ρ = Mass density of the liquid, N = Speed in rpm, D = Diameter of the runner, B = Width of the runner and µ = Dynamic viscosity

[AU, Nov / Dec - 2011]

3.95) The capillary rise h is found to be influenced by the tube diameter D, density ρ, gravitational acceleration g and surface tension σ. Determine the dimensionless parameters for the correlation of experimental results.

[AU, Nov / Dec - 2011]



3.96) Using dimensional analysis, obtain a correlation for the frictional torque due to rotation of a disc in a viscous fluid. The parameters influencing the torque can be identified as the diameter, rotational speed, viscosity and density of the fluid. [AU, Nov / Dec - 2011] 3.97) The drag force on a smooth sphere is found to be affected by the velocity of flow, u, the diameter D of the sphere and the fluid properties density ρ and viscosity μ. Find the dimensionless groups to correlate the parameters.

[AU, Nov / Dec - 2011]

3.98) State Buckingham's π - theorem. What do you mean by repeating variables? How are the repeating variables selected in dimensional analysis? 3.99) State Buckingham's π - theorem. What are the considerations in the choice of repeating variables?


3.100) Express efficiency in terms of dimensionless parameters using density, viscosity, angular velocity, diameter of rotor and discharge using Buckingham π theorem.

[AU, Nov / Dec - 2009]

3.101) State the Buckingham π theorem. What are the criteria for selecting repeating variable in this dimensional analysis?

[AU, Nov / Dec - 2009]

3.102) State Buckingham – π theorem. Mention the important principle for selecting the repeating variables.

[AU, May / June - 2009]

3.103) State and prove Buckingham π theorem. [AU, Nov / Dec – 2009, April / May - 2010] 3.104) Using Buckingham’s π- theorem show that the velocity through a circular orifice is given by V = √(2gH) φ [(D/H), (μ/ρVH) Where H is the head causing the flow D is the diameter of the orifice μ is the coefficient of viscosity ρ is the mass density g is the acceleration due to gravity


3.105) Using Buckingham's π- theorem, show that the pressure difference ∆P in a pipe of diameter D and length l due to turbulent flow depends on the velocity V, viscosity µ, density ρ and roughness k. 3.106) The efficiency (η) of a fan depends on ρ (density), μ (viscosity) of the fluid, ω (angular velocity), d(diameter of rotor) and Q(discharge). Express η in terms of nonCE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 54


dimensional parameters. Use Buckingham's theorem. [AU, April / May - 2010, 2011] 3.107) The efficiency (η) of a fan depends on ρ (density), μ (viscosity) of the fluid, ω (angular velocity), d(diameter of rotor) and Q(discharge). Express η in terms of nondimensional parameters. Use Rayleigh’s method.


3.108) The pressure difference Δp in a pipe of diameter D and length L due to viscos flow depends on the velocity V, viscosity µ and density ρ. Using Buckingham's π theorem, obtain an expression for Δp. [AU, May / June – 2014, April / May - 2015] 3.109) The power required by the pump is a function of discharge Q, head H, acceleration due to gravity g, viscosity μ, mass density of the fluid ρ, speed of rotation N and impeller diameter D. Obtain the relevant dimensionless parameters. [AU, May / June - 2012] 3.110) State Buckingham's π -theorem. The discharge of a centrifugal pump (Q) is dependent on N (speed of pump), d (diameter of impeller), g (acceleration due to gravity), H (manometric head developed by pump) and ρ and µ (density and dynamic viscosity of the fluid). Using the dimensional analysis and Buckingham's π -theorem, prove that it is given by

[AU, May / June - 2013]

𝑄 = 𝑁𝑑3 𝑓 (

𝑔𝐻 𝜇 , ) 𝑁 2 𝑑2 𝑁𝑑2 𝜌

3.111) Consider viscous flow over a very small object. Analysis of the equations of motion shows that the inertial terms are much smaller than viscous and pressure terms. Fluid density drops out, and these are called creeping flows. The only important parameters are velocity U, viscosity µ, and body length scale d. For threedimensional bodies,. Like spheres, creeping flow analysis yields very good results. It is uncertain, however, if creeping flow applies to two-dimensional bodies, such as cylinders, since even though the diameter may be very small, the length of the cylinder is infinite. Let us see if dimensional analysis can help. (1) Apply the Pi theorem to two-dimensional drag force F2-D, as a function of the other parameters. Be careful: two-dimensional drag has dimensions of fake per unit length, not simply force. (2) Is your analysis in part (1) physically plausible? If not, explain why not. (3) It turns out that fluid density ρ cannot be neglected in analysis of creeping flow over two dimensional bodies. Repeat the dimensional analysis, this time including ρ CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 55


as a variable, and find the resulting non dimensional relation between the parameters in this problem.

[AU, Nov / Dec - 2013]

3.112) Oil is moved up in a lubricating system by a rope dipping in the sump containing oil and moving up. The quantity of oil pumped Q, depends on the speed u of the rope, the layer thickness 6, the density and viscosity of the oil and acceleration due to gravity. Obtain the dimensionless parameters to correlate the flow. [AU, Nov / Dec - 2014] 3.113) When fluid in a pipe is accelerated linearly from rest, it begins as laminar flow and then undergoes transition to turbulence at a time t, which depends upon the pipe diameter D, fluid acceleration a, density ρ and viscosity µ. Arrange this into a dimensionless relation between t and D.

[AU, Nov / Dec - 2013]

3.114) What are the similarities between model and prototype? Mention the applications of model testing.

[AU, May / June - 2013]

PROBLEMS 3.115) Find the discharge through a weir model by knowing the discharge over the actual (proto type) weir is measured as 1.5m3/s. The horizontal dimension of the model = 1/50 of the horizontal dimensions of the proto type and the vertical dimension of the model = 1/10 of the vertical dimension of the proto type. (Hint: Apply Froude model law)


3.116) Model of an air duct operating with water produces a pressure drop of 10 kN/m2 over 10 m length. If the scale ratio is 1/50. Density of water is 1000 kg/m3 and density of air is 1.2 kg/m3. Viscosity of water is 01.001 Ns/m2 and viscosity of air 0.00002 Ns/m2. Estimate corresponding drop in a 20m long air duct. [AU, Nov / Dec - 2004, 2005, April / May - 2010] 3.117) A model of a hydroelectric power station tail race is proposed to build by selecting vertical scale 1 in 50 and horizontal scale 1 in 100. If the design pipe has flow rate of 600m3/s and allow the discharge of 800m3/s. Calculate the corresponding flow rates for the model testing.


3.118) A pipe of diameter 1.5 m is required to transport an oil of specific gravity 0.90 and viscosity 3 * 10-2 poise at the rate 3000 litre / sec. Test where conducted on a



15cm diameter pipe using water at 20º C. Find the velocity and the rate of flow in model. Viscosity of water at 20ºC = 0.01poise.

[AU, Nov / Dec - 2012]

3.119) In order to predict the pressure in a large air duct model is constructed with linear dimensions (1/10)th that of the prototype and the water was used as the testing fluid. If water is 1000 times denser than that of air and has 100 times the viscosity of air, determine the pressure drop in the prototype, for the conditions corresponding to a pressure drop of 70kPa, in the model.

[AU, May / June - 2009]

3.120) In an aero plane model of size 1/10 of its prototype, the pressure drop is 7.5kN/m2. The model is tested in water; find the corresponding drop in prototype. Assume density of air = 1.24kg/m3; density of water = 1000kg/m3; viscosity of air = 0.00018 poise; viscosity of water = 0.01 poise.

[AU, May / June - 2007]

3.121) A geometrically similar model of an air duct is built to 1/25 scale and tested with water which is 50 times more viscous and 800 times denser than air. When tested under dynamically similar conditions, the pressure drop is 200 kN/m2 in the model. Find the corresponding pressure drop in the full scale prototype and express in cm of water.

[AU, Nov / Dec – 2010, May / June - 2014]

3.122) Model tests have conducted to study the energy losses in a pipe line of 1m diameter required to transport kerosene of specific gravity 0.80 and dynamic viscosity 0.02 poise at the rate of 2000 litre/sec. Tests were conducted on a 10cm diameter pipe using water at 20°C. What is the flow rate in the model? If the energy head loss in 30m length of the model is measured as 44cm of water, what will be the corresponding head loss in the prototype? What will be the friction factor for the prototype pipe.

[AU, May / June - 2012]

3.123) In a geometrically similar model of spillway the discharge per meter length is 0.2m3/sec. if the scale of the model is 1/36, find the discharge per meter run of the prototype.

[AU, May / June - 2014]

3.124) A spillway model is to be built to a geometrically similar scale of

1 50

- across a

flume of 600 mm width. The prototype is 15 m high and maximum head on it is expected to be 1.5 m.  What height of model and what head on the model should be used?



 If the flow over the model at a particular head is 12 litres per second, what flow per metre length of the prototype is expected?  If the negative pressure in the model is 200 mm, what is the negative pressure in prototype? Is it practicable?

[AU, May / June - 2013]

3.125) The characteristics of the spillway are to be studied by means of a geometrically similar modal constructed to the scale ratio of 1:10.  If the maximum rate of flow in the prototype is 28.3m3, what will be the corresponding flow in model?  If the measured velocity in the model at a point on the spillway is 2.4m/s, what will be the corresponding velocity in prototype?  If the hydraulic jump at the foot of the model is 50mm high, what will be the height of jump in prototype?  If the energy dissipated per second in the model is 3.5Nm, what energy is dissipated per second in the prototype?


3.126) Vortex shedding at the rear of a structure of a given section can create harmful periodic vibration. To predict the shedding frequency, a smaller model is to be tested in a water tunnel. The air speed is expected to be about 75 kmph. If the geometric scale is 1 : 6.5 and the water temperature is 25°C determine the speed to be used in the tunnel. Consider air temperature as 38°C. If the shedding frequency of the model was 60 Hz, determine the shedding frequency of the prototype. The dimensions of the structure are diameter 0.12 m and height 0.36 m.

[AU, Nov / Dec - 2014]

3.127) An agitator of diameter D rotates at a speed N in a liquid of density ρ and viscosity μ. Show that the power required to mix the liquid is expressed by a functional form




UNIT – IV – PUMPS PART - A 4.1) Define centrifugal pump. 4.2) Mention the main parts of the Centrifugal pump. 4.3) How centrifugal pumps are classified based on casing?


4.4) Define impeller. 4.5) Define casing. 4.6) List the commonly used casings in centrifugal pumps.

[AU, Nov / Dec - 2010]

4.7) What is the role of a volute chamber of a centrifugal pump? [AU, Nov / Dec - 2005] 4.8) What precautions are to be taken while starting and closing the centrifugal pump? [AU, May / June - 2012] 4.9) Define priming of centrifugal pump. 4.10) What is priming?

[AU, Nov / Dec - 2010]

4.11) Why priming is necessary in a centrifugal pump? [AU, May / June - 2007, April / May - 2010] 4.12) What is meant by priming of pumps?


4.13) What is priming? Why is it necessary?

[AU, Nov / Dec - 2011]

4.14) Define cavitation.

[AU, Nov / Dec - 2008]

4.15) Define cavitation in a pump.

[AU, May / June - 2007]

4.16) What is the effect of cavitation in pump?


4.17) What are the effects of cavitation? Give necessary precautions against cavitations?

[AU, May / June - 2012]

4.18) What is cavitation? What causes it?

[AU, Nov / Dec - 2013]

4.19) Define the characteristic curves of centrifugal pump. 4.20) List out the types of characteristic curves. 4.21) What are operating characteristics curves of centrifugal pump? [AU, April / May - 2015] 4.22) Define multistage centrifugal pump and give its function. 4.23) List the losses in centrifugal pump.

[AU, Nov / Dec - 2014]



4.24) What are the advantages of centrifugal pump over reciprocating pumps? [AU, May / June - 2009] 4.25) Tabulate the causes and remedies for a centrifugal pump, when pump fails to pump the fluid.


4.26) What is a delivery pipe? 4.27) Define manometric efficiency and mechanical efficiency of a centrifugal pump. [AU, April / May - 2015] 4.28) What is the maximum theoretical suction head possible for a centrifugal pump? [AU, April / May - 2008] 4.29) Define suction head and manometric head of a centrifugal pump. [AU, Nov / Dec - 2012] 4.30) Define - manometric head and write its mathematical equation. [AU, Nov / Dec - 2013] 4.31) Define ‘Net Positive Suction Head’

[AU, Nov / Dec - 2014]

4.32) What do you mean by ‘Net Positive Suction Head’ (NPSH)? [AU, May / June - 2014] 4.33) What is meant by NPSH?

[AU, Nov / Dec - 2014]

4.34) How does the specific speed of a centrifugal pump differ from that of a turbine? 4.35) Write the equation for specific speed for pumps and also for turbine. [AU, Nov / Dec - 2005] 4.36) Define specific speed as applied to pumps. 4.37) Define specific speed.


4.38) What is specific speed of a pump? How are pumps classified based on this number?

[AU, Nov / Dec - 2009]

4.39) Give examples of machines handling gases with high pressure rise. 4.40) What do you mean by manometric efficiency and mechanical efficiency of a centrifugal pump?

[AU, Nov / Dec - 2007]

4.41) Define pump. 4.42) What is the principle of pump?

[AU, Nov / Dec - 2009]

4.43) Give the classification of pumps. 4.44) What is a positive displacement pump? 4.45) Define non - positive displacement pump (or) roto dynamic pump. CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 60


4.46) List the types of positive displacement pumps. 4.47) Under what conditions would you suggest use of double-suction pump and a multistage pump?

[AU, Nov / Dec - 2010]

4.48) What are roto dynamic pumps? Give examples.

[AU, Nov / Dec - 2009]

4.49) List the types of roto dynamic pumps. 4.50) What is a reciprocating pump? 4.51) Why the reciprocating pump is called a positive displacement pump? [AU, April / May - 2011] 4.52) How are reciprocating pumps classified?

[AU, Nov / Dec - 2011]

4.53) What are the materials used for manufacturing reciprocating pumps? [AU, Nov / Dec - 2014] 4.54) Define a single acting reciprocating pump. 4.55) Define a double acting reciprocating pump. 4.56) Brief the working of double acting reciprocating pump. [AU, April / May - 2011] 4.57) List the advantages of double acting reciprocating pump. [AU, Nov / Dec - 2014] 4.58) When will you select a reciprocating pump?

[AU, Nov / Dec - 2005]

4.59) Draw the relationship between discharge and crank angle for a single acting pump.

[AU, Nov / Dec - 2013]

4.60) What is the function of non – return valve in a reciprocating pump? [AU, May / June - 2012] 4.61) Distinguish between centrifugal pump and reciprocating pump. [AU, Nov / Dec – 2005, 2012] 4.62) Mention the significance of 'back leakage'.

[AU, Nov / Dec - 2013]

4.63) Define slip of a reciprocating pump. What is negative slip? When does negative slip occur? 4.64) Define slip of reciprocating pump.

[AU, April / May - 2010, Nov / Dec - 2012]

4.65) When does negative slip occur?

[AU, Nov / Dec - 2008]

4.66) What is negative slip in a reciprocating pump? What are the causes for it? [AU, May / June - 2013] 4.67) Define slip of a pump. When does negative slip occur?

[AU, Nov / Dec - 2003]



4.68) Define slip and percentage of slip of a reciprocating pump. [AU, Nov / Dec – 2008, 2010] 4.69) Define slip, negative slip in reciprocating pump. 4.70) Define slip and percentage slip.


4.71) What is the % of slip in reciprocating pump?

[AU, May / June– 2012]

4.72) Discuss – slip and volumetric efficiency.


4.73) Define slip in reciprocating machines.

[AU, Nov / Dec - 2011]

4.74) Distinguish between pumps in series and pumps in parallel. [AU, April / May - 2005] 4.75) What is percentage slip in reciprocating pump?

[AU, Nov / Dec - 2006]

4.76) Can actual discharge be greater than theoretical discharge in a reciprocating pump?

[AU, Nov / Dec - 2009]

4.77) Which factors determine the maximum speed of reciprocating pump? [AU, Nov / Dec - 2009] 4.78) What factors govern the speed of reciprocating pump? [AU, May / June - 2012] 4.79) Define co-efficient of discharge. 4.80) Brief on acceleration head.

[AU, Nov / Dec - 2011]

4.81) Define rotary pump. 4.82) What are rotary pumps? Give examples


4.83) What is a rotary pump? Give its classification.


4.84) Define gear pump. 4.85) What is an air vessel? 4.86) What is the function of air vessel? [AU, Nov / Dec – 2008, May / June - 2009, April / May - 2010] 4.87) What is an air vessel in reciprocating pump?

[AU, May / June - 2006]

4.88) Mention the working principle of an Air-vessel.


4.89) What is an air vessel? List the objectives that would be fulfilled by the use of air vessels. 4.90) What is an air vessel? What are its uses?


4.91) What are the uses of air vessels?

[AU, May / June - 2014]

4.92) What are the advantages of air vessel?

[AU, May / June - 2013]



4.93) State the advantages of fitting air vessels in reciprocating pumps. [AU, May / June - 2009] 4.94) Define indicator diagram. State its uses.


4.95) What is indicator diagram?

[AU, May / June - 2009]

4.96) Draw the ideal indicator diagram.


4.97) Write down the formula for discharge, work done and power required for a double acting reciprocating pump. 4.98) What is the main difference between a single acting and double acting reciprocating pump? 4.99) Give the types of rotary pumps. 4.100) What is the formula for work done by a reciprocating pump? 4.101) Give the formula for discharge through a double acting reciprocating pump. 4.102) A single acting reciprocating pump, running at 50rpm. The diameter of piston = 20cm and length = 40cm. Find the theoretical discharge of the pump. [AU, April / May - 2011] 4.103) A centrifugal pump delivers 20 litres/s of water against a head of 850 mm at 900 rpm. Find the specific speed of pump.


4.104) The following data refer to a centrifugal pump which is designed to run at 1500 rpm. D1 = 100 mm, D2 = 300 mm, B1 = 50 mm, B2 = 20 mm, Vf1= 3 m/s. Find the velocity of flow at outlet.


4.105) A pump is to discharge 0.82 m3/s at a head of 42 m when running at 300 rpm. What type of pump will be required?

[AU, Nov / Dec - 2011]

PART - B 4.106) Draw typical velocity triangles for fluid motion along a series of moving curve vanes and derive Euler’s equation of energy transfer.

[AU, Nov / Dec - 2009]

4.107) Explain the construction and working of a centrifugal pump with a neat sketch. 4.108) Explain the operation of centrifugal pump with the help of a neat sketch. Write short notes on different types of casing used in centrifugal pumps. [AU, May / June - 2007] 4.109) What is the role of volute chamber of a centrifugal pump? Define manometric head.

[AU, Nov / Dec - 2009]



4.110) Sketch and briefly describe the volute diffusion type pumps. What function is served by volute chamber in a centrifugal pump?

[AU, May / June - 2012]

4.111) Compare the advantages and disadvantages of centrifugal, submersible and jet pumps.


4.112) What is priming in a centrifugal pump? Why is it necessary? [AU, Nov / Dec - 2005] 4.113) Obtain the expression for work done by impeller of a centrifugal pump on water per second per unit weight of water.


4.114) Describe multi-stage pump with impeller in series and impellers in parallel. [AU, May / June - 2014] 4.115) Define the manometric efficiency of a centrifugal pump? [AU, Nov / Dec - 2006] 4.116) Define cavitation and discuss its causes, effects and prevention. [AU, April / May - 2008] 4.117) Define cavitation. What are the effects of cavitation? Give the necessary precaution against cavitation.

[AU, May / June – 2009, 2014]

4.118) Define cavitation and explain the various effects of cavitation. [AU, April / May - 2011] 4.119) Draw the velocity triangle for a centrifugal pump and obtain the expression for the work done.


4.120) What is specific speed of pump? [AU, April / May – 2004, May / June - 2009] 4.121) Define speed of a centrifugal pump. How does it differ from that of turbine? [AU, May / June– 2007, 2012] 4.122) State the expression for the specific speed of a pump. What is its use? [AU, Nov / Dec – 2007, 2012] 4.123) What do you understand by characteristics curves of a centrifugal pump? Explain them with neat sketches.

[AU, Nov / Dec - 2008]

4.124) Explain in detail about the performance curves for pumps and turbines. [AU, April / May - 2011] 4.125) Determine the minimum speed for starting a centrifugal pump. [AU, Nov / Dec - 2009] CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 64


4.126) Explain briefly the following efficiencies of a centrifugal pump (i) Manometric efficiency (ii) Volumetric efficiency

[AU, May / June - 2014]

4.127) Discuss - characteristics of centrifugal pump at constant speed. [AU, Nov / Dec - 2013] 4.128) Explain the characteristics curves of a centrifugal pump. [AU, Nov / Dec - 2009] 4.129) Discuss on the performance characteristics of centrifugal pumps. [AU, Nov / Dec - 2014] 4.130) Explain about the performance characteristics of centrifugal pumps. [AU, Nov / Dec - 2014] 4.131) Define specific speed of a centrifugal pump. Derive expression for the same in the terms of head ‘H’, discharge ‘Q’ and speed ‘N’

[AU, May / June - 2007]

4.132) Enumerate the losses that occur during the operation of the centrifugal pump. [AU, May / June - 2009] 4.133) Distinguish between roto dynamic pump and positive displacement pump with simple sketch.


4.134) How rotary pumps are classified. Explain the working principles of any one type of rotary pump with the aid of a neat sketch. [AU, Nov / Dec – 2008, May / June– 2012] 4.135) Discuss the working of rotary positive displacement pumps. [AU, April / May - 2011] 4.136) Discuss in detail about rotary positive displacement pumps. [AU, Nov / Dec - 2011] 4.137) With neat sketches, discuss about the rotary positive displacement pump. [AU, Nov / Dec - 2013] 4.138) With an example, explain in detail the working principle and construction of rotary pumps with neat diagram.

[AU, May / June - 2012]

4.139) Classify pumps. Explain the working of double acting reciprocating pump with a neat diagram. 4.140) Discuss on the cascade theory.

[AU, Nov / Dec - 2009, April / May - 2010] [AU, Nov / Dec - 2014]

4.141) Describe the working and principles of a reciprocating pump. [AU, Nov / Dec – 2005, April / May - 2011] CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 65


4.142) What is a reciprocating pump? Describe the principle and working of a reciprocating pump with a neat sketch. 4.143) Draw a neat sketch of reciprocating pumps. List the components and briefly explain their functions.

[AU, Nov / Dec - 2003]

4.144) Describe the principle and working of a reciprocating pump with a neat sketch. [AU, Nov / Dec - 2008] 4.145) Explain the working principle of reciprocating pump with neat sketch. [AU, Nov / Dec - 2008] 4.146) Explain the working principle of a reciprocating pump with neat diagram in detail and state its advantages and disadvantages over centrifugal pump. [AU, May / June - 2012] 4.147) Explain with a neat sketch the working of single – acting reciprocating pump. Also obtain the expression for weight of water delivers by the pump per second. [AU, April / May - 2015] 4.148) With a neat sketch explain the working of double acting reciprocating pump with its performance characteristics.

[AU, Nov / Dec - 2011]

4.149) Derive an expression for acceleration head developed in a reciprocating pump. 4.150) Explain the working principle of single and double acting reciprocating pumps with neat diagram in detail. Also explain the effects of inertia pressure and friction on the performance of the pump using indicator diagrams with and without air vessel.

[AU, Nov / Dec - 2010]

4.151) Sketch and describe the working principle of double acting reciprocating pump with indicator diagram.

[AU, Nov / Dec - 2009]

4.152) Differentiate between single acting and double acting pump. [AU, Nov / Dec - 2009] 4.153) Discuss on the following: Working of double acting pump, indicator diagram, acceleration head, friction head.

[AU, Nov / Dec - 2013]

4.154) Define indicator diagram. Prove that the area of the indicator diagram is proportional to the work done by the reciprocating pump. [AU, May / June - 2014] 4.155) Prove that work done by the pump is proportional to the area of the indicator diagram.

[AU, May / June - 2009]



4.156) Show that the work done by a reciprocating pump is equal to the area of the indicator diagram.


4.157) Write briefly on the following.  Rotary pumps and their classifications.  Indicator diagram for reciprocating pump.


4.158) Define slip, percentage slip and negative slip of a reciprocating pump. [AU, May / June - 2009] 4.159) Define: slope, % of slip and negative slop with respect to reciprocating pump. [AU, May / June - 2009] 4.160) Define % of slip and indicator diagram, with respect to reciprocating pump. [AU, May / June - 2007] 4.161) What is % of slip in reciprocating pump?


4.162) What is an air vessel? Describe the function of the air vessel for reciprocating pumps. 4.163) What is an air vessel? What are the uses/advantages of fitting air vessel in a reciprocating pump?

[AU, May / June - 2007]

4.164) What is air vessel and write the expression for work done by reciprocating pump fitted with air vessel.


4.165) What is an air vessel? Derive the expression for the percentage work saved by using an air vessel.

[AU, Nov / Dec - 2012]

4.166) What is an air vessel? What are the advantages of fitting air vessel in a reciprocating pump?

[AU, Nov / Dec - 2007]

4.167) Calculate the work saved by fitting an air vessel for a double acting single cylinder reciprocating pump.


4.168) Describe the function of the air vessel. [AU, Nov / Dec - 2008, May / June– 2012] 4.169) What are the functions of air vessel in a positive displacement pump? [AU, Nov / Dec - 2009] 4.170) Explain in detail about the concept of pressure vessels with its characteristics. [AU, Nov / Dec - 2014]



4.171) Determine the % of work saved in one cycle when air vessel is provided on the delivery side of a single cylinder single acting reciprocating pump. [AU, May / June - 2012] 4.172) Explain the various types of rotary pumps with its construction details and its applications.

[AU, Nov / Dec - 2014]

4.173) Explain the working principle of Gear pump with neat sketch. [AU, Nov / Dec - 2008] 4.174) With a neat sketch, explain the working of a gear pump. [AU, Nov / Dec - 2010] 4.175) Explain the construction and working of the following rotary pumps with neat sketches. (a)

Gear pump

(b) Vane pump [AU, Nov / Dec – 2007, May / June - 2014]

4.176) Explain in detail the working principle and construction of rotary pumps with neat sketch.

[AU, May / June - 2013]

4.177) Explain the working of the following pumps with the help of neat sketches and mention two applications of each. (i) External gear pump

(ii) Lobe pump

(iii) Vane pump (iv) Screw pump. [AU, April / May - 2010]

4.178) Write a short note on following types of rotary pumps: (i) Internal gear pump

(ii) External gear pump

(iii) Vane pump

(iv) Root pump


4.179) Discuss the working of Lobe and vane pumps.

[AU, Nov / Dec - 2014]

4.180) Explain in detail the working of a gear pump with a neat sketch. [AU, April / May, Nov / Dec - 2011] 4.181) Explain the working of vane pump with neat diagram. [AU, May / June - 2012] 4.182) Discuss briefly the working principle of vane pump with a schematic diagram. [AU, Nov / Dec - 2012] 4.183) Explain the working principle of screw pump and gear pump with neat diagram in detail.

[AU, Nov / Dec - 2010]

4.184) Draw and explain the indicator diagram for a reciprocating pump including the effect of friction and acceleration. CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 68


4.185) Derive an expression for the percentage work saved by using an air vessel with (i) single acting and

(ii) double acting reciprocating pump.

PROBLEMS 4.186) A centrifugal pump is provided at a height of 5m above the sump water level and the outlet of the delivery pipe is 10m above the sump. The vane angle at outlet is 50°. The velocity of flow through the impeller is constant at 1.6m/s. Find : [AU, Nov / Dec - 2008]  The pressure head at inlet to the wheel  The pressure head at outlet of the wheel. Assume that the velocity of water in the pipes is equal to the velocity of flow through the impeller. Ignore losses 4.187) The following observations are made while conducting a performance test on centrifugal pump. Determine the overall efficiency of the pump. Discharge of water is 1.8m3/s. Diameter of suction and delivery pipe are 15cm and 10cm respectively. The suction and delivery gauge readings are 25cm of mercury and 175 kN/m2 respectively. The height of delivery gauge over suction gauge is 0.5m. The output of driving motor is 9.555kW.


4.188) The head — discharge characteristics of a centrifugal pump is given below.

The pump delivers fresh water through a 500 m long, 15 cm diameter pipe line having friction coefficient of f = 0.025. The static lift is 15 m. Neglecting minor losses in the pipe flow, find (i) the discharge of the pump under the above conditions (ii) driving power of the pump motor. Assume a pump efficiency of 72%. [AU, Nov / Dec - 2010] 4.189) The internal and external diameters of the impeller of a centrifugal pump are 200mm and 400mm respectively. The pump is running at 1200 rpm. The vane angles of the impeller at inlet and outlet are 20°and 30° respectively. The water enters the



impeller radically and the velocity of flow is constant. Determine the work done by the impeller per unit weight of water.

[AU, Nov / Dec – 2008, 2012]

4.190) The internal and external diameter of an impeller of a centrifugal pump which is running at 1000 r.p.m, are 200 mm and 400 mm respectively. The discharge through pump is 0.04 m3/s and velocity of flow is constant and equal to 2.0 d s . The diameters of the suction and delivery pipes are 150mm and 100mm respectively and suction and delivery heads are 6 m (abs.) and 30 m (abs.) of water respectively. If the outlet vane angle is 45º and power required to drive the pump is 16.186 kW, determine: (i) Vane angle of the impeller at inlet, (ii) The overall efficiency of the pump, and (iii) Manometric efficiency of the pump.

[AU, May / June - 2013]

4.191) A centrifugal pump with backward-curved blades has the following measured performance when tested with water at 20°C :

Estimate the best efficiency point and the maximum efficiency. Also, estimate the most efficient flow rate, and the resulting head and brake power, if the diameter is doubled and the rotation speed is increased by 50%.

[AU, Nov / Dec - 2011]

4.192) The impeller of a centrifugal pump is 300mm outside diameter and 150mm inside diameter. The impeller vane angles are 30° and 25° at the inner and outer peripheries respectively and the speed is 1450rpm. The velocity of the flow through the impeller is constant. Find the work done by the impeller per N of water. [AU, Nov / Dec - 2009] 4.193) A centrifugal pump running at 800rpm is working against a total head of 20.2m. The external diameter of impeller is 480mm and the outlet width is 60mm. If the vane angle at outlet is 40° and manometric efficiency is 70%, determine  Flow velocity at outlet  Absolute velocity of water leaving the vane  Angle made by the absolute velocity at outlet with direction of motion



 Rate of flow through the pump [AU, Nov / Dec - 2009, April / May - 2010] 4.194) A centrifugal pump running at 1440rpm has an impeller diameter of 0.42m. The backward curved blade outlet angle is 35° to the tangent. The flow velocity at outlet is 10m/s. Determine the static head through which water will be lifted. In case a diffuser reduces the outlet velocity to 40% of the velocity at the impeller outlet, what will increase in the static head?


4.195) The dimensionless specific speed of a centrifugal pump is 0.06. Static head is 32 m. Flow rate is 50 1/s. The suction and delivery pipes are each of diameter 15 cm. The friction factor is 0.02. Total length is 60 m other losses equal 4 times the velocity head in the pipe. The vanes are forward curved at 120º. The width is one tenth of the diameter. There is a 7% reduction in flow area due to the blade thickness. The manometric efficiency is 80%. Determine the impeller diameter if inlet is radial. [AU, Nov / Dec - 2014] 4.196) A centrifugal pump running at 1200rpm has a discharge of 13m3/min. The pump has manometric efficiency of 85% and working against a head of 22m. The impeller has an outlet vane angle of 40º. If the velocity of the flow at the outlet is 2.6m/s. Determine the diameter of the impeller and width of the impeller at the outlet. [AU, Nov / Dec - 2012] 4.197) A centrifugal pump running at 920 rpm and delivering 0.32 m3/s of water against a head of 28 m, the flow velocity being 3 m/s. If the manometric efficiency is 80% determine the diameter and width of the impeller. The blade angle at outlet is 25º. [AU, Nov / Dec - 2014] 4.198) A centrifugal pump is to discharge 0.12 m3/s at a speed of 1400rpm with a head of 30m. The impeller diameter is 275mm, its width at outlet is 50mm. The manometric efficiency is 78%. Calculate the vane angle at the outer periphery of the impeller.


4.199) A Centrifugal pump impeller runs at 80 rpm and has outlet vane angle of 60°. The velocity of flow is 2.5 m/s throughout and diameter of the impeller at exit is twice that at inlet. If the manometric head is 20 m and the manometric efficiency is 75 percent, determine the diameter of the impeller at the exit and the inlet vane angle. [AU, Nov / Dec - 2011] CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 71


4.200) A pump has to supply water which is at 70°C water at 90 m3/min and 1800 rpm. Find the type of pump needed, the power required, and the impeller diameter if the required pressure rise for one stage is 200 kPa; and 1250 kPa. [AU, Nov / Dec - 2011] 4.201) A centrifugal pump with an impeller diameter of 0.4 m runs at 1450 rpm. The angle at outlet of the backward curved vane is 25º with tangent. The flow velocity remains constant at 3 m/s. If the manometric efficiency is 84% determine the fraction of the kinetic energy at outlet recovered as static head. [AU, Nov / Dec - 2013] 4.202) The impeller of a centrifugal pump is 300mm in diameter and having a width of 50mm at the periphery. It has blades whose tip angles are inclined backwards at 60° from the radius. The pump delivers 17m3/min of water and the impeller rotates at 1000rpm. Assuming that the pump is designed to admit liquid radially, calculate  Speed and direction of water as it leaves impeller  Torque exerted by the impeller on water  Shaft power required  Lift of the pump Assume the mechanical efficiency = 95% and the hydraulic efficiency = 75% [AU, May / June – 2007, 2012] 4.203) A centrifugal pump discharges 2000 l/s of water per second developing a head of 20m when running at 300rpm. The impeller diameter at the outlet ant the outflow velocity is 1.5m and 3m/s respectively. It vanes are set back at an angle of 30° at the outlet, determine  Manometric efficiency  Power required by the pump If inner diameter is 750mm, find the minimum speed to start the pump. [AU, May / June - 2012] 4.204) The impeller of a centrifugal pump has an external diameter of 450mm and internal diameter of 200mm and it runs at 1440rpm. Assuming a constant radial flow through the impeller at 2.5m/s and the vanes at exit are set back at an angle of 25°. Determine CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 72


 Inlet vane angle  The angle, absolute velocity of water at exit makes with the tangent and  The work done per N of water.

[AU, Nov / Dec - 2006]

4.205) A centrifugal pump has 30 cm and 60 cm diameters at inlet and outlet. The inlet and outlet vane angles are 30° and 45° respectively. Water enters at a velocity of 2.5 m/s radially. Find the speed of impeller in rpm and the power of the pump if the flow is 0.2 m3/s.


4.206) A centrifugal pump has an impeller diameter 500mm in diameter running at 40 rpm. The discharge at the inlet is entirely radial. The velocity of the flow at outlet is 1m/s. The vanes are curved backwards at outlet at 30º to the wheel tangent. If the discharge of the pump is 0.14m3/s, calculate the impeller power and the torque on the shaft.


4.207) A centrifugal pump delivers water against a net head of 14.5 meters and a design speed of 1000 rpm. The vanes are curved back to an angle of 30° with the periphery. The impeller diameter is 300 mm and outlet width 50 mm. Determine the discharge of the pump if the manometric efficiency is 95%.

[AU, Nov / Dec - 2007]

4.208) A centrifugal pump with 1.2m diameter runs at 200rpm and discharge 1880 litres/s, against an average lift of 6m. The angle which the vanes make at exit with the tangent to the impeller is 26° and the radial velocity of the flow is 2.5m/s. Find the manometric efficiency and at least speed to start the pump against the head of 6m. Assume the inner diameter of the impeller as 0.6m.

[AU, May / June - 2009]

4.209) A single stage centrifugal pump with impeller diameter of 30cm rotates at 2000rpm and lifts 3m3 of water per second to a height of 30m with an efficiency of 75%. Find the number of stages and diameter of each impeller of a similar multistage pump to lift 5m3 of water per second to a height of 300m when rotating at 1500rpm. [AU, May / June - 2009] 4.210) A centrifugal pump having an outer diameter equal to two times the inner diameter and running at 1000 rpm. Works against a total head of 40m. The velocity of flow through the impeller is constant and equal to 2.5m/sec. The vanes are set back at an angle of 40° at outlet. If the outer diameter of the impeller is 500mm and width at outlet is 50mm, determine the CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 73


i) Vane angle at inlet ii) Manometric efficiency iii) Work done by impeller on water per second. 4.211) The outer diameter of an impeller of a centrifugal pump is 400mm and outlet width is 50mm. The pump is running at 800rpm and working against a total head of 15m. The vanes angle at outlet is 40° and the manometric efficiency is 75%. Determine the velocity of flow at inlet, velocity of water leaving the vane, angle made by the absolute velocity at outlet with direction of motion at outlet, and the [AU, Nov / Dec – 2007, 2012]

discharge.

4.212) The centrifugal pump has the following characteristic. Outer diameter of impeller = 800mm; width of the impeller vane at outlet = 100mm; angle of the impeller vanes at outlet = 40°. The impeller runs at 550 rpm and delivers 0.98 m 3/s under an effective head of 35m. A 500 kW motor is used to drive the pump. Determine the manometric, mechanical and overall efficiencies of the pump. Assume waters enter impeller vanes radially at inlet. [AU, April / May – 2003, 2010] 4.213) A centrifugal pump delivers water against a net head of 14.5m and design speed of 1000rpm. The vanes are curved back angle of 30° with the periphery. The impeller diameter is 300mm and the outlet width 50mm. Determine the discharge of the pump if manometric efficiency is 95%.

[AU, Nov / Dec - 2007]

4.214) A centrifugal pump, in which water enters radially, delivers water to a head of 165m. The impeller has a diameter of 360mm and width 180mm at inlet and the corresponding dimensions at the outlet are 720mm and 90mm respectively. Its rotational speed is 1200 rpm. The blades are curved backward at 30° to the tangent at exit and discharge is 0.389 m3/s. Determine

[AU, May / June - 2007]

 Theoretical head developed  Manometric efficiency  Pressure rise across the impeller assuming losses equal to 12% of velocity head at exit.  Pressure rise and the loss of head in the volute casing  The vane angle at inlet and



 Power required to drive the pump assuming an overall efficiency of 70%. What would be the corresponding mechanical efficiency? 4.215) Compute the overall efficiency of a centrifugal pump from the following test data. Suction gauge reading = 27.5kPa(vac) and delivery gauge reading = 152(gauge) height of the delivery gauge over suction gauge is 0.4m, discharge is 2100mm. Diameter of the suction pipe is 15cm and diameter of delivery pipe is 10cm. the motor power = 12MHP and fluid water.

[AU, Nov / Dec - 2009]

4.216) A centrifugal pump id to discharge 0.118m3/s at a speed of 1450rpm against a head of 25m. The impeller diameter is 25cm, its width at outlet is 5cm and manometric efficiency is 75%. Determine the vane angle at the outer periphery of the impeller and draw its velocity triangle.


4.217) A centrifugal pump delivers 0.18 m3/s of water against a head of 12 m and runs at 620 rpm. The outer and inner diameters of impeller are 0.4 m and 0.2 m respectively and the vanes are bent back at 38º C to the tangent at exit. If the area of flow remains at 0.1 m2 from inlet to outlet, calculate manometric efficiency, vane angle at inlet and loss of head at inlet to impeller when the discharge is reduced by 40% without changing the speed.

[AU, Nov / Dec - 2014]

4.218) A centrifugal pump delivers 400 litres/s of water to a height of 20m through a pipe diameter 15cm and length 100m. The pump has an overall efficiency of 70% and the friction coefficient is 0.15. Determine the power required to drive the pump. [AU, Nov / Dec - 2010] 4.219) A radial flow impeller has a diameter 25 cm and width 7.5 cm at exit. It delivers 120 lps of water against a head of 24 m at 1440 rpm. Assuming that the vanes block the flow area by5 percent and the hydraulic efficiency as 0.8, estimate the vane angle at exit. Also calculate the torque exerted on the driving shaft if the mechanical efficiency is 95 percent. 4.220) A single acting reciprocating pump, running at 50rpm, delivers 0.01m3/sec of water. The diameter of the piston is 200mm and stroke length 400mm. Determine the  theoretical discharge of the pump  co-efficient of discharge



 slip and the percentage slip of the pump [AU, Nov / Dec – 2007, 2008, May / June– 2012] 4.221) For a single acting reciprocating pump, piston diameter is 150 mm, stroke length is 300 mm, and rotational speed is 50 r.p.m. The pump is required to lift water to a height of 18 m. Determine the theoretical discharge. If the actual discharge is 4.0 lit/sec, and the mechanical efficiency is 80% determine the volumetric efficiency, slip, theoretical power and the actual power required.

[AU, Nov / Dec - 2010]

4.222) A single – acting reciprocating pump has a plunger diameter of 250mm and stroke of 450mm. It is driven at 60rpm and undergoes SHM. The length and diameter of the delivery pipe are 60m and 100mm respectively. Determine the power saved in overcoming the friction in the delivery pipe, due to fitting of an air vessel on the delivery side of the pump. Assume the friction factor f = 0.01 the pipe friction formula hf=(flv2/2gd

)

[AU, Nov / Dec - 2007]

4.223) A single acting reciprocating pump is to raise a liquid of density 1200kg/m3 through a vertical height of 11.5m, from 2.5m below pump axis to 9m above it. The plunger which moves in SHM, has diameter 125mm and stroke 225mm. The suction and delivery side pipes are 75mm diameter and 3.5 and 13.5m long, respectively. There is a large air vessel fitted on the delivery pipe near to the pump axis. But there is no air vessel on the suction pipe. If separation takes place at 8.829 N/cm2 below atmospheric pressure, find the maximum speed at which the pump can run without separation taking place and the power required to drive the pump. Assume there is no slip in the pump and f = 0.08 the pipe friction formula hf=(flv2/2gd) [AU, Nov / Dec - 2007] 4.224) A single acting reciprocating pump has a plunger of diameter 30 cm and stroke of 20 cm. If the speed of the pumps is 30 rpm and it delivers to6.5 lit/s of water, find the coefficient of discharge and the percentage slip of the pump. [AU, April / May - 2011] 4.225) The piston area of a single acting reciprocating pump 0.15 m2 and stroke is 30 cm. The water is lifted through a total head of 15 m. The area of delivery pipe is 0.03 m2. If the pump is running at 50rpm, find the percentage slip, coefficient of discharge and the power required to drive the pump. The actual discharge is 35 litres per second. Take mechanical efficiency is 0.85.

[AU, Nov / Dec - 2011]



4.226) A single acting reciprocating pump has a diameter (piston) of 150mm and stroke length 350 mm. The center of the pump is 3.5 m above the water surface in the sump and 22 m below the delivery water level. Both the suction and delivery pipes have the same diameter of 100 mm and are 5 m and 30 m long respectively. If the pump is working at 30 rpm determine the pressure heads on the piston at the beginning, middle and end of both suction and delivery strokes. [AU, Nov / Dec - 2011] 4.227) Calculate the rate of flow in and out of the air vessel on the delivery side in a single acting reciprocating pump of 220 mm bore and 330 mm stroke running at 50 rpm. Also find the angle of crank rotation at which there is no flow into or out of the air vessel.

[AU, Nov / Dec - 2011]

4.228) In a single acting reciprocating pump the bore and stroke are 100 and 150 mm. respectively. The static head requirements are 4 m suction and 18 m delivery. If the pressure at the end of delivery is atmospheric calculate the operating speed. The diameter of the delivery pipe is 75 mm and the length of the delivery pipe is 24 m. Determine the acceleration head at θ = 33 from the start of delivery. [AU, Nov / Dec - 2011] 4.229) A double - acting reciprocating pump, running at 40rpm is discharging 1m3 of water per minute. The pump has a stroke of 400mm. The diameter of the piston is 200mm. The delivery and suction heads are 20m and 5m respectively. Find the slip of the pump and the power required to drive the pump. 4.230) The cylinder bore diameter of a single acting reciprocating pump is150mm and its stroke length is 300mm. The pump runs at 50 rpm and lifts water through a height of 25m. The delivery pipe is 22m long and 100mm in diameter. Find the theoretical discharge and the theoretical power required to run the pump. If the actual discharge is 4.2 litres/s. Find the percentage of slip. [AU, April / May - 2004, Nov / Dec - 2005, 2012] 4.231) The diameter and stroke of a single acting reciprocating pump are 120 mm and 300 mm respectively. The water is lifted by a pump through a total head of 25 m. The diameter and length of delivery pipe are 100 mm and 20 m. respectively. find out:



(i)

Theoretical discharge and theoretical power required to run the pump if its speed is60 rpm.

(ii)

Percentage slip, if the actual discharge is 2.95 1/s and

(iii) The acceleration head at the beginning and middle of the delivery stroke. [AU, April / May - 2010] 4.232) The length and diameter of a suction pipe of a single acting reciprocating pump are 5 m and 10 cm respectively. The pump has a plunger of diameter 150 mm and a stroke length of 300 mm. The center of the pump is 4 m above the water surface in the sump. The atmospheric pressure head is 10.3m of water and the pump runs at 40 rpm. Determine the i) Pressure head due to acceleration at the beginning of the suction stroke. ii) Maximum pressure head due to acceleration. iii) Pressure head in the cylinder at the beginning and at the end of the stroke. 4.233) Consider a double acting reciprocating pump running at 40rpm. The pump delivers 1m3/min of water. The piston diameter is 20cm and the stroke length is 40cm. The delivery and the suctions heads are 20m and 5m respectively. Calculate the % slip and the power required to drive the pump.

[AU, Nov / Dec - 2010]

4.234) The diameter and the stroke of a single acting reciprocating pump are 200mm and 400mm respectively, the pump runs at 60 rpm and lifts 12 litres of water per second through a height of 25m. The delivery pipe is 20m long and 150mm in diameter. Find (i) theoretical power required to run the pump (ii) % of slip and (iii) acceleration head at the beginning and middle of the delivery stroke. [AU, Nov / Dec - 2003] 4.235) The diameter and stroke length of a single acting reciprocating pump are 75 mm and 150 mm respectively. Supply of water to the pump is from a sump 3 m below the pump through a pipe of 5 m long and 40 mm in diameter. The pump delivers water to a tank located at 12 m above the pump through a pipe 30 mm in diameter and 15 m long. Assuming that a separation of flow occurs at 75 kN/m2 (below the atmospheric pressure), find the maximum speed at which the pump may be operated without any separation.

[AU, May / June - 2007]



4.236) The cylinder of a single- acting reciprocating pump is 15 cm in diameter and 30 cm in stroke. The pump is running at 30 r.p.m. and discharge water to a height of 12 m. The diameter and length of the delivery pipe are 10 cm and 30 m respectively. If a large air vessel is fitted in the delivery pipe at a distance of 2 m from the centre of the pump, find the pressure head in the cylinder. (i) At the beginning of the delivery stroke, and (ii) In the middle of the delivery stroke. Take f = 0.01. [AU, May / June - 2013] 4.237) A double acting pump with 35 cm bore and 40 cm stroke runs at 60 strokes per minute. The suction pipe is 10m long and delivery pipe is 200m long. The diameter of the delivery pipe is 15 cm. The pump is situated at a height of 2.5 m above the sump; the outlet of the delivery pipe is 70 m above the pump. Calculate the diameter of the suction pipe for the condition that separation is avoided. Assume separation to occur at an absolute pressure head is 2.5m of water. Find the Horsepower required to drive the pump neglecting all losses other than friction in the pipes assuming friction factor f as 0.02.

[AU, Nov / Dec - 2008]

4.238) A double acting reciprocating pump is running at 30rpm. Its bore and stroke are 250mm and 400mm respectively. The pump lift water from sump 3.8m below and delivers it to a tank located at 65m above the axis of the pump. The lengths of suction and delivery pipes are 6m and 150m respectively. The diameter of the delivery pipe is 100mm. if an air vessel of adequate capacity has been fitted on the delivery side of the pump, determine  The minimum diameter of the suction pipe to prevent separation of flow, assuming the minimum head to prevent occurrence of separation is 2.5m 4.239) The maximum gross head against which the pump has to work and the corresponding power of motor. Assume the mechanical efficiency = 78% and slip = 1.5%; Hatm = 10m; F=0.012.

[AU, May / June - 2007]

4.240) The plunger diameter and the stroke length of a single acting reciprocating pump are 300mm and 500mm respectively. The speed of the pumps is 60rpm. The diameter and length of the delivery pipe are 150mm and 60m respectively. If the pump is equipped with an air vessel at delivery side at the center line of the pump, find the power saved in overcoming friction in delivery pipe. Assume Darcy’s CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 79


friction factor as 0.04, and plunger undergoes a simple harmonic motion. [AU, May / June - 2009] 4.241) The plunger diameter and the stroke length of a single acting reciprocating pump are 300mm and 500mm respectively. The speed of the pumps is 50rpm. The diameter and length of the delivery pipe are 150mm and 55m respectively. If the pump is equipped with an air vessel at delivery side at the center line of the pump, find the power saved in overcoming friction in delivery pipe. Assume Darcy’s friction factor as 0.01.

[AU, May / June - 2014]

4.242) Determine the maximum speed in rpm at which a single acting reciprocating pump without an air vessel of the following details can be operated without causing separation at any stage during the operation of the pump. Compute the discharge at this speed. What would be the speed and discharge if air vessel is fitted near the pump on the suction side? The fluid is water. Assume f= 0.01 for the pipes. Diameter of plunger = 15cm, stroke = 22.5cm, Suction pipe diameter = 10cm, length = 50m, static suction head = 4m, static delivery head = 25m, atmospheric pressure = 101kPa and vapor pressure of water = 25.5kPa(abs)


4.243) The diameter and length of a single acting reciprocating pump are 100mm and 200mm respectively. The pump is used to deliver water to the tank 14m above the pump through a pipe of 30mm in diameter and 18m long by taking its supply from the sump 2m below the pump, through a pipe 40mm in diameter and 6m long. If separation occurs at 78.48kN/m2, below the atmospheric pressure find the maximum speed at which the pump can be operated without separation. Assume 1 atm pressure = 10.3m of water column and the plunger undergoes simple harmonic motion. [AU, May / June - 2009] 4.244) Determine the maximum operating speed in rpm and the maximum capacity in lps of a single acting reciprocating pump with the following details. Plunger diameter = 25cm, stroke = 50cm, suction pipe diameter = 15cm, length = 9cm, delivery pipe diameter = 10cm, length = 36cm, static suction head = 3m, static delivery head = 20m, atmospheric pressure = 76cm of mercury, vapour pressure of water = 25kPa.

[AU, Nov / Dec - 2009]

4.245) A reciprocating pump handling water with a bore of 110mm and stroke of 205mm runs at 38rpm. The delivery pipe is of 90mm diameter and 30m long. An air CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 80


vessel of sufficient volume is added at a distance of 2.5m from the pump. Determine the acceleration head with and without air vessel.


4.246) A single cylinder double acting reciprocating pump has a piston diameter of 300mm and stroke length of 400mm. When the pump runs at 45rpm, it discharges 0.039m3/s under a total head of 15m. What will be the volumetric efficiency, work done per second and power required if the mechanical efficiency of the pump is 75%.

[AU, May / June - 2012]

4.247) The indicator diagram of a single acting reciprocating pump gives effective delivery head of 5m and 23m with crank at inner and outer dead center respectively. What is the static delivery head of reciprocating pump?




UNIT – V – TURBINES PART - A 5.1) Define turbo machines. 5.2) Define turbine. 5.3) What is a pump turbine? Is it the same as turbine pump? [AU, April / May - 2015] 5.4) Classify fluid machines.


5.5) Give the classification of turbines. 5.6) How are hydraulic turbines classified [AU, May / June - 2009, 2014, Nov / Dec - 2009 April / May - 2011] 5.7) What are high head turbines? Give example.

[AU, Nov / Dec - 2009]

5.8) State the principles on which turbo-machines are based.

[AU, Nov / Dec - 2010]

5.9) Explain specific speed.

[AU, Nov / Dec - 2005]

5.10) Define specific speed.

[AU, Nov / Dec - 2009]

5.11) Define specific speed of a turbine.

[AU, Nov / Dec – 2003,

2008, 2009, May / June–2007, 2009, April / May –2010, 2011] 5.12) Define specific speed of a turbine. What is its usefulness? [AU, Nov / Dec - 2007] 5.13) How is specific speed of a turbine defined?

[AU, May / June - 2006]

5.14) What is meant by specific speed of a turbine?


5.15) Why not the specific speed of a hydraulic turbine is calculated using watts, instead of metric horse power?


5.16) Write the equation for specific speed for pumps and also for turbine. [AU, Nov / Dec - 2012] 5.17) Define specific speed and unit speed of a turbine.


5.18) List the range of head for various turbines.


5.19) What is hydraulic turbine?

[AU, May / June - 2006]

5.20) State and concise on Euler turbine equation.

[AU, Nov / Dec - 2014]

5.21) Classify turbines according to flow.

[AU, Nov / Dec - 2005]

5.22) Define impulse turbine and give examples. 5.23) Explain the working of impulse turbine.


5.24) Define reaction turbine and give examples. 5.25) What is reaction turbine? Give examples




5.26) Differentiate between reaction turbine and impulse turbine. [AU, Nov / Dec - 2003, April / May - 2008, 2015, May / June - 2012] 5.27) What is a ‘breaking jet’ in Pelton wheel/turbine? [AU, May / June - 2007, Nov / Dec – 2007, 2012] 5.28) Draw velocity triangle diagram for Pelton wheel turbine. [AU, Nov / Dec - 2008, 2014] 5.29) Define tangential flow turbine. 5.30) Define radial flow - turbine. 5.31) Define axial flow turbine. 5.32) Define mixed flow turbine. 5.33) Define the flow ratio of reaction radial flow turbine.

[AU, Nov / Dec - 2012]

5.34) Draw a sketch of a Francis turbine and name its components. [AU, April / May - 2005] 5.35) List the main parts of Kaplan turbine.

[AU, Nov / Dec - 2012]

5.36) What is draft tube?

[AU, Nov / Dec - 2012]

5.37) What is a draft tube? Explain why it is necessary in reaction turbine. 5.38) What is draft tube? In which type of turbine is mostly used? [AU, Nov / Dec - 2003] 5.39) Write the function of draft tube in turbine outlet? [AU, April / May - 2005, 2008, Nov / Dec - 2011] 5.40) What is the function of draft tube? [AU, May / June– 2007, Nov / Dec - 2009] 5.41) What are the different types of draft tubes?

[AU, Nov / Dec - 2009]

5.42) Why does a Pelton wheel not possess any draft tube? [AU, May / June - 2012] 5.43) Mention the importance of Euler turbine equation.

[AU, Nov / Dec - 2011]

5.44) What are the different efficiencies of turbine to determine the characteristics of turbine?

[AU, May / June – 2012]

5.45) Define hydraulic efficiency of turbine 5.46) Define hydraulic efficiency and jet ratio of a Pelton wheel. [AU, Nov / Dec - 2010] 5.47) Define hydraulic efficiency and axial thrust of a roto-dynamic hydraulic machine. [AU, May / June - 2013] CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 83


5.48) What is meant by hydraulic efficiency of turbine? [AU, Nov / Dec – 2012, 2013] 5.49) Define hydraulic efficiency and overall efficiency of a turbine. [AU, Nov / Dec - 2012] 5.50) Define -volumetric efficiency of turbine.

[AU, Nov / Dec - 2014]

5.51) What are the different efficiencies of turbine to determine the characteristics of turbine?

[AU, Nov / Dec - 2006]

5.52) Define overall efficiency and plant efficiency of turbines. [AU, May / June– 2007, 2012] 5.53) Draw the characteristics curves of a turbine with head variation. [AU, April / May - 2005] 5.54) What is the difference between a turbine and a pump? [AU, Nov / Dec – 2010, May / June - 2012] 5.55) Differentiate between pumps and turbines. [AU, May / June, Nov / Dec – 2007, 2008] 5.56) A shaft transmits 150 Kw at 600 rpm. What is the torque in Newton –meters? [AU, April / May - 2011] 5.57) The mean velocity of the buckets of the Pelton wheel is 10 m/s. The jet supplies water at 0.7 m3/s at a head of 30 m. The jet is deflected through an angle of 160° by the bucket. Find the hydraulic efficiency. Take CV = 0.98. [AU, April / May - 2010] 5.58) A water turbine has a velocity of 8.5m/s at the entrance of draft tube and velocity of 2.2m/s at exit. The frictional loss is 0.15m and the tail race water is 4m below the entrance of draft tube. Calculate the pressure head at entrance. [AU, April / May - 2011] PART – B 5.59) Derive the general equation of turbo machines and draw the inlet and outlet triangles. 5.60) How will you classify the turbines?


5.61) Enumerate the differences between an impulse turbine and reaction turbine. [AU, April / May - 2015]



5.62) Describe briefly the function of the various main components of a Pelton wheel turbine with neat sketches. 5.63) Describe briefly the functions of various components of Pelton turbine with neat sketches.

[AU, Nov / Dec - 2008]

5.64) Explain the component parts and working of a Pelton wheel turbine. [AU, April / May - 2010] 5.65) Define and derive an expression for specific speed of a turbine. 5.66) Explain the terms unit power, unit speed and unit discharge with reference to a turbine. 5.67) Explain the hydraulic efficiency of a turbine.

[AU, Nov / Dec - 2009]

5.68) Sketch the velocity triangles at inlet and outlet of a Pelton wheel. 5.69) Draw inlet and outlet velocity triangles for a Pelton turbine and indicate the direction of various velocity components. Also obtain the expression for the work done per second by water on the runner of the Pelton wheel. [AU, April / May - 2015] 5.70) What is breaking jet in Pelton wheel turbine? [AU, April / May – 2004, Nov / Dec - 2005, May / June– 2012] 5.71) Differentiate Pelton wheel turbine with Francis turbine. [AU, April / May - 2005] 5.72) Distinguish between reaction turbine and impulse turbine. [AU, May / June - 2013] 5.73) Give the comparison between impulse and reaction turbine. [AU, Nov / Dec - 2005] 5.74) With the help of neat diagram explain the construction and working of a Pelton wheel turbine.

[AU, Nov / Dec - 2005]

5.75) With a neat sketch, explain the working of a Pelton wheel. [AU, April / May - 2008] 5.76) With a neat sketch, explain the working of a Pelton wheel. Also obtain the expression of the work done.

[AU, Nov / Dec - 2012]

5.77) Obtain an expression for power developed in a reaction turbine. [AU, Nov / Dec - 2011] 5.78) What is the condition for hydraulic efficiency of a Pelton wheel to be maximum? [AU, Nov / Dec - 2005] CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 85


5.79) Explain the construction and working of the following turbines with neat sketches. (i) Pelton wheel turbine (ii) Francis turbine (iii) Kaplan turbine 5.80) Compare radial flow and axial flow turbo machines. 5.81) Draw the inlet and outlet velocity triangles for an inward flow reaction turbine indicating the various components.

[AU, Nov / Dec - 2009]

5.82) Derive an expression for the maximum hydraulic efficiency of an impulse turbine. 5.83) Obtain an expression for the work done per second by water on the runner of a Pelton wheel. Hence derive an expression for maximum efficiency of the Pelton wheel giving the relationship between the jet speed and bucket speed. [AU, Nov / Dec - 2007] 5.84) Obtain the expression for the work done per second by water on the runner of a Pelton wheel and draw inlet and outlet velocity triangles for a Pelton turbine and indicates the direction of various velocities.

[AU, May / June - 2009]

5.85) Derive the velocity triangle for Pelton wheel and obtain the expression for the work done.


5.86) Sketch the velocity triangles at inlet and outlet of Pelton wheel. [AU, Nov / Dec - 2006] 5.87) Derive the expression for efficiency and work done for a Pelton wheel and draw the velocity triangles.

[AU, May / June - 2012]

5.88) Explain how the net head on the reaction turbine is increased with the use of draft tube.


5.89) Derive Euler’s equation of motion for turbines and obtain the components of energy transfer with a construction of velocity triangles. [AU, May / June - 2012] 5.90) An inward flow reaction turbine has inlet and outlet vane angles φ and Ф are both equal to 90°. If H = head of the machine, α = guide vane angle and C = ratio of velocity of flow at outlet and inlet, show that the peripheral velocity and hydraulic efficiency are given by

[AU, Nov / Dec - 2009]



5.91) Show that the hydraulic efficiency for a Francis turbine having velocity flow through runner as constant given by relation.


5.92) An inward flow reaction turbine discharges radially and the velocity of flow is constant, show that the hydraulic efficiency can be expressed by

Where α and θ are the guide and vane angles at inlet. 5.93) Write a short note on Governing of Turbines.


5.94) Classify hydraulic machines and give one example for each. [AU, Nov / Dec - 2008] 5.95) Explain the working principle of Kaplan turbine and derive the working proportion of its design.

[AU, Nov / Dec - 2008]

5.96) Draw a neat sketch of Kaplan turbine, name the parts and briefly explain the working.

[AU, May / June - 2007]

5.97) Draw a schematic diagram of a Kaplan turbine and explain its construction and Working.

[AU, May / June - 2014]

5.98) Explain with help of a diagram, the essential features of Kaplan turbine. [AU, Nov / Dec - 2009] 5.99) Draw a schematic diagram of a Kaplan turbine and explain briefly its construction and working. Obtain an expression for work done by the runner. [AU, Nov / Dec - 2011] 5.100) Discuss about construction details of Kaplan turbine with a neat sketch. [AU, Nov / Dec - 2014] 5.101) What is function draft tube in Francis turbine? [AU, April / May – 2003, 2010] CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 87


5.102) Discuss about draft tube and its types.

[AU, Nov / Dec - 2014]

5.103) Derive an expression for the efficiency of draft tube.

[AU, Nov / Dec - 2006]

5.104) Derive an expression for specific speed. What is the significance of specific speed of turbine?

[AU, May / June - 2009]

5.105) How is a specific speed of the turbine, defined?

[AU, May / June - 2009]

5.106) Write a note on performance curves of turbine.


5.107) Show that the overall efficiency of a hydraulic turbine is the product of volumetric, hydraulic and mechanical efficiencies.

[AU, May / June - 2007]

5.108) Define: Hydraulic efficiency and overall efficiency with respect to turbines. [AU, Nov / Dec - 2007] 5.109) Explain the different types of the efficiency of a turbine. [AU, Nov / Dec - 2008] 5.110) Explain the load efficiency characteristics of hydraulic turbines with a diagram. [AU, Nov / Dec - 2013] 5.111) Mention three to four most striking characteristics of Pelton wheel, Francis turbine and Kaplan turbine.


5.112) Discuss the performance characteristics of reaction turbine in detail. [AU, April / May - 2011] 5.113) Discuss briefly the characteristics curves of hydraulic turbines. [AU, Nov / Dec - 2010] PROBLEMS 5.114) A turbine develops 9000kW when running at speed of 140rpm and under a head of 30m. Determine the specific speed of the turbine. Derive the expression used in above problem.

[AU, Nov / Dec - 2008]

5.115) A Pelton wheel is to be designed for the following specifications : a. Shaft power =11,772 KW ; head = 380 metres; speed = 750 rpm, b. Overall efficiency=86%. Jet diameter is not to exceed one-sixth of the wheel diameter. Determine the i)

Wheel diameter

iii)

Diameter of the jet.

ii)

Number of jets required [AU, Nov / Dec - 2012]

5.116) A Pelton wheel is to be designed for a head of 60m when running at 200 rpm. The Pelton wheel develops 95.6475 kW shaft power. The velocity of the buckets is CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 88


equal to 0.45 times the velocity of the jet. Overall efficiency = 0.85 and co-efficient of velocity is equal to 0.98. 5.117) A Pelton wheel has to be designed for the following data. Power to be developed = 6000kW; Net head available = 300m; Speed = 550rpm; Ratio of jet diameter to wheel diameter = 1/10 and overall efficiency = 85%. Find the no of jets, diameter of jet, diameter of wheel and quantity of water required.

[AU, Nov / Dec - 2006]

5.118) A Pelton wheel is to be designed for the following specifications: Shaft power

= 11,772 kW

Head (H)

= 380m

Speed

= 750rpm

Overall efficiency (η0) = 86% Jet diameter

> 1/6 wheel diameter.

Determine: The wheel diameter, the number of jets required and diameter of the jet.

[AU, Nov / Dec - 2007]

5.119) A single jet Pelton wheel runs at 300 rpm under a head of 510 m. The jet diameter is 200 mm and its deflection inside the bucket is 165°. Assuming that its relative velocity is reduced by 15% due to friction, determine (i) water power (ii) resultant force on bucket and (iii) overall efficiency. [AU, May / June - 2007, 2012] 5.120) Determine the rpm, work done per second, power and overall efficiency of a Pelton wheel from the following data. Head = 150m, Wheel diameter = 0.75m, Jet diameter =4cm, Deflection angle of buckets = 172º, Cv of nozzle = 0.98, Speed ratio = 0.42 and surface roughness factor of vanes = 0.97.


5.121) A Pelton wheel supplied water from reservoir under a gross head of 112m and the friction losses in pen stock amounts to 20m of head. The water from pen stock is discharged through a single nozzle of diameter of 100mm at the rate of 0.30m 3/s. Mechanical losses due to friction amounts to 4.3kW of power and the shaft power available is 208kW. Determine velocity of jet, water power at inlet to runner, power losses in nozzles, power lost in runner due to hydraulic resistance. [AU, May / June - 2007] 5.122) A Pelton wheel is having a mean bucket diameter of 1 m and is running at 1000 rpm. The net head on the Pelton wheel is 700 m. If the side clearance angle is 15°and CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 89


the discharge through the nozzle is 0.1m3/sec, find the i) power available at the nozzle and ii) hydraulic efficiency of the turbine. Take CV=1. [AU, Nov / Dec - 2007] 5.123) A Pelton wheel has a mean bucket speed of 12 m/s and supplied with water at the rate of 0.7 m3/s under a head of 300 m. If the buckets deflect the jet through an angle of 160°, find the power developed and hydraulic efficiency of the turbine. [AU, April / May - 2008] 5.124) A Pelton wheel has a mean bucket speed of 10m/s with a jet of water flowing at the rate of0.7 m3/s under a head of 30m. The buckets deflect the jet through an angle of 160°. Calculate the power given by the water to the runner and the hydraulic efficiency of the turbine. Assuming the coefficient of velocity as 0.98 [AU, April / May - 2004, Nov / Dec - 2005, 2010, 2012, May / June - 2009] 5.125) A Pelton wheel which is receiving water from a penstock with a gross head of 510m. One - third of Gross head is lost in the penstock. The rate of flow through the nozzle fitted at the end of the penstock is 2.2 m3/sec. The angle of deflection of the jet is 165°. Determine (1) The power given by the water to the runner (2) Hydraulic efficiency of the Pelton wheel. Take Cv=1 and speed ratio =0.45 [AU, May / June - 2014] 5.126) A Pelton turbine is required to develop 9000 kW when working under a head of 300m the impeller may rotate at 500 rpm. Assuming a jet ratio of 10 and overall efficiency of 85% calculate

[AU, Nov / Dec - 2003]

(i)

Quantity of water required

(ii)

Diameter of the wheel

(iii)

Number of jets

(iv)

Number and size of the bucket vanes on the runner

5.127) The nozzle of a Pelton wheel gives a jet of 9cm diameter and velocity 75m/s. Coefficient of velocity is 0.978. The pitch circle diameter is 1.5m and the deflection angle of the buckets is 170°. The wheel velocity is 0.46 times the jet velocity. Estimate the speed of the Pelton wheel turbine in rpm, theoretical power developed and also the efficiency of the turbine.


5.128) A Pelton turbine having 1.6m bucket diameter develops a power of 3600kW at 400rpm, under a net head of 275m. If the overall efficiency is 88%, and the CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 90


coefficient of velocity is 0.97, find speed ratio, discharge, diameter of the nozzle and specific speed.

[AU, May / June - 2007]

5.129) A Pelton wheel has a mean bucket speed of 12m/s and supplied with water at the rate of 0.7m3/s under a head of 300m. If the buckets deflect the jet through an angle of 160° find the power developed and hydraulic efficiency of the turbine. [AU, April / May - 2008] 5.130) A Pelton turbine is to produce 18MW under a head of 450 m when running at 480 rpm. If D/d ratio is 10, determine the number of jets required. [AU, Nov / Dec - 2011] 5.131) Consider an impulse wheel with a pitch diameter of 2.75m and a bucket angle of 170°. If the velocity is 58m/s, the jet diameter is 100mm, and the rotational speed is 320rpm, find the force on the buckets, the torque on the runner, and the power transferred to the runner. Assume v2 = 0.9v1.


5.132) A gas turbine operates between 1000k and 650 k temperature limits taking in air 20 kg/s at 125 m/s and discharging at 300 m3/s. Estimate the power developed by the turbine. Given Cp=995 J / Kg.K.


5.133) A reaction turbine at 450rpm, head 120m, diameter at inlet 120cm flow area 0.4m2 has angles made by absolute and relative velocities at inlet 20° and 60° respectively. Find volume flow rate, H.P and efficiency.

[AU, Nov / Dec - 2009]

5.134) An inward flow reaction turbine has internal and external diameter as 0.85m and 1m respectively. The hydraulic efficiency of turbine is 0.92 under a head of 60m. The velocity of flow at outlet is 3m/s and discharge at outlet is radial. The vane angle at the outlet is 18° and width of the wheel is 75mm. Calculate the guide blade angle, turbine speed, vane angle at inlet and power developed by the turbine. [AU, April / May - 2011] 5.135) An inward flow reaction turbine has external and internal diameters as 0.9m and 0.45m respectively. The turbine is running at 200 rpm and width of the turbine at inlet is 200mm. The velocity of flow through the runner is constant and is equal to 1.8m/sec. The guide blades make an angle of 10° to the tangent of the wheel and the discharge at the outlet of the turbine is radial. Determine the i)

Absolute velocity of water at inlet of runner

ii) Velocity of whirl at inlet CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 91


iii) Relative velocity at inlet iv) Runner blade angles v) Width of the runner at outlet vi) Mass of water flowing through the runner per second vii) Head at the inlet of the turbine viii) Power developed and hydraulic efficiency of the turbine. 5.136) An inward flow reaction turbine having an overall efficiency of 80% is required to deliver 136 kW. The head H is 16 m and the peripheral velocity is 3.3 √H. The radial velocity of flow at inlet is 1.1√H. The runner rotates at 120 rpm. The hydraulic losses in the turbine are 15% of the flow available energy. Determine (i) diameter of the runner, (ii) guide vane angle, (iii) the runner blade angle at inlet and (iv) the discharge through the turbine.

[AU, Nov / Dec - 2010]

5.137) In an outward flow reaction turbine, the internal and external diameters are 2m and 2.7m respectively. The turbine speed is 275rpm and the water flow rate is 5.5m3/s. The width of the runner is constant at the inlet and outlet and equal to 250mm. The head acting on the turbine is 160m. The vanes have negligible thickness and the discharge at the outlet is radial. Determine the vane angles and velocity of the flow at inlet and outlet.

[AU, Nov / Dec - 2012]

5.138) In a hydroelectric station, water is available at the rate of 175m3/s under head of 18m. The turbine run at a speed of 150 rpm, with overall efficiency of 82%. Find the number of turbines required, if they have the maximum specific speed of 460. [AU, Nov / Dec - 2005] 5.139) A radial flow impeller has a diameter 25 cm and width 7.5 cm at exit. It delivers 120 liters of water per second against a head of 24 m at 1440 rpm. Assuming the vanes block the flow area by 5% and hydraulic efficiency 0.8, estimate the vane angle at exit. Also calculate the torque exerted on the driving shaft in the mechanical efficiency is 95%

[AU, Nov / Dec - 2003]

5.140) A 50m/s velocity jet of water strikes without shock, a series of vanes moving at 15m/s. The jet is inclined at an angle of 20° to the direction of motion of vanes. The relative velocity of jet at outlet is 0.9 times of the values at inlet and the absolute velocity of water exit is to be normal to the motion of vanes. Determine the vane



angle at entrance and exit. Also determine work done on vanes per second N of water supplied by the jet.


5.141) In an inward radial flow turbine, water enters at an angle of 22 ° to the wheel tangent to the outer rim and leaves at 3 m/s. The flow velocity is constant through the runner. The inner and outer diameters are 300 mm and 600 mm respectively. The speed of the runner is 300 rpm. The discharge through the runner is radial. Find the (i)Inlet and outlet blade angles. (ii) Taking inlet width as 150 mm and neglecting the thickness of the blades, find the power developed by the turbine.


5.142) The velocity of the whirl at the inlet to the runner of an inward flow reaction turbine is 3.15√H m/s and the velocity of flow at inlet is 1.05√H m/s. The velocity of whirl at exist is 0.22√H m/s in the same direction as at inlet and the flow at exist is 0.83√H m/s, where H is head of water 30m. The inner diameter of the runner is 0.6 times the outer diameter. Assuming hydraulic efficiency of 80%. Compute angles of the runner vanes at inlet and exist.

[AU, April / May – 2003, 2010]

5.143) Design a Francis Turbine runner with the following data: Net head = 70m speed N = 800 rpm. Output power 400 Kw Hydraulic efficiency = 95% Overall efficiency = 85% Flow ratio = 0.2 Breadth ratio = 0.1 Inner diameter is 1/3 outer diameter. Assume 6% circumferential area of the runner to be occupied by the thickness of the vanes. The flow is radial at exit and remains constant throughout. [AU Nov / Dec - 2008] 5.144) A Francis turbine developing 16120 kW under a head of 260 m runs at 600 rpm. The runner outside diameter is 1500 mm and the width is 135 mm. The flow rate is 7 m3/s. The exit velocity at the draft tube outlet is 16 m/s. Assuming zero whirl velocity at exit and neglecting blade thickness determine the overall and hydraulic efficiency and rotor blade angle at inlet. Also find the guide vane outlet angle. [AU, Nov / Dec - 2014] 5.145) Calculate guide blade angles, vane angles, runner diameters at inlet and outlet and width of the wheel at outlet for a Francis turbine with the following data: Net head: 70 m; Speed: 720 rpm; Shaft Power: 310 kW; Overall efficiency: 0.85;



Hydraulic efficiency: 0.9; Flow ratio: 0.2; Breadth ratio: 0.1; OD/ID ratio: 1.8; The thickness of vanes occupy 7.5% of circumferential area of runner velocity of flow is Constant and discharge is radial at outlet.

[AU, Nov / Dec - 2014]

5.146) The following data is given for a Francis Turbine Net head = 60m speed N = 700 rpm. Shaft power 294.3 kW Hydraulic efficiency = 93% Overall efficiency = 84% Flow ratio = 0.2 Breadth ratio = 0.1 Inner diameter is 1/2 outer diameter. Assume 5% circumferential area of the runner to be occupied by the thickness of the vanes. Velocity of flow is constant at inlet and outlet and discharge is radial outlet. Determine

[AU, Nov / Dec - 2012]

 Guide blade angle  Runner vane angle at inlet and outlet  Diameter of the runner at inlet and outlet  Width of the wheel at inlet 5.147) The inner and outer diameters of an inward flow reaction turbine are 50 cm and 100 cm respectively. The vanes are radial at inlet and discharge is also radial. The inlet guide vanes angle is 10°. Assuming the velocity of flow as constant and equal to 3 m/s, find the speed of the runner and the vane angle at the outlet. [AU, April / May - 2008] 5.148) A reaction turbine works at 450rpm under a head of 120metres. Its diameter at inlet is 120cm and the flow area is 0.4m2. The angles made by absolute and relative velocities at inlet are 20° and 60° respectively with the tangential velocity. Determine the  Volume flow rate  Power developed  Hydraulic efficiency.

[AU, Nov / Dec - 2007]

5.149) A turbine is to operate under a head of 25m at 200rpm. The discharge is 9cumec. If the efficiency is 90%, determine the i) Specific speed of the turbine ii) Power generated iii) Type of turbine



5.150) A Francis turbine with overall efficiency of 75% is required to produce 149.26kN. It is working against a head of 7.62m. The peripheral velocity is 0.26√(2gH) and the radial velocity of flow at inlet is 0.96√(2gH). The wheel runs at 150rpm and the hydraulic losses in the turbine account for 22% of the available energy. Assume radial discharge; determine the guide blade angle, the wheel vane angle at inlet, diameter of the wheel at inlet and width of the wheel at inlet. [AU, May / June – 2009, 2013] 5.151) A Francis turbine with overall efficiency of 76% and hydraulic efficiency of 80% is required to produce 150kW. It is working against a head of 8m. The peripheral velocity is 0.25√(2gH) and the radial velocity of flow at inlet is 0.95√(2gH). The wheel runs at 150rpm. Assume radial discharge; determine the guide blade angle, the wheel vane angle at inlet, diameter of the wheel at inlet and width of the wheel at inlet.

[AU, Nov / Dec – 2009, April / May - 2010]

5.152) A dam on a river is being sited for a hydraulic turbine. The flow rate is 1600 m3/h, the available head is 25 m, and the turbine speed is to be 460 rpm. Discuss the estimated turbine size and feasibility for a Francis turbine; and a Pelton wheel. [AU, Nov / Dec - 2011] 5.153) A turbine is to operate under a head of 25m at 200rpm. The discharge is 9 cumec. If the efficiency is 90%, determine the performance of the turbine under a head of 20 meters.

[AU, Nov / Dec - 2007]

5.154) A reaction turbine works at 450 rpm under a head of 120 m. Its diameter at inlet is 120 cm and the flow area is 0.4 m2. The angles made by the absolute and relative velocity at inlet are 20° and 60° respectively, with the tangential velocity. Determine the volume flow rate, the power developed and the hydraulic efficiency. [AU, Nov / Dec - 2007] 5.155) Calculate the diameter and speed of the runner of a Kaplan turbine developing6000 kW under an effective head of 5 m. Overall efficiency of the turbine is 90% and the diameter of the boss is 0.4 times the external diameter of the runner. The turbine speed ratiois 2.0. And flow ratio is 0.6.

[AU, Nov / Dec - 2006]

5.156) A Kaplan turbine runner is to be designed to develop 7357.5kW shaft power. The net available head is 5.50m. Assume that the speed ratio is 2.09 and flow ratio



is 0.68, and the overall efficiency is 60%. The diameter of the boss is 1/3 rd of the diameter of the runner, its specific speed.

[AU, May / June - 2009]

5.157) A Kaplan turbine runner is to be designed to develop 7360kW. The net available head is 5.5m. Assuming the speed ratio is 2.09 and the flow ratio is 0.68 and the overall efficiency is 60%. The diameter of the boss is one third of the diameter of the runner. Find the diameter of the runner, its speed and its specific speed. [AU, Nov / Dec - 2009] 5.158) A Kaplan turbine working under a head of 20 m develops 15 MV brake power. The hub diameter and runner diameter of the turbine are 1.5 m and 4 m respectively. The guide blade angle at the inlet is 30°. The discharge is radial. Find the runner vane angles and turbine speed. Take hydraulic and overall efficiency as 90% and 80 %


5.159) A Kaplan turbine is to be designed to develop 9100kW. The net available head is 5.6m/ If the speed ratio is 2 and flow ratio is 0.68, overall efficiency 86% and the diameter of the boss is 1/3 the diameter of the runner. Find the diameter of the runner, its speed and specific speed of turbine.


5.160) A Kaplan turbine delivers 10 MW under a head of 25 m. The hub and tip diameters are 1.2 m and 3 m. Hydraulic and overall efficiencies are 0.90 and 0.85. If both velocity triangles are right angled triangles, determine the speed, guide bladeoutlet angle and blade outlet angle.

[AU, Nov / Dec – 2013, 2014]

5.161) The hub diameter of a Kaplan turbine working under a head of 12m, is 0.35 times the diameter of the runner. The turbine is running at 100 rpm. If the vane angle of the extreme edge of the runner at outlet is 15º and the flow ratio is 0.6, find the diameter of the runner, diameter of the boss and the discharge through the runner. The velocity at the whirl at outlet is given as zero.



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R.M.K COLLEGE OF ENGINEERING AND TECHNOLOGY RSM NAGAR, PUDUVOYAL-601206

DEPARTMENT OF MECHANICAL ENGINEERING

CE6451 – FLUID MECHANICS & MACHINERY

III SEM MECHANICAL ENGINEERING Regulation 2013

ANNA UNIVERSITY 2 MARKS QUESTIONS & ANSWERS PREPARED BY R.ASHOK KUMAR M.E (CAD)


UNIT - I - FLUID PROPERTIES AND FLOW CHARACTERISTICS 1.1) Define fluid. Give examples.

[AU, Nov / Dec - 2010]

A fluid is a substance which is capable of flowing. It has no definite shape. 1.2) How fluids are classified?


 Ideal and Real fluids  Newtonian and Non – Newtonian fluids. 1.3) Distinguish between solid and fluid.

[AU, May / June - 2006]

Solid

Fluid

 Solids have their own shape

 Fluids not have their own shape

 Solids are compressible

 Fluids are incompressible

 They offer resistance to change

 They do not offer resistance to change in shape

in shape 1.4) Differentiate between solids and liquids.

[AU, May / June - 2007]

Solid

Liquid

 Solids have their own shape

 Fluids not have their own shape

 Solids are compressible

 Fluids are incompressible

 They offer resistance to change

 They do not offer resistance to

in shape

change in shape

1.5) Discuss the importance of ideal fluid.


 Ideal fluid: a fluid with no friction  Also referred to as an inviscid (zero viscosity) fluid  Internal forces at any section within are normal (pressure forces)  Practical applications: many flows approximate frictionless flow away from solid boundaries.  Do not confuse ideal fluid with a perfect (ideal) gas. 1.6) What is a real fluid?


 The fluid which posses viscosity is known as real fluid 1.7) Define Newtonian and Non – Newtonian fluids.

[AU, Nov / Dec - 2008]

A real fluid, in which the shear stress is directly proportional to the rate of shear strain (or velocity), is known as Newtonian fluid CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 2


A real fluid, in which the shear stress is not proportional to the rate of shear strain (or velocity gradient), is known as Non – Newtonian fluid 1.8) What are Non – Newtonian fluids? Give example.

[AU, Nov / Dec - 2009]

A real fluid, in which the shear stress is not proportional to the rate of shear strain (or velocity gradient), is known as Non – Newtonian fluid Examples – Paint, Toothpaste and Printer’s Ink 1.9) Differentiate between Newtonian and Non – Newtonian fluids. [AU, Nov / Dec - 2007] Newtonian fluid  A real fluid, in which the shear stress is directly proportional to the rate of shear strain (or velocity gradient)  Examples – Water & Kerosene

Non – Newtonian fluid  A real fluid, in which the shear stress is not proportional to the rate of shear strain (or velocity gradient)  Examples – Paint, Toothpaste and Printer’s Ink

1.10) What is Thyxotrphic fluid?

[AU, Nov / Dec - 2003]

The fluid which possess a definite yield stress but then the relationship between shear stress and angular deformation is non – linear are called as thixotrophic fluid. Example printer ink and lipstick 1.11) Define - Incompressible fluid.

[AU, Nov / Dec - 2014]

A liquid is considered to be incompressible only when there is a change in volume of a liquid that occurs under smaller pressure variation. 1.12) Define Pascal’s law.

[AU, Nov / Dec – 2005, 2008]

The normal stress acting at a point in a fluid id independent of the orientation of the surface on which it acts. 1.13) Define mass density and weight density.

[AU, Nov / Dec - 2007]

Mass density of the fluid is defined as the ratio of the mass of a fluid to its volume. Weight density of a fluid is the ratio between the weight of a fluid to its volume



1.14) Distinguish between the mass density and weight density. [AU, May / June - 2009] Mass Density  Mass density of the fluid is

Weight Density  Weight density of a fluid is the

defined as the ratio of the mass

ratio between the weight of a

of a fluid to its volume.

fluid to its volume

 The unit of mass density kg/m3

 The unit of mass density N/m3

1.15) Define the term specific volume and express its units. [AU, April / May - 2011] Specific volume is defined as the volume of a fluid occupied by a unit mass or volume per unit mass of the fluid. The unit of specific volume is m3/kg. 1.16) Define specific weight and density.

[AU, May / June - 2012]

Density of the fluid is defined as the ratio of the mass of a fluid to its volume. Specific Weight of a fluid is the ratio between the weight of a fluid to its volume 1.17) Define density and specific gravity of a fluid.

[AU, Nov / Dec - 2012]

Density of the fluid is defined as the ratio of the mass of a fluid to its volume. Specific gravity is defined as the ratio of the weight density of a fluid to the weight density of the standard fluid. 1.18) What is specific weight and specific gravity of a fluid? [AU, April / May - 2010] Specific Weight of a fluid is the ratio between the weight of a fluid to its volume Specific gravity is defined as the ratio of the weight density of a fluid to the weight density of the standard fluid. 1.19) What is specific gravity? How is it related to density? [AU, April / May - 2008] Specific gravity is defined as the ratio of the weight density of a fluid to the weight density of the standard fluid.



The density of a liquid = Specific gravity of the liquid * weight density of water 1.20) What is viscosity? What is the cause of it in liquids and in gases? [AU, Nov / Dec - 2005] Viscosity is defined as the property of a fluid which offers resistance to the movement of one layer of fluid over another adjacent layer of the fluid. Viscosity increases with increase in temperature in case of gases whereas it decrease in case of liquid 1.21) Define Viscosity and give its unit.

[AU, Nov / Dec 2003]

Viscosity is defined as the property of a fluid which offers resistance to the movement of one layer of fluid over another adjacent layer of the fluid. Unit for viscosity is

𝑵𝑺 𝒎𝟐

1.22) Define Newton’s law of viscosity.

[AU, Nov / Dec - 2012]

The shear force acting between two layers of fluid is proportional to the difference in their velocities and the area is inversely proportional to the distance between two plates. 1.23) State the Newton's law of viscosity. [AU, April / May, Nov / Dec - 2005, May / June - 2007] The shear force acting between two layers of fluid is proportional to the difference in their velocities and the area is inversely proportional to the distance between two plates. 1.24) Define Newton’s law of viscosity and write the relationship between shear stress and velocity gradient?

[AU, Nov / Dec - 2006]

The shear force acting between two layers of fluid is proportional to the difference in their velocities and the area is inversely proportional to the distance between two plates.

𝜏= 𝜇 1.25) What is viscosity and give its units?

𝑑𝑢 𝑑𝑦 [AU, April / May - 2011]

Viscosity is defined as the property of a fluid which offers resistance to the CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 5


movement of one layer of fluid over another adjacent layer of the fluid. Unit for viscosity is

𝑵𝑺 𝒎𝟐

1.26) Define coefficient of viscosity.


The Newton’s law of viscosity states theta the shear stress on a fluid element layer is directly proportional to the rate of the shear strain. The constant of proportionality is called the coefficient of viscosity

𝜏= 𝜇

𝑑𝑢 𝑑𝑦

1.27) Define coefficient of volume of expansion.

[AU, Nov / Dec - 2012]

Coefficient of volume of expansion is defined as the amount of expansion (or contraction) per unit length of a material resulting from one degree change in temperature 1.28) Define relative or specific viscosity.

[AU, May / June - 2013]

It is the ratio of dynamic viscosity of fluid to dynamic viscosity of water at 20º C. 1.29) Define kinematic viscosity.

[AU, Nov / Dec - 2009]

The kinematic viscosity is defined ratio between the dynamic viscosity and density of the fluid. 1.30) Define kinematic and dynamic viscosity.

[AU, May / June - 2006]

The Kinematic Viscosity is defined ratio between the dynamic viscosity and density of the fluid. The Dynamic Viscosity is defined as the shear stress required to produce unit rate of shear deformation. 1.31) Define dynamic viscosity.


The Dynamic Viscosity is defined as the shear stress required to produce unit rate of shear deformation. 1.32) What is kinematic viscosity? State its units?

[AU, May / June - 2014]

The Kinematic Viscosity is defined ratio between the dynamic viscosity and density of the fluid. The unit of kinematic viscosity is m2/sec and also known as stoke.



1.33) Define the terms kinematic viscosity and give its dimensions. [AU, May / June - 2009] The Kinematic Viscosity is defined ratio between the dynamic viscosity and density of the fluid. The unit of kinematic viscosity is m2/sec and also known as stoke. 1.34) Differentiate between kinematic viscosity of liquids and gases with respect to pressure.

[AU, Nov / Dec - 2013]

For liquids, the kinematic viscosity is practically independent of pressure. For gases, the kinematic viscosity is inversely proportional to density and thus pressure since the density of a gas is proportional to its pressure. 1.35) What is the importance of kinematic viscosity?

[AU, Nov / Dec - 2014]

Kinematic viscosity is the only fluid property will relate density and absolute viscosity. As the Gases are compressible, viscosity of gases should be specified through kinematic viscosity rather than Absolute viscosity. Also the kinematic viscosity value of any fluid will be for a standard temperature & pressure (STP) not like absolute viscosity. Hence Kinematic viscosity is an important property of any fluid 1.36) Write the units and dimensions for kinematic and dynamic viscosity. [AU, Nov / Dec - 2005] The unit of kinematic viscosity is m2/sec and also known as stoke. The Unit for dynamic viscosity is

𝑵𝑺 𝒎𝟐

1.37) What are the units and dimensions for kinematic and dynamic viscosity of a fluid?

[AU, Nov / Dec - 2006, 2012] The unit of kinematic viscosity is m2/sec and also known as stoke. The Unit for dynamic viscosity is

𝑵𝑺 𝒎𝟐



1.38) Differentiate between kinematic and dynamic viscosity. [AU, May / June - 2007, Nov / Dec – 2008, 2011] Kinematic Viscosity

Dynamic viscosity

 The Kinematic Viscosity is defined

ratio

between

the

 The Dynamic Viscosity is defined as the shear stress

dynamic viscosity and density of

required to produce unit rate of

the fluid.

shear deformation.

 The unit of kinematic viscosity

 The Unit for dynamic viscosity is

is m2/sec and also known as

𝑵𝑺

stoke.

𝒎𝟐

 It is concerned with length and time only

 It is not concerned with length and time only

1.39) How does the dynamic viscosity of liquids and gases vary with temperature? [AU, Nov / Dec - 2007, April / May - 2008] Dynamic Viscosity is defined as the property of a fluid which offers resistance to the movement of one layer of fluid over another adjacent layer of the fluid. Dynamic Viscosity increases with increase in temperature in case of gases whereas it decrease in case of liquid 1.40) What are the variations of viscosity with temperature for fluids? [AU, Nov / Dec - 2009] Viscosity decrease when there is increase in temperature of a fluid. 1.41) Why is it necessary in winter to use lighter oil for automobiles than in summer? To what property does the term lighter refer? [AU, Nov / Dec - 2010] Oil will congeal in the winter by making the engine and transmission system stiff during winter. This will lead to consume more power from battery. It will be difficult to start the car with less battery power. The use of lighter will remain more fluid than heavy oil during winter. The term lighter refers to specific gravity of oil which indirectly relates with density. The lighter oil has specific gravity less than unity.



1.42) Define the term pressure. What are its units?

[AU, Nov / Dec - 2005]

Pressure is an expression of force exerted on a surface per unit area. The standard unit of pressure is the Pascal. 1.43) Define eddy viscosity. How it differs from molecular viscosity? [AU, Nov / Dec - 2010] Eddy viscosity is defined as the turbulent transfer of momentum by eddies giving rise to an internal fluid friction with respect to the action of molecular viscosity in laminar flow much large scale. But molecular viscosity is transfer of mass motion momentum alone by random motion of individual molecules. 1.44) Define surface tension.

[AU, May / June - 2006]

Surface tension is defined as the tensile force acting on the surface of a liquid in contact with gas or on the surface between two immiscible liquids such that the contact surface behaves like a membrane under tension. 1.45) Define surface tension and expression its unit.


Surface tension is defined as the tensile force acting on the surface of a liquid in contact with gas or on the surface between two immiscible liquids such that the contact surface behaves like a membrane under tension. The unit is N/m. 1.46) Define capillarity.


Capillarity is defined as phenomenon of rise or fall of a liquid surface in the small tube relative to the adjacent general level of liquid when the tube is held vertically in the liquid. 1.47) What is meant by vapour pressure of a fluid?


The vapour molecules get accumulated in the space between the free liquid surface and top of the vessel. These accumulated vapour exerts a pressure on the liquid surface. This pressure is known as vapour pressure. 1.48) Brief on the significance of vapour pressure.

[AU, Nov / Dec - 2014]

Vapour pressure is the only property of a liquid responsible for cavitation phenomena. For any temperature there should be a vapour pressure, so, during the fluid motion at ambient temperature, if any obstructions are there results to sudden increase in pressure. This leads to achieve the vapour pressure and convert the portion of liquid into high intensity gas bubbles causes to cavitation. CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 9


1.49) What do you mean by capillarity?

[AU, Nov / Dec - 2009]

Capillarity is phenomenon of rise or fall of a liquid surface in the small tube relative to the adjacent general level of liquid when the tube is held vertically in the liquid. 1.50) Define compressibility of the fluid. [AU, Nov / Dec – 2008, May / June - 2009] Compressibility is the property by virtue of fluid undergoes a change in volume under the action of external pressure. It is the reciprocal of bulk modulus. 1.51) Define compressibility and viscosity of a fluid.


Compressibility is the property by virtue of fluid undergoes a change in volume under the action of external pressure. It is the reciprocal of bulk modulus. Viscosity is defined as the property of a fluid which offers resistance to the movement of one layer of fluid over another adjacent layer of the fluid. 1.52) Define coefficient of compressibility.

[AU, Nov / Dec - 2010]

Coefficient of compressibility is defined the decrease in volume per unit volume of a substance resulting from a unit increase in pressure 1.53) List the components of total head in a steady, in compressible irrotational flow.

[AU, Nov / Dec - 2009]  Pressure Head (Dynamic Head)  Kinetic Head  Potential Head

1.54) Define the bulk modulus of fluid.

[AU, Nov / Dec - 2008]

Bulk modulus is defined as ratio of change in pressure to rate of change in volume due do change in pressure. 1.55) Define - compressibility and bulk modulus.

[AU, Nov / Dec – 2011]

Compressibility is the property by virtue of fluid undergoes a change in volume under the action of external pressure. It is the reciprocal of bulk modulus. Bulk modulus is defined as ratio of change in pressure to rate of change in volume due do change in pressure.



1.56) Differentiate between the steady and unsteady flow. [AU, May / June - 2006] Steady flow

Unsteady flow

 Steady flow is defined as that type of

flow

which

characteristics

like

the

fluid

velocity,

 Unsteady flow is defined as that type of flow which the fluid characteristics

like

velocity,

pressure, density at a point do not

pressure, density at a point

change with time

changes with respect to time

1.57) When is the flow regarded as unsteady? Give an example for unsteady flow. [AU, April / May - 2003] Unsteady flow is defined as that type of flow which the fluid characteristics like velocity, pressure, density at a point changes with respect to time. Water flowing from dam. 1.58) Differentiate between steady flow and uniform flow. [AU, Nov / Dec - 2007] Steady flow

Uniform flow

 Steady flow is defined as that type of

flow

which

characteristics

like

the

fluid

velocity,

pressure, density at a point do not

 Uniform flow is defined as that type of flow which velocity at any given time does not change with respect to space.

change with time.

1.59) Differentiate between laminar and turbulent flow. [AU, Nov / Dec – 2005, 2008, April / May - 2015] Laminar flow

Turbulent flow

 Laminar flow is defined as that

 Turbulent flow is defines as that

type of flow in which the fluid


particles move along well –

particles move in a zig – zag way.

denied path or stream line.  The stream lines are straight and parallel to each other

 The stream lines are not straight to each other



1.60) Distinguish between Laminar and Turbulent flow. [AU, April / May - 2010] Laminar flow

Turbulent flow







denied path or stream line.  The stream lines are straight and

 The stream lines are not straight

parallel to each other

to each other

1.61) State the criteria for laminar flow.

[AU, Nov / Dec - 2008]

Laminar flow is defined as that type of flow in which the fluid particles move along well – denied path or stream line. The stream lines are straight and parallel to each other. 1.62) State the characteristics of laminar flow.


Laminar flow is defined as that type of flow in which the fluid particles move along well – denied path or stream line. The stream lines are straight and parallel to each other. The particles move smoothly over the adjacent layer. 1.63) What are the characteristics of laminar flow?

[AU, May / June - 2014]

Laminar flow is defined as that type of flow in which the fluid particles move along well – denied path or stream line. The stream lines are straight and parallel to each other. The particles move smoothly over the adjacent layer. 1.64) Mention the general characteristics of laminar flow.[AU, May / June - 2013] Laminar flow is defined as that type of flow in which the fluid particles move along well – denied path or stream line. The stream lines are straight and parallel to each other. The particles move smoothly over the adjacent layer. 1.65) Define stream line.

[AU, Nov / Dec - 2007]

In Euler’s approach, the velocity vector is defines as a function of time and space coordinates. If for a fixed instance time a space curve is drawn so that it is tangent everywhere to the velocity vector, then the curve is called as stream line. 1.66) Define streamline and path line in fluid flow.

[AU, Nov / Dec - 2005]

In Euler’s approach, the velocity vector is defines as a function of time and space coordinates. If for a fixed instance time a space curve is drawn so that it is tangent everywhere to the velocity vector, then the curve is called as stream line. CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 12


Path line are the outcome of the Lagrange method in describing fluid flow and show the paths of different fluid particles as a function of time. 1.67) What is stream line and path line in fluid flow?


In Euler’s approach, the velocity vector is defines as a function of time and space coordinates. If for a fixed instance time a space curve is drawn so that it is tangent everywhere to the velocity vector, then the curve is called as stream line. Path line are the outcome of the Lagrange method in describing fluid flow and show the paths of different fluid particles as a function of time. 1.68) What is a streamline?

[AU, Nov / Dec - 2010]

In Euler’s approach, the velocity vector is defines as a function of time and space coordinates. If for a fixed instance time a space curve is drawn so that it is tangent everywhere to the velocity vector, then the curve is called as stream line. 1.69) Define streak line.


A streak line at any instant of time is the locus of the temporary location of all particles that have passed through a fixed point in the flow field. 1.70) Define stream function.


Stream function is defined as the scalar function of space and time, such that its partial derivative with respect to any direction gives the velocity component at right angles to that direction 1.71) Define control volume.


The region in which the mass crosses the system boundary is called control volume. A control volume is a mathematical abstraction employed in the process of creating mathematical models of physical processes. 1.72) What is the use of control volume?


When the fluid is in motion, it is convenient to consider a certain control volume and study the quantity of the fluid entering and leaving the control volume in a definite period of time. It is an imaginary volume bounded by the control surface. 1.73) Distinguish between a control and differential control volume. [AU, April / May - 2011] The region in which the mass crosses the system boundary is called control



volume. A control volume is a mathematical abstraction employed in the process of creating mathematical models of physical processes. The control volume in which the conservation of mass equation is applied is called a differential control volume. 1.74) What is meant by continuum?

[AU, Nov / Dec - 2008]

A continuous distribution of matter with no void or empty spaces is called as continuum. For mechanical analysis, a fluid is consider to be continuum. Example water flowing in a pipe. 1.75) Write down the equation of continuity.

[AU, Nov / Dec –2008, 2009, 2012]

𝜕 𝜕 𝜕 (𝜌𝑢) + (𝜌𝑣) + (𝜌𝑤) = 0 𝜕𝑥 𝜕𝑦 𝜕𝑧 1.76) State the continuity equation in one dimensional form? [AU, May / June - 2012]

𝜕 (𝜌𝑢) = 0 𝜕𝑥 1.77) State the general continuity equation for a 3 - D incompressible fluid flow. [AU, May / June - 2007, Nov / Dec - 2012]

𝜕𝑢 𝜕𝑣 𝜕𝑤 + + =0 𝜕𝑥 𝜕𝑦 𝜕𝑧 1.78) State the continuity equation for the case of a general 3-D flow. [AU, Nov / Dec - 2007]

𝜕 𝜕 𝜕 (𝜌𝑢) + (𝜌𝑣) + (𝜌𝑤) = 0 𝜕𝑥 𝜕𝑦 𝜕𝑧 1.79) State the equation of continuity in 3dimensional incompressible flow. [AU, Nov / Dec - 2005]

𝜕𝑢 𝜕𝑣 𝜕𝑤 + + =0 𝜕𝑥 𝜕𝑦 𝜕𝑧 1.80) State the assumptions made in deriving continuity equation. [AU, Nov / Dec - 2011]  The liquid is ideal and incompressible  The flow is steady and continuous  The velocity is uniform over the cross section and equal to mean velocity CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 14


 The force only acting on the fluids are the gravity force and the pressure force  All the frictional losses are negligible 1.81) Write the Euler's equation.


𝑑𝑝 + 𝑣𝑑𝑣 + 𝑔. 𝑑𝑧 = 0 𝜌 1.82) What is Euler’s equation of motion?

[AU, Nov / Dec - 2008]

𝑑𝑝 + 𝑣𝑑𝑣 + 𝑔. 𝑑𝑧 = 0 𝜌 1.83) State the empirical pressure density relation for a liquid. [AU, Nov / Dec - 2014] 1.84) Write the Bernoulli’s equation in terms of head. Explain each term. [AU, Nov / Dec - 2007]

𝑝 𝑣2 + + 𝑧 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑤 2𝑔 𝑝 = 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝐸𝑛𝑒𝑟𝑔𝑦 𝑤 𝑣2 = 𝐾𝑖𝑛𝑒𝑡𝑖𝑐 𝐸𝑛𝑒𝑟𝑔𝑦 2𝑔 𝑧 = 𝐷𝑎𝑡𝑢𝑚 𝐸𝑛𝑒𝑟𝑔𝑦 1.85) What are the basic assumptions made is deriving Bernoulli’s theorem? [AU, Nov / Dec – 2005, 2012]  The liquid is ideal and incompressible  The flow is steady and continuous  The velocity is uniform over the cross section and equal to mean velocity  The force only acting on the fluids are the gravity force and the pressure force  All the frictional losses are negligible 1.86) List the assumptions which are made while deriving Bernoulli’s equation. [AU, May / June – 2009, 2012]  The liquid is ideal and incompressible  The flow is steady and continuous CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 15


 The velocity is uniform over the cross section and equal to mean velocity  The force only acting on the fluids are the gravity force and the pressure force  All the frictional losses are negligible 1.87) State the assumptions used in the derivation of the Bernoulli's equation. [AU, Nov / Dec - 2014]  The liquid is ideal and incompressible  The flow is steady and continuous  The velocity is uniform over the cross section and equal to mean velocity  The force only acting on the fluids are the gravity force and the pressure force  All the frictional losses are negligible 1.88) What are the applications of Bernoulli’s theorem? [AU, April / May - 2010]  Venturimeter  Orifice meter  Pitot tube 1.89) List the types of flow measuring devices fitted in a pipe flow, which uses the principle of Bernoulli’s equation.

[AU, May / June - 2012]

 Venturimeter  Orifice meter  Pitot tube 1.90) Mention the uses of manometer.

[AU, Nov / Dec - 2009]

 It used to measure pressure of the fluid 1.91) State the use of venturimeter.

[AU, May / June - 2006]

Venturimeter is a device used to measure the rate of flow fluid through the pipelines. 1.92) Write the impulse momentum equation.

[AU, May / June - 2007]

F = ma Where 𝑎 = 𝑑𝑣/𝑑𝑡

Let m be constant 𝐹=𝑚

𝑑𝑣 𝑑𝑡



𝐹=

𝑑 (𝑚𝑣) 𝑑𝑡

1.93) What do you understand by impulse momentum equation? [AU, May / June - 2013] Impulse momentum equation states that the impulse of force acting on the fluid mass in a short interval of time is equal to the change in momentum in the direction of the force. 1.94) State the momentum equation. When can it applied.[AU, May / June - 2009] It states that “The force F acting on a fluid of mass ‘m’ in a short interval of time ‘dt’ is equal to change in momentum d(mv) in the direction of force. F = ma Where 𝑎 = 𝑑𝑣/𝑑𝑡

Let m be constant 𝐹=𝑚 𝐹=

𝑑𝑣 𝑑𝑡

𝑑 (𝑚𝑣) 𝑑𝑡

1.95) State the usefulness of momentum equation as applicable to fluid flow phenomenon.

[AU, May / June– 2007, Nov / Dec - 2012]

The momentum equation is used to determine the resultant force exerted on the force boundary of the flow passage by a stream of flowing fluid as the flow changes its direction. The practical applications are  Flow through bend pipes  Jet propulsions and propellers  Hydraulic jump in open channels  Fluid flow through stationary and moving plates  Non uniform flow through sudden enlarged pipes 1.96) What is the moment of momentum equation?

[AU, May / June - 2014]

Moment of momentum equation is derived from moment of momentum principle which states that the resulting torque acting on a rotating fluid is equal to rate of change of moment of momentum. CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 17


Moment of moment equation

𝑇 = 𝜌𝑄 (𝑉2 𝑟2 − 𝑉1 𝑟1 ) V1 & V2 = Velocity of fluid at section 1 & 2 r1 & r2 = Radius of curvature of fluid at section 1 & 2 ρ = Density of fluid Q = Flow rate of the fluid 1.97) Calculate the density of one litre petrol of specific gravity 0.7? [AU, April / May - 2011] Given: Volume of petrol = 1 litre = 1 *10-3m3 Specific gravity

S = 0.7

Solution:

𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 𝑆 =

𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑝𝑒𝑡𝑟𝑜𝑙 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟

𝜌𝑝 = 𝑆 ∗ 𝜌𝑤 = 0.7 * 1000 𝝆𝒑 = 700 kg/m3 1.98) If a liquid has a viscosity of 0.051 poise and kinematic viscosity of 0.14 stokes, calculate its specific gravity.


Given: Viscosity

µ = 0.051 poise = = 0.0051

0.051 10

𝑘𝑔

𝑠𝑚

Kinematic viscosity

= 0.7 stokes =0.7 ∗ 10−4 𝑚2 /𝑠

Solution:

𝑘𝑖𝑛𝑒𝑚𝑎𝑡𝑖𝑐 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 =

𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 𝐷𝑒𝑛𝑠𝑖𝑡𝑦



0.7 ∗ 10−4 =

0.0051 𝐷𝑒𝑛𝑠𝑖𝑡𝑦

𝜌 = 728.57 kg/m3

𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 𝑆 = 𝑆=

𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑙𝑖𝑞𝑢𝑖𝑑 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟

728.57 1000

𝑺 = 𝟎. 𝟕𝟐𝟖𝟓𝟕 1.99) Calculate the mass density and specific volume of one litre of a liquid which weighs 7 N.


Given: 7N =

7

= 0.7135 kg

Mass

m

=

Volume

V

= 1 litre = 1*10-3 m3

9.81

Solution: 𝑀𝑎𝑠𝑠 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 =

𝑀𝑎𝑠𝑠 𝑜𝑓 𝑓𝑙𝑢𝑖𝑑 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑓𝑙𝑢𝑖𝑑

0.7135 1 ∗ 10−3 𝒌𝒈⁄ 𝝆 = 𝟕𝟏𝟑. 𝟓𝟓𝟕 𝒎𝟑 1 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑉𝑜𝑙𝑢𝑚𝑒 = 𝑀𝑎𝑠𝑠 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑚𝑎𝑠𝑠 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 =

𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑉𝑜𝑙𝑢𝑚𝑒 =

1 713.557

𝟑 𝑺𝒑𝒆𝒄𝒊𝒇𝒊𝒄 𝑽𝒐𝒍𝒖𝒎𝒆 = 𝟏. 𝟒𝟎 ∗ 𝟏𝟎−𝟑 𝒎 ⁄𝒌𝒈

1.100) A soap bubble is formed when the inside pressure is 5 N/m2above the atmospheric pressure. If surface tension in the soap bubble is 0.0125 N/m, find the diameter of the bubble formed.


Given: p = 5 N/m2

σ = 0.0125 N/m



Solution:

𝒑= 5=

𝟖𝝈 𝒅

8 ∗ 0 .0125 𝑑

d = 0.02m 1.101) The converging pipe with inlet and outlet diameters of 200 mm and 150 mm carries the oil whose specific gravity is 0.8. The velocity of oil at the entry is 2.5 m/s, find the velocity at the exit of the pipe and oil flow rate. [AU, April / May - 2010] Given: D1 = 200 mm

D2 = 150mm

S = 0.8

V1 = 2.5m/s

Solution: Discharge Q = A1V1 𝜋 2

𝑄 =

4

∗ 0.2 ∗ 2.5

Q = 0.0785 m3/sec According to continuity equation

A1V1 = A2V2

𝜋 𝜋 ∗ 0.22 ∗ 2.5 = ∗ 0.152 ∗ 𝑉2 4 4 𝑉2 = 4.44𝑚/𝑠 1.102) Find the height through which the water rises by the capillary action in a 2mm bore if the surface tension at the prevailing temperature is0.075 g/cm. [AU, April / May - 2003] Given: d = 0.2cm

σ = 0.75*10-3 kg/cm

Solution:

𝑐𝑎𝑝𝑖𝑙𝑙𝑎𝑟𝑦 𝑟𝑖𝑠𝑒 (ℎ) =

4𝜎 𝑤𝑑

𝑤 = 𝜌𝑔 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 20


= 1000 * 9.81 = 9810 kg/m3 =0.00981kg/cm3

ℎ =

4𝜎 𝑤𝑑

4 ∗ 0.75 ∗ 10−3 ℎ= 0.00981 ∗ 0.2 h = 1.52cm 1.103) Find the height of a mountain where the atmospheric pressure is 730mm of Hg at normal conditions.

[AU, Nov / Dec - 2009]

Given: h = 730mm of Hg = 0.73m Solution: Specific weight (𝑤) = 𝜌𝑔 w = 13.6 * 9.81 = 133.416 kg/m3 Height of the mountain = H =

𝑃𝑎𝑡𝑚 𝜌𝑤 ∗ 𝑔

133.416 ∗ 0.73 1000 ∗ 9.81 H = 9.93m

1.104) Suppose the small air bubbles in a glass of tap water may be on the order of 50 μ m in diameter with surface tension 0.0125 N/m. What is the pressure inside these bubbles?

[AU, Nov / Dec - 2010]

Given: d = 50 * 10-3m

σ = 0.0125 N/m

Solution:

𝒑= 𝑝=

𝟖𝝈 𝒅

8 ∗ 0 .0125 50 ∗ 10−3

p = 2.05 N/m2 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 21


1.105) An open tank contains water up to depth of 2.85m and above it an oil of specific gravity 0.92 for the depth of 2.1m. Calculate the pressures at the interface of two liquids and at the bottom of the tank. [AU, April / May - 2011] Given: Height of water

Z1 = 2.85m

Height of oil

Z2 = 2.1m

Specific gravity of oil

S0 = 0.92

Density of water

ρ1 = 100 kg/m3

Density of oil

ρ2 = 0.92 * 1000 = 920 kg/m3

Solution: Pressure intensity at interface of liquid: p=ρ*g*z p = ρ2 * g * z2 = 920 * 9.81 * 2.1 p = 18952.92 N/m2 Pressure intensity at bottom of the tank p = ρ1 * g1 * z1 + ρ2 * g2 * z2 = 1000 * 9.81 * 2.85 + 920 * 9.81 * 2.1 p = 46911.42 N/m2 1.106) Two horizontal plates are placed 12.5mm apart, the space between them is being filled with oil of viscosity 14 poise. Calculate the shear stress in the oil if the upper plate is moved with the velocity of 2.5m/s. [AU, May / June - 2012] Given: dy = 0.0125 m

µ = 14 poise = 1.4 Ns/m2

u = 2.5m/s

Solution: 𝜏= 𝜇

𝑑𝑢 𝑑𝑦

du = change in velocity between plates = u – 0 = 2.5m/sec 𝜏 = 1.4 ∗

2.5. 0.125

𝝉 = 𝟐𝟖𝟎 𝑵/𝒎𝟐 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 22


UNIT - II - FLOW THROUGH CIRCULAR CONDUCTS 2.1) How are fluid flows classified?

[AU, May / June - 2012]

 Steady and Unsteady flow  Uniform and Non – uniform flow  Laminar and Turbulent  Compressible flow and Incompressible flow  Rotational and Irrotational flow  One, Two and Three dimensional flow 2.2) Distinguish between Laminar and Turbulent flow. Laminar flow

[AU, Nov / Dec - 2006]

Turbulent flow







denied path or stream line.  The stream lines are straight and

 The stream lines are not straight to each other

parallel to each other

2.3) Write down Hagen Poiseuille’s equation for laminar flow. [AU, April / May - 2005, Nov / Dec - 2012]

𝑝1 − 𝑝2 32𝜇𝑢𝐿 = 𝜌𝑔 𝜌𝑔𝐷2 Where p1 and p2 pressure at inlet and outlet of the pipe µ = Dynamic viscosity u = Velocity of the fluid L = Length of the pipe D = Diameter of the pipe 2.4) Write the Hagen – Poiseuille’s Equation and enumerate its importance. [AU, April / May - 2011]

𝑝1 − 𝑝2 32𝜇𝑢𝐿 = 𝜌𝑔 𝜌𝑔𝐷2 Where p1 and p2 pressure at inlet and outlet of the pipe



µ Dynamic viscosity u Velocity of the fluid L Length of the pipe D Diameter of the pipe 2.5) State Hagen – Poiseuille’s formula for flow through circular tubes. [AU, May / June - 2012]

𝑝1 − 𝑝2 32𝜇𝑢𝐿 = 𝜌𝑔 𝜌𝑔𝐷2 Where p1 and p2 pressure at inlet and outlet of the pipe µ Dynamic viscosity u Velocity of the fluid L Length of the pipe D Diameter of the pipe 2.6) Write down the Darcy - Weisbach’s equation for friction loss through a pipe [AU, Nov / Dec - 2009, April / May - 2011]

4𝑓𝐿𝑉 2 ℎ𝑓 = 2𝑔𝐷 f = coefficient of friction L = length of the pipe V =velocity of the fluid D = diameter of the pipe g = acceleration due to gravity 2.7) What is the relationship between Darcy Friction factor, Fanning Friction [AU, Nov / Dec – 2010, May / June - 2012]

Factor and Friction coefficient? Darcy Friction factor Dimensionless used

in

calculations.

fluid

Fanning Friction Factor

number Dimensionless flow used

in

fluid

Friction coefficient

number Friction factor is the factor flow equating

the

Darcy- calculations. It is related to proportionality

Weisbach equation relates the shear stress at the wall above losses hl to length of pipe as: L, diameter D, and velocity

two

for

the

head

loss

friction equation. DarcyWeisbach friction factor, is



V

by

a

dimensionless

four times the size of the

friction factor1 f

Fanning friction factor, also called f.

2.8) Mention the types of minor losses.


The losses due to disturbance in the flow pattern is called as minor losses.  Loss due to sudden enlargement  Loss due to sudden contraction  Loss due to entrance  Loss due to exit  Loss due to bends or pipe fittings  Head loss due to an obstacle in a pipe 2.9) List the minor losses in flow through pipe. [AU, April / May - 2005, May / June - 2007]  Loss due to sudden enlargement  Loss due to sudden contraction  Loss due to entrance  Loss due to exit  Loss due to bends or pipe fittings  Head loss due to an obstacle in a pipe 2.10) What are minor losses? Under what circumstances will they be negligible? [AU, May / June - 2012] The losses due to disturbance in the flow pattern is called as minor losses. In case of long pipe, it does not makes any serious effect. 2.11) Distinguish between the major loss and minor losses with reference to flow through pipes.

[AU, May / June - 2009]

Major loss  The major loss of energy is due to friction

Minor loss  The losses due to disturbance in the flow pattern is called as major loss



 It depends on roughness of pipe,

 It occurs due to sudden expansion

length, velocity and diameter of

or contraction, valves, fittings,

pipe

bends and at entrance and exit of pipe

 Dracy formula is used as major formula

 Dracy formula is not used for minor losses

 Major losses cannot be neglected

 Minor losses is neglected in case of large pipe

2.12) List the causes of minor energy losses in flow through pipes. [AU, Nov / Dec - 2009]  Loss due to sudden enlargement  Loss due to sudden contraction  Loss due to entrance  Loss due to exit  Loss due to bends or pipe fittings  Head loss due to an obstacle in a pipe 2.13) What do you understand by minor energy losses in pipes? [AU, Nov / Dec - 2008] The losses due to disturbance in the flow pattern is called as minor losses. It occurs due to sudden expansion or contraction, valves, fittings, bends and at entrance and exit of pipe 2.14) What are ‘major’ and ‘minor losses’ of flow through pipes? [AU, May / June 2007, Nov / Dec - 2007, 2012, April / May - 2010] The major loss of energy is due to friction. It depends on roughness of pipe, length, velocity and diameter of pipe. The minor loss due to disturbance in the flow pattern is called as minor losses. It occurs due to sudden expansion or contraction, valves, fittings, bends and at entrance and exit of pipe



2.15) List the minor and major losses during the flow of liquid through a pipe. [AU, April / May - 2008] The major loss of energy is due to friction. It depends on roughness of pipe, length, velocity and diameter of pipe. The minor loss due to disturbance in the flow pattern is called as minor losses. It occurs due to sudden expansion or contraction, valves, fittings, bends and at entrance and exit of pipe 2.16) Enlist the various minor losses involved in a pipe flow system. [AU, Nov / Dec - 2008]  Loss due to sudden enlargement  Loss due to sudden contraction  Loss due to entrance  Loss due to exit  Loss due to bends or pipe fittings  Head loss due to an obstacle in a pipe 2.17) Write the expression for calculating the loss due to sudden expansion of the pipe.

[AU, April / May - 2015] (𝑽𝟏 − 𝑽𝟐 )𝟐 𝒉𝒆 = 𝟐𝒈 V1 = Velocity at inlet V2 = Velocity at outlet g = Acceleration due to gravity

2.18) What factors account in energy loss in laminar flow. [AU, May / June - 2012]  Due to friction between the inner circumference of a pipe and fluid flow  Due to viscosity of a fluid (friction between the internal molecules of a fluid) 2.19) What is meant by laminar flow instability?

[AU, Nov / Dec - 2014]

Stability of laminar flow is disturbed by infinitesimal particles (Small change in pressure, Temperature, viscosity, density & other fluid and flow properties) are leads to converting the laminar flow into turbulent flow, even though the Reynold’s no is with in laminar flow range. The above phenomena is called laminar flow instability. CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 27


2.20) Differentiate between pipes in series and pipes in parallel. [AU, Nov / Dec - 2006] Pipe in series

Pipe in parallel

 When the pipe of different length

 When a pipeline divides into two

and diameters are connected to

or more parallel pipes which

each other to form a pipe line the

again join together at downstream

such a pipeline is called as pipe in

then that pipe is said to parallel  Discharge in the main pipe is

series  Discharge in each pipe will be

equal to sum of discharge in each of the parallel pipes Q = Q1 + Q2

same Q = Q1 = Q2

2.21) What is Darcy's equation? Identify various terms in the equation. [AU, April / May - 2011]

4𝑓𝐿𝑉 2 ℎ𝑓 = 2𝑔𝐷 f = coefficient of friction L = length of the pipe V =velocity of the fluid D = diameter of the pipe g = acceleration due to gravity 2.22) When is the pipe termed to be hydraulically rough? [AU, Nov / Dec - 2009]  The pipe which has poor internal surface finish.  The pipe should have very high friction factor  The pipe should have rough surface. 2.23) What is the physical significance of Reynold's number? [AU, May / June, Nov / Dec - 2007]  Motion of air planes  Flow is incompressible fluid in close pipes  Motion of submarines  Flow around structures and other bodies immersed fully in moving fluids



2.24) Define Reynolds Number.

[AU, Nov / Dec - 2012]

It is defined as the ratio of inertia force of a flowing fluid and viscous force of the fluid. 2.25) What are the uses of Moody’s diagram?

[AU, Nov / Dec - 2008, 2012]

 It is used for determining friction factor for any turbulent flow problem  It can be used for non-circular conduits and also for open channels. 2.26) Mention the use of Moody diagram.


 It is used for determining friction factor for any turbulent flow problem  It can be used for non-circular conduits and also for open channels. 2.27) State the importance of Moody's chart.

[AU, Nov / Dec - 2014]

The Moody’s chart is a graph plotted to find Darcy – Weisbach friction factor for commercial pipe. The diagram is plotted in the form of frictional factor verses Reynold’s number for various values of relative roughness (R/k). The curve is plotted using the following equation

𝑅⁄ 𝑅 𝑘 ) − 2 𝑙𝑜𝑔10 ( ) = 1.74 − 2 𝑙𝑜𝑔10 (1 + 18.71 𝑘 𝑅𝑒 √𝑓 √𝑓 1

 It is used for determining friction factor for any turbulent flow problem  It can be used for non-circular conduits and also for open channels. 2.28) How does surface roughness affect the pressure drop in a pipe if the flow is turbulent?

[AU, Nov / Dec - 2013]

In turbulent flow, the tubes with rough surface have much higher friction factors than the tubes with smooth surface, and thus much larger pressure drop. 2.29) A piping system involves two pipes of different diameters (but of identical length, material, and roughness) connected in parallel. How would you compare the flow rates and pressure drops in these two pipes?

[AU, Nov / Dec - 2013]

For a piping system that involves two different pipes of different diameters connected in parallel. The flow rate through the larger diameter pipe is larger and the pressure drop through both pipes is the same.



2.30) What do you mean by flow through parallel pipes? [AU, May / June – 2013 When the pipe divides into two or more branches and again join together downstream to form a single pipe then it is called as pipes in parallel. The governing equations are: Q = Q1 + Q2 hf1 = hf2 2.31) Give the expression for power transmission through pipes? [AU, Nov / Dec - 2008] Power available at the outlet of the pipe 𝑃 = 𝑤𝑄ℎ 𝜋 4𝑓𝐿𝑉 2 2 𝑃 = 𝑤 ∗ ∗ 𝐷 ∗ 𝑣 ∗ (𝐻 − ) 4 2𝑔𝐷 Maximum power transmission ℎ𝑓 =

𝐻 3

The power transmitted through the pipe is maximum when head lost due to friction in the pipe is equal to 1/3 of the total head supplied. 2.32) Define boundary layer and boundary layer thickness. [AU, Nov / Dec – 2007, 2008, 2012] The variation of velocity from zero to free stream velocity in the direction normal to the boundary takes place in a narrow region in the vicinity of solid boundary. This narrow region of the fluid is called as boundary layer. Boundary layer thickness as the distance from the boundary of the solid body measured in y – direction to the point, where the velocity of the fluid is approximately equal to 0.99 times the free stream velocity of the fluid. 2.33) Define boundary layer thickness. [AU, May / June - 2006, Nov / Dec - 2009] Boundary layer thickness as the distance from the boundary of the solid body measured in y – direction to the point, where the velocity of the fluid is approximately equal to 0.99 times the free stream velocity of the fluid. 2.34) What is boundary layer? Give its sketch of a boundary layer region over a flat plate.

[AU, April / May – 2003, 2010]



The variation of velocity from zero to free stream velocity in the direction normal to the boundary takes place in a narrow region in the vicinity of solid boundary. This narrow region of the fluid is called as boundary layer.

2.35) What is boundary layer? Why is it significant?

[AU, Nov / Dec - 2009]

The variation of velocity from zero to free stream velocity in the direction normal to the boundary takes place in a narrow region in the vicinity of solid boundary. This narrow region of the fluid is called as boundary layer.

2.36) Give the classification of boundary layer flow based on the Reynolds number. [AU, April / May - 2015]  Laminar boundary layer  Transition boundary layer  Turbulent boundary layer



2.37) What is boundary layer and write its types of thickness? [AU, Nov / Dec – 2005, 2006] The variation of velocity from zero to free stream velocity in the direction normal to the boundary takes place in a narrow region in the vicinity of solid boundary. This narrow region of the fluid is called as boundary layer. Types of boundary layer  Displacement thickness  Momentum thickness  Energy thickness 2.38) What do you understand by the term boundary layer? [AU, Nov / Dec - 2008] The variation of velocity from zero to free stream velocity in the direction normal to the boundary takes place in a narrow region in the vicinity of solid boundary. This narrow region of the fluid is called as boundary layer. 2.39) What is a laminar sub layer?

[AU, Nov / Dec - 2010]

Within a turbulent boundary layer zone, if the boundary is smooth, a thin layer adjacent to the plate surface over which the flow is assumed to be laminar is called laminar sub – layer. The velocity distribution in the laminar sub – layer is assumed to be linear. 2.40) Define momentum thickness and energy thickness. [AU, May / June – 2007, 2012] Momentum thickness is defined as the distance measured perpendicular to the boundary of the solid body, by which the boundary should be displaced to compensate for the reduction in momentum of the flowing fluid on account of boundary layer formation. Energy thickness is defined as the distance measured perpendicular to the boundary of the solid body, by which the boundary should be displaced to compensate for the reduction in kinetic energy of the flowing fluid on account of boundary layer formation.



2.41) Define the term boundary layer.

[AU, May / June - 2009]

The variation of velocity from zero to free stream velocity in the direction normal to the boundary takes place in a narrow region in the vicinity of solid boundary. This narrow region of the fluid is called as boundary layer. 2.42) What is boundary layer separation?

[AU, Nov / Dec - 2012]

The boundary layer is formed on the flat plate when it is held immersed in a flowing liquid. If the immersed plate or body is curved or angular one, the boundary layer does not stick to the whole surface and gets separated from it. This phenomenon is known as boundary layer separation. 2.43) What do you mean by displacement thickness and momentum thickness? [AU, Nov / Dec - 2008] Displacement thickness is defined as the distance, measured perpendicular to the boundary of the solid body, by which the boundary should be displaced to compensate for reduction in flow rate on account of boundary layer formation. Momentum thickness is defined as the distance measured perpendicular to the boundary of the solid body, by which the boundary should be displaced to compensate for the reduction in momentum of the flowing fluid on account of boundary layer formation. 2.44) What do you understand by hydraulic diameter?

[AU, Nov / Dec - 2011]

Hydraulic diameter is the effective diameter of wetted surface when the flow takes through the system. It is the ratio of wetted area to the wetted perimeter. 2.45) What is hydraulic gradient line?

[AU, May / June - 2009]

Hydraulic gradient line is defined as the line which gives the sum of pressure head and datum head of the flowing fluid in a pipe with respect to some reference line or it is the line which is obtained by joining top of all vertical ordinates, showing the pressure head of a flowing fluid in a pipe from the center pipe. 2.46) Define hydraulic gradient and energy gradient.

[AU, Nov / Dec - 2011]

Hydraulic gradient is the piezometric head which is the sum of potential head and datum head. Energy gradient is the sum of hydraulic gradient and kinetic head.



2.47) Brief on HGL.


Hydraulic Gradient Line is defined as the line which gives the sum of pressure head and datum head of the flowing fluid in a pipe with respect to some reference line or it is the line which is obtained by joining top of all vertical ordinates, showing the pressure head of a flowing fluid in a pipe from the center pipe. 2.48) Differentiate between Hydraulic gradient line and total energy line. [AU, Nov / Dec - 2003, April / May - 2005, 2010, May / June–2007, 2009] Hydraulic Gradient Line

Total Energy Line

 It is the sum of pressure head and

 Total energy line is the sum of

datum head with respect to datum

velocity head, pressure head and

line.

datum head.

 Hydraulic grade line less below total energy line by

𝑉2

 Total energy line has above hydraulic grade line by

2𝑔

𝑉2 2𝑔

2.49) Differentiate hydraulic gradient line and energy gradient line. [AU, May / June - 2014] Hydraulic Gradient Line

Energy Gradient Line

 Pressure Energy alone plotted along the flow to some specified

 The total energy plotted along the flow to some specified scale gives the energy line.

scale gives the energy line.  The plot of

𝑃

+ 𝑧 along the flow 𝛾

is called the hydraulic gradient line.  The

 Energy line is the plot of

𝑃 𝛾

+

𝑉2 𝑧 + 2𝑔 along the flow. It is constant along the flow when

hydraulic

gradient

line

provides useful information about pressure variations (static head) in a flow.

losses are negligible  The

hydraulic

gradient

line

provides useful information about total head variations in a flow.



2.50) Differentiate between hydraulic grade line and energy grade line. [AU, Nov / Dec - 2014] Hydraulic Grade Line

Energy Grade Line

 Pressure Energy alone plotted along the flow to some specified

 The total energy plotted along the flow to some specified scale gives the energy line.

scale gives the energy line.  The plot of

𝑃 𝛾

+ 𝑧 along the flow

is called the hydraulic gradient line.  The

 Energy line is the plot of

𝑃 𝛾

+

𝑉2 𝑧 + 2𝑔 along the flow. It is constant along the flow when

hydraulic

gradient

line

provides useful information about pressure variations (static head) in a flow. 2.51) What is T.E.L?

losses are negligible  The

hydraulic

gradient

line

provides useful information about total head variations in a flow. [AU, Nov / Dec - 2009]

Total Energy Line is defined as the line which gives the sum of pressure head, datum head and kinetic head of a flowing fluid in a pipe with respect to reference line. It is also defined as the line which is obtained by joining the tops of all vertical ordinates showing the sum of pressure head and kinetic head from the center of the pipe. 2.52) Distinguish between hydraulic and energy gradients. [AU, Nov / Dec - 2011] Hydraulic gradient is the piezometric head which is the sum of potential head and datum head. Energy gradient is the sum of hydraulic gradient and kinetic head. 2.53) What are stream lines, streak lines and path lines in fluid flow? [AU, Nov / Dec –2006, 2009] In Euler’s approach, the velocity vector is defines as a function of time and space coordinates. If for a fixed instance time a space curve is drawn so that it is tangent everywhere to the velocity vector, then the curve is called as stream line. Path line are the outcome of the Lagrange method in describing fluid flow and show the paths of different fluid particles as a function of time. CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 35


A streak line at any instant of time is the locus of the temporary location of all particles that have passed through a fixed point in the flow field. 2.54) Define flow net.

[AU, Nov / Dec - 2008]

A grid obtained by drawing a series of equipment lines and steam lines is called a flow net. The flow net is an important tool is analysis two dimensional irrotational flow problems. 2.55) What is flow net and state its use?


A grid obtained by drawing a series of equipment lines and steam lines is called a flow net. The flow net is an important tool is analysis two dimensional irrotational flow problems. 2.56) Define lift.

[AU, Nov / Dec - 2005]

The component of total force in the direction perpendicular to the direction of flow is known as lift. 2.57) Define the terms: drag and lift.


The component of total force in the direction of flow of fluid is known as drag. The component of total force in the direction perpendicular to the direction of flow is known as lift. 2.58) Give the expression for Drag coefficient and Lift coefficient. [AU, April / May - 2011] Drag coefficient Cd is defined by

𝐹𝐷 =

1 𝜌 𝑉 2 𝐶𝑑 𝐴 2

FD = The drag force, which is by definition the force component in the direction of the flow velocity

ρ = The mass density of the fluid V = The velocity of the object relative to the fluid A = The reference area

Cd = the drag coefficient – a dimensionless coefficient related to the object's geometry and taking into account both skin friction and form drag



The lift coefficient CL is defined by 𝐶𝐿 =

𝐿 𝑞𝑆

Where L = The lift force S = Plan form area and q = The fluid dynamic pressure. 2.59) Considering laminar flow through a circular pipe, draw the shear stress and velocity distribution across the pipe section.

[AU, Nov / Dec - 2010]

2.60) Considering laminar flow through a circular pipe, obtain an expression for the velocity distribution.

[AU, Nov / Dec - 2012]

𝑢= −

1 𝜕𝑝 (𝑡𝑦 − 𝑦 2 ) 2𝜇 𝜕𝑥

In the above equation µ, ∂p/∂x and t are constant. 2.61) A circular and a square pipe are of equal sectional area. For the same flow rate, determine which section will lead to a higher value of Reynolds number. [AU, Nov / Dec - 2011] Area of square section

AS = Area of circular section

AC

𝜋 2 𝐷 4 Where L is the side of a square and D be the diameter of a 𝐿2 =

circular section. CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 37


L = 0.886 D Reynold’s number for circular section

𝑅𝑒 𝑐𝑖𝑟𝑐𝑢𝑙𝑎𝑟 =

𝜌𝑣𝐷 𝜇

Reynold’s number for square section

𝑅𝑒 𝑠𝑞𝑢𝑎𝑟𝑒

𝜌𝑣𝐿 = 𝜇

𝑅𝑒 𝑠𝑞𝑢𝑎𝑟𝑒 = 0.886 𝑅𝑒 𝑐𝑖𝑟𝑐𝑢𝑙𝑎𝑟 2.62) A 20cm diameter pipe 30km long transport oil from a tanker to the shore at 0.01m3/s. Find the Reynolds number to classify the flow. Take the viscosity μ = 0.1 Nm/s2 and density ρ = 900 kg/m3 for oil.


Given: D = 0.2m

L = 30 * 103m

Q = 0.01m3/s

μ = 0.1 Nm/s2

ρ = 900 kg/m3 Solution: Cross sectional area:

𝜋 2 𝐷 4 𝜋 𝐴 = ∗ 0.22 4 𝐴=

𝐴 = 0.03141𝑚2 Velocity of the flow

𝑄 𝑣= 𝐴 0.01 𝑣= 0.03141 𝑣 = 0.318 𝑚/𝑠 𝑅𝑒 =

𝜌𝑣𝐷 𝜇



𝑅𝑒 =

900 ∗ 0.318 ∗ 0.2 0.1

𝑅𝑒 = 572.95 < 2000 The flow is laminar 2.63) Find the loss of head when a pipe of diameter 200 mm is suddenly enlarged to a diameter 0f 400 mm. Rate of flow of water through the pipe is 250 litres/s. [AU, April / May - 2010] Given: D1 = 200mm

D2 = 400mm

Q = 0.250m3/s

Solution: From continuity equation:

𝑄 = 𝐴1 𝑉1 𝜋 . 250 = ∗ 0.22 ∗ 𝑉1 4 𝑉1 = 7.95 𝑚/𝑠 From continuity equation:

𝑄 = 𝐴2 𝑉2 𝜋 . 250 = ∗ 0.42 ∗ 𝑉2 4 𝑉2 = 1.98 𝑚/𝑠 Head loss due to enlargement

(𝑉1 − 𝑉2 )2 ℎ𝑒 = 2𝑔 (7.95 − 1.98)2 ℎ𝑒 = 2 ∗ 9.81 ℎ𝑒 = 1.81𝑚



UNIT - III - DIMENSIONAL ANALYSIS 3.1) What do you understand by fundamental units and derived units? [AU, April / May - 2010] The physical parameters are independent of each other called fundamental or primary quantities / parameters. Example: Mass, length and time The parameters which are expressed in terms of primary quantities are called secondary or derived quantities. Example: velocity, force and power. 3.2) Differentiate between fundamental units and derived units. Give examples. [AU, Nov / Dec - 2011] Fundamental Units  The physical parameters are independent of each other called fundamental or primary quantities / parameters.  Example: Mass, length and time

Derived Units  The

parameters

which

are

expressed in terms of primary quantities are called secondary or derived quantities.  Example: velocity, force and power.

3.3) What do you mean by dimensional analysis?

[AU, Nov / Dec - 2009]

Dimensional analysis is a mathematical technique which deals with the dimensions of the physical quantities involved in the phenomenon. Some complex problems in nature and very difficult to solve. This type of problem can be simplified by using dimensional analysis. 3.4) Brief on dimensional variables with examples.

[AU, Nov / Dec - 2014]

Dimensional variables are the quantities that actually vary during a given case and would be plotted against each other to show the data.

In the above equation dimensional variables are S and t

In the above equation dimensional variables are p, V, and z. CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 40


3.5) Brief on Intuitive method. Give some examples.

[AU, Nov / Dec - 2014]

Most Dimensional analysis methods are called as Intuitive method, with the help of units and dimensions they are able to form a physical relationship among several variables. Examples Buckingham π Theorem & Rayleigh's method of dimensional analysis 3.6) What is dimensional homogeneity and write any one sample equation? [AU, Nov / Dec - 2006] Dimensional analysis is based on the principle that the variables in a physical phenomenon is arranged properly to give an equation which is dimensionally homogenous. To check the dimensional homogeneity of the Dracy’s Equation.

𝑓𝑙𝑉 2 ℎ𝑓 = 2𝑔𝑑 Dimension of L.H.S

=

Dimension of R.H.S

=

hf

=L

𝑓𝑙𝑉 2 2𝑔𝑑

=

1∗𝐿∗(𝐿/𝑇)2 𝐿

2∗( 2 )∗𝐿 𝑇

=L

Where f constant is taken as 1 and number 2 is neglected Dimension of L.H.S

=

Dimension of R.H.S

3.7) Explain the term dimensional homogeneity.

[AU, Nov / Dec - 2011]

The law of Fourier principle of dimensional homogeneity states “an equation which expresses a physical phenomenon of fluid flow should be algebraically correct and dimensionally homogenous” Dimensional analysis is based on the principle that the variables in a physical phenomenon is arranged properly to give an equation which is dimensionally homogenous. To check the dimensional homogeneity of the Dracy’s Equation.

𝑓𝑙𝑉 2 ℎ𝑓 = 2𝑔𝑑 Dimension of L.H.S Dimension of R.H.S

= =

hf

=L


=

1∗𝐿∗(𝐿/𝑇)2 𝐿

2∗( 2 )∗𝐿 𝑇

=L




=

Dimension of R.H.S

3.8) State a few applications, usefulness of ‘dimensional analysis’. [AU, May / June - 2007]  It is used to change the theoretical equation into a simple dimensionless form.  By dimensional analysis, any complex fluid flow phenomenon can be easily solved.  It helps to convert the units of quantities from one system to another system. 3.9) What is a dimensionally homogenous equation? Give example. [AU, Nov / Dec - 2003] Dimensional analysis is based on the principle that the variables in a physical phenomenon is arranged properly to give an equation which is dimensionally homogenous. To check the dimensional homogeneity of the Dracy’s Equation.

𝑓𝑙𝑉 2 ℎ𝑓 = 2𝑔𝑑 Dimension of L.H.S Dimension of R.H.S

= =

hf

=L


=

1∗𝐿∗(𝐿/𝑇)2 𝐿

2∗( 2 )∗𝐿 𝑇

=L


=

Dimension of R.H.S

3.10) Cite examples for dimensionally homogeneous and non-homogeneous equations.

[AU, Nov / Dec - 2010]

Dimensionally homogeneous equation  Head loss in flow through pipes  Reynolds number  Bernoulli’s equation Non – homogenous equation  Equation of simple harmonic motion CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 42


 The second order linear equation of both free and forced damped oscillation 3.11) Check whether the following equation is dimensionally homogeneous. Q =Cd .a √(2 gh) .

[AU, April / May - 2011] 𝑄 = 𝐶𝑑 ∗ 𝑎 √2𝑔ℎ

Dimension of each parameter = L3T-1

Q

=

Discharge

Cd

=

Coefficient of discharge = 1

a

=

Area

= L2

g

=

Acceleration

= LT-2

h

=

Height

=L

𝐿3 𝑇 −1 = 𝐿2 ∗ (𝐿𝑇 −2 ∗ 𝐿)1/2 𝐿3 𝑇 −1 = 𝐿2 ∗ (𝐿2 𝑇 −2 )1/2 𝐿3 𝑇 −1 = 𝐿3 𝑇 −1 Since both the sides are identical. The given equation is dimensionally homogenous 3.12) Write the dimensions of surface tension and vapour pressure in MLT system.

[AU, April / May - 2015] Surface tension

=

MT-2

Vapour pressure

=

ML-1T-2

3.13) Give the Rayleigh method to determine dimensionless groups. [AU, Nov / Dec - 2011]  First the functional relationship is written with the given data. Consider X as a variable which depends on X1, X2, X3… Xn. So, the functional equation is written as X = f (X1, X2, X3… Xn)  Then the equation is expressed in the terms of a constant with exponents like powers of a, b, c … Therefore the equation is again written as

X = Φ(X1a, X2b, X3c… Xnz). Here Φ = constant. a ,b,

c…z are arbitrary constants.



 The values of a, b, c … z are determined with the help of dimensional homogeneity. It means, the powers of the fundamental dimensions on both sides are compared to obtain the values of exponents.  Finally, the exponent’s power values are substituted in the functional equation and simplified to obtain the suitable form. 3.14) State any two choices of selecting repeating variables in Buckingham π theorem.

[AU, April / May - 2011]  No repeating variable should be dimensionless  The selected two repeating variables should not have the same dimensions.  The selected repeating variables should be independent as far as possible.

3.15) State Buckingham’s π theorem.

[AU, Nov / Dec – 2008, 2012]

It states that if there are ‘n’ variables in a dimensionally homogenous equation and if these variables contain ‘m’ fundamental dimensions (M, L, T) then they are grouped into (n – m), dimensionless independent π – terms. 3.16) The excess pressure Δp inside a bubble is known to be a function of the surface tension and the radius. By dimensional reasoning determine how the excess pressure. Will vary if we double the surface tension and the radius. [AU, Nov / Dec - 2013]

∆𝑝 = 𝑓(𝑎 , 𝑟) = (𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 )𝑎𝑎 𝑟 𝑏 𝐹 𝐹 𝑎 ( 2 ) = ( ) (𝐿)𝑏 𝐿 𝐿 F: a =1

L: -a+b = -2 b = -1 𝜎 ∆𝑝 = 𝑟

If σ is doubled Δp is doubled If r is doubled Δp is half 3.17) Distinguish between Rayleigh's method and Buckingham's π- theorem. [AU, April / May - 2011]



Buckingham's π- theorem

Rayleigh's method  The expression is determined for a

variable

depending

upon

maximum three or four variables

 It is easy for the number of independent variables being more than three or four

only  This method is difficult for more

 In this method ‘n’ variables can be used without any difficulties

than four variables

3.18) What are the similitudes that should exist between the model and its prototype?


 Geometric similitude  Kinematic similitude  Dynamic similitude 3.19) What are the types of similarities?

[AU, Nov / Dec - 2012]

 Geometric similarity  Kinematic similarity  Dynamic similarity 3.20) What is meant by dynamic similarity?

[AU, Nov / Dec - 2008]

Dynamic similarity means the similarity of forces between the model and prototype. Thus the dynamic similarity is said to exist between the model and the prototype if the ratios of the corresponding forces acting at the corresponding points are equal. Let (Fi)p

= Inertia force at a point in prototype

(Fv)p

= Viscous force at a point in prototype

(Fg)p

= Gravity force at a point in prototype

(Fi)m

= Inertia force at a point in model

(Fv)m

= Viscous force at a point in model

(Fg)m

= Gravity force at a point in model

Fr

= Force ratio (𝐹𝑔 )𝑝 (𝐹𝑖 )𝑝 (𝐹𝑣 )𝑝 = = = 𝐹𝑟 (𝐹𝑖 )𝑚 (𝐹𝑣 )𝑚 (𝐹𝑔 )𝑚



3.21) What is dynamic similarity?

[AU, Nov / Dec - 2009]

Dynamic similarity means the similarity of forces between the model and prototype. Thus the dynamic similarity is said to exist between the model and the prototype if the ratios of the corresponding forces acting at the corresponding points are equal. Let (Fi)p

= Inertia force at a point in prototype

(Fv)p

= Viscous force at a point in prototype

(Fg)p

= Gravity force at a point in prototype

(Fi)m

= Inertia force at a point in model

(Fv)m

= Viscous force at a point in model

(Fg)m

= Gravity force at a point in model

Fr

= Force ratio (𝐹𝑔 )𝑝 (𝐹𝑖 )𝑝 (𝐹𝑣 )𝑝 = = = 𝐹𝑟 (𝐹𝑖 )𝑚 (𝐹𝑣 )𝑚 (𝐹𝑔 )𝑚

3.22) What is meant by kinematic similarity?

[AU, Nov / Dec - 2014]

Kinematic similarity means similarity of motion between model and prototype. Thus the similarity is said to exist between the model and prototype if the ratios of the velocity and acceleration at the corresponding points in the model and the corresponding points in the prototype are the same. Let Vp1

= Velocity of fluid at a point 1 in prototype

Vp2

= Velocity of fluid at a point 2 in prototype

ap1

= Acceleration of fluid at a point 1 in prototype

ap2

= Acceleration of fluid at a point 2 in prototype

Vm1

= Velocity of fluid at a point 1 in model

Vm2

= Velocity of fluid at a point 2 in model

am1

= Acceleration of fluid at a point 1 in model

am2

= Acceleration of fluid at a point 2 in model 𝑉𝑝1 = 𝑉𝑚2 𝑎𝑝1 = 𝑎𝑚2

𝑉𝑝2 = 𝑉𝑟 𝑉𝑚2 𝑎𝑝2 = 𝑎𝑟 𝑎𝑚2



3.23) What is similarity in model study?


Similitude is defined as the similarity between the model and its prototype in every respect, which means that the model and prototype have similar properties or model and prototype are completely similar. There are three types of similarities exists between the model and prototype  Geometric Similarity  Kinematic Similarity  Dynamic Similarity 3.24) What is scale effect in physical model study? [AU, Nov / Dec – 2005, 2006, May / June– 2012] It is impossible to product the exact behavior of the prototype by model testing alone. The two models of same prototype behavior will be different. Scale ratios will not be same. So discrepancy between models and prototype will always occur. It is known as scale effect. 3.25) Mention the circumstances which necessitate the use of distorted models. [AU, Nov / Dec - 2010]  To maintain accuracy  To maintain turbulent flow  To accommodate available facilities  To obtain suitable bed materials  To obtain required roughness condition. 3.26) Write down the dimensionless number for pressure. [AU, Nov / Dec - 2011] Pressure

P

= ML-1T-2

3.27) Give the dimensions of power and specific weight. Power

P

= ML2T-2

Specific weight

w

= ML-2T-2

[AU, Nov / Dec - 2009]

3.28) Give the dimensions of the following physical quantities: surface tension and dynamic viscosity. Surface tension

[AU, May / June - 2013] σ

Dynamic viscosity µ

= MT-2 = ML-1T-1

3.29) Define Reynold’s number. What its significance?

[AU, Nov / Dec - 2010]



It is defined as the ratio of inertia force of a flowing fluid and viscous force of the fluid.  Motion of air planes  Flow is incompressible fluid in close pipes  Motion of submarines  Flow around structures and other bodies immersed fully in moving fluids 3.30) Define Reynold’s number and state its significance? [AU, April / May - 2015] It is defined as the ratio of inertia force of a flowing fluid and viscous force of the fluid.  Motion of air planes  Flow is incompressible fluid in close pipes  Motion of submarines  Flow around structures and other bodies immersed fully in moving fluids 3.31) Define Reynold’s number and Froude’s numbers. [AU, Nov / Dec – 2007, 2011] Reynold’s number is defined as the ratio of inertia force of a flowing fluid and viscous force of the fluid. Froude’s number is defined as the square root of the ratio of inertia force of a slowing fluid to the gravity force. 3.32) Define Froude's number. [AU, Nov / Dec – 2005, 2009, 2008, April / May – 2010, May / June - 2012] Froude’s number is defined as the square root of the ratio of inertia force of a slowing fluid to the gravity force. 3.33) Define the Froude's dimensionless number.

[AU, May / June - 2014]

Froude’s number is defined as the square root of the ratio of inertia force of a slowing fluid to the gravity force. 3.34) State Froude's model law.

[AU, May / June - 2013]

Froude model law is the law in which the models are based on Froude number which means for dynamic similarity between the model and prototype, the Froude number for both model and prototype must be equal. Froude model law is applicable when the gravity force is only predominant force which controls the flow in addition to the force of inertia. CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 48


3.35) Define Euler's number.

[AU, May / June - 2009]

Euler’s number is the ratio of the square root of inertia force and pressure force. 3.36) Define Euler number and Mach number.

[AU, May / June - 2007]

Euler’s number is the ratio of the square root of inertia force and pressure force. Mach’s number is defined as the square root of the ratio of the inertia force of a flowing fluid to the elastic force. 3.37) Define Reynold’s number and Mach number.

[AU, Nov / Dec - 2012]

Reynold’s number is defined as the ratio of inertia force of a flowing fluid and viscous force of the fluid. Mach’s number is defined as the square root of the ratio of the inertia force of a flowing fluid to the elastic force. 3.38) Define Mach number.

[AU, May / June - 2009]

Mach’s number is defined as the square root of the ratio of the inertia force of a flowing fluid to the elastic force. 3.39) Define -Mach number and state its application.

[AU, Nov / Dec - 2014]

Mach’s number is defined as the square root of the ratio of the inertia force of a flowing fluid to the elastic force. Its applications are  Aerodynamic testing  Under water testing of torpedoes  Water – hammer problems 3.40) What is Mach number? Mention its field of use.


Mach’s number is defined as the square root of the ratio of the inertia force of a flowing fluid to the elastic force. It is used in  Aerodynamic testing  Under water testing of torpedoes  Water – hammer problems



UNIT – IV – PUMPS 4.1) Mention the main parts of the Centrifugal pump.

[AU, Nov / Dec - 2012]

 Impeller  Casing  Suction pipe  Delivery pipe  Strainer and foot valve  Delivery valve 4.2) How centrifugal pumps are classified based on casing? [AU, May / June - 2006]  Volute pump or constant velocity pump  Vortex pump or variable velocity pump  Diffuser or turbine pump 4.3) List the commonly used casings in centrifugal pumps. [AU, Nov / Dec - 2010]  Volute casing  Vortex casing  Volute casing with guide blades 4.4) What is the role of a volute chamber of a centrifugal pump? [AU, Nov / Dec - 2005]  To guide water to and from the impeller  To partially convert the kinetic energy into pressure energy 4.5) What precautions are to be taken while starting and closing the centrifugal pump?

[AU, May / June - 2012]  While starting the pump. The delivery valve is closed. Priming of the pump is carried out.  Before stopping the pump, it is necessary to close the delivery pipe otherwise the back flow of liquid may take place from the high head reservoir.



4.6) What is priming?

[AU, Nov / Dec - 2010]

Priming of a centrifugal pump is defined as the operation in which the suction pipe, casing of the pump and a portion of the delivery pipe up to the delivery valve is completely filled up from outside source with the liquid to be raised by the pump before starting the pump. Thus the air from these parts of the pump is removed and these parts are filled with the liquid to be pumped. 4.7) Why priming is necessary in a centrifugal pump? [AU, May / June - 2007, April / May - 2010] Priming of a centrifugal pump is defined as the operation in which the suction pipe, casing of the pump and a portion of the delivery pipe up to the delivery valve is completely filled up from outside source with the liquid to be raised by the pump before starting the pump. Thus the air from these parts of the pump is removed and these parts are filled with the liquid to be pumped. If the pump is started with air pockets inside the impeller may give rise to vortices and causes the discontinuity of flow. Under these conditions, the flow of fluid does no commence and the pump runs dry. It causes the rubbing and seizing of the wearing rings, increases noise level and vibrations and finally may cause series damage to pump. 4.8) What is meant by priming of pumps?


Priming of a centrifugal pump is defined as the operation in which the suction pipe, casing of the pump and a portion of the delivery pipe up to the delivery valve is completely filled up from outside source with the liquid to be raised by the pump before starting the pump. Thus the air from these parts of the pump is removed and these parts are filled with the liquid to be pumped. 4.9) What is priming? Why is it necessary?

[AU, Nov / Dec - 2011]

Priming of a centrifugal pump is defined as the operation in which the suction pipe, casing of the pump and a portion of the delivery pipe up to the delivery valve is completely filled up from outside source with the liquid to be raised by the pump before starting the pump. Thus the air from these parts of the pump is removed and these parts are filled with the liquid to be pumped. If the pump is started with air pockets inside the impeller may give rise to vortices and causes the discontinuity of flow. Under these conditions, the flow of CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 51


fluid does no commence and the pump runs dry. It causes the rubbing and seizing of the wearing rings, increases noise level and vibrations and finally may cause series damage to pump. 4.10) Define cavitation.

[AU, Nov / Dec - 2008]

Cavitation is defined as the phenomenon of formation of vapour bubbles of a flowing liquid in a region where the pressure of the liquid falls below the vapour pressure and the sudden collapsing on these vapour in a region of high pressure. 4.11) Define cavitation in a pump.

[AU, May / June - 2007]

Cavitation is defined as the phenomenon of formation of vapour bubbles of a flowing liquid in a region where the pressure of the liquid falls below the vapour pressure and the sudden collapsing on these vapour in a region of high pressure. 4.12) What is the effect of cavitation in pump?


 The metallic surfaces are damaged and cavities are formed on the surfaces.  Due to sudden collapse of vapour bubble, considerable noise and vibrations are produced.  The efficiency of a pump decreases due to cavitation.  Due to pitting action, the surface on the impeller becomes rough. 4.13) What are the effects of cavitation? Give necessary precautions against cavitation?

[AU, May / June - 2012]

The effects of cavitation are  The metallic surfaces are damaged and cavities are formed on the surfaces.  Due to sudden collapse of vapour bubble, considerable noise and vibrations are produced.  The efficiency of a pump decreases due to cavitation.  Due to pitting action, the surface on the impeller becomes rough. Precautions against cavitation  The pressure of the flowing liquid in any part of the hydraulic system should not allowed to fall below its vapour pressure. If the flowing liquid is water, then the absolute pressure head should not be below 2.5m of water. CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 52


 The special materials or coatings such as aluminum – bronze and stainless steel, which are cavitation resistant materials, should be used. 4.14) What is cavitation?

[AU, Nov / Dec - 2013]

Cavitation is defined as the phenomenon of formation of vapour bubbles of a flowing liquid in a region where the pressure of the liquid falls below the vapour pressure and the sudden collapsing on these vapour in a region of high pressure. 4.15) List the losses in centrifugal pump.

[AU, Nov / Dec - 2014]

 Mechanical friction losses between the fixed and rotating parts in the bearings and gland and packing.  Disc friction loss between the impeller surfaces and the fluid.  Leakage and recirculation losses. The recirculation is along the clearance between the impeller and the casing due to the pressure difference between the hub and tip of the impeller 4.16) What are the advantages of centrifugal pump over reciprocating pumps? [AU, May / June - 2009]  Its discharge capacity is much higher  It can also be used for highly viscous fluids like oils, muddy and sewage water, chemicals, paper pulp less  Being high speed machine it can be directly coupled to the prime mover  It is compact, smaller in size and has low weight for the same discharge capacity  Maintenance cost is comparatively very low. 4.17) What is the maximum theoretical suction head possible for a centrifugal pump?


𝑣𝑠 2 ℎ𝑠 = 𝐻𝑎 − 𝐻𝑣 − − ℎ𝑓𝑠 2𝑔 hs

=

Ha

=

Hv =

= Height of inlet of pump from datum line 𝑝𝑎 ⁄𝜌𝑔 𝑝𝑣 ⁄𝜌𝑔

= Atmospheric pressure head (meter of liquid) = Vapour pressure head (meter of liquid)

vs

=

= Velocity of liquid through suction pipe

hfs

=

= Loss of head in foot valve, strainer and suction pipe



4.18) Tabulate the causes and remedies for a centrifugal pump, when pump fails to pump the fluid. S.No

Fault

[AU, April / May - 2015] Other

Cause

Symptoms

Remedies  Stop and reprime.

 Pump has lost its water  Suction and delivery gauges read zero 1

No Output

due to air lock in suction

 Remake pipe joints.

pipe, air leaks in suction  Tighten pipe, air leaks in

glands or

stuffing boxes, or level

repack

of water dropped below

lengthen

strainers

suction pipe to lower strainer

 Suction gauge reads

 Speed too low to

zero but

overcome the total head,

delivery

or choke in delivery

gauge

pipe

normal Poor Output : it should be note that unless a 2

flow meter

 Surging in delivery pressure gauge

is provided,  Suction the pump

gauge shows

attendant

high

has very

vacuum,

 Increase speed.  Clear choke in delivery pipe.  Increase

 Air leak in suction pipe or stuffing boxes or air entering strainer

speed.  Clear choke in delivery pipe.

 Chocked strainer, foot valve or suction pipe.  Vibration and noise due to cavitation

 Clean strainer, foot valve or suction pipe



little to

vibration and

inform him

noise

that the  Clean

output of

 Impeller partly chocked. impeller. the pump is  Suction gauge shows  Partial choke in delivery  Clean choke not normal low vacuum

pipe

in delivery pipe  Replace or

 Pump not

 Motor defective

overhaul

running upto  Voltage low speed

 Check and

 Belt slipping

rectify  Tighten belt

4.19) Define suction head and manometric head of a centrifugal pump. [AU, Nov / Dec - 2012] Suction head (hs) is the vertical height of the center line of the centrifugal pump above the water surface in the tank or pump from which water is lifted. This height is also called suction lift. The Manometric head (Hm) is defines as the head against which a centrifugal pump has to work. 4.20) Define - manometric head and write its mathematical equation. [AU, Nov / Dec - 2013] The Manometric head (Hm) is defines as the head against which a centrifugal pump has to work. Hm = Head imparted by the impeller to the water – loss of head in the pump

𝑉𝑑 2 𝐻𝑚 = ℎ𝑠 + ℎ𝑑 + ℎ𝑓𝑠 + ℎ𝑓𝑑 + 2𝑔 ℎ𝑠 = Suction head ℎ𝑑 = Delivery head ℎ𝑓𝑠 = Frictional head loss in suction pipe CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 55


ℎ𝑓𝑑 = Frictional head loss in delivery pipe 𝑉𝑑 = Velocity of water in delivery pipe 4.21) What do you mean by ‘Net Positive Suction Head’ (NPSH)? [AU, May / June - 2014] The Negative Positive Suction Head (NPSH) is defined as the absolute pressure head at the inlet to pump, minus the vapour pressure head (in absolute units) plus the velocity head. NPSH = Absolute pressure head at inlet of the pump – vapour pressure head (absolute units) + velocity head 4.22) Define ‘Net Positive Suction Head’

[AU, Nov / Dec - 2014]

The Negative Positive Suction Head (NPSH) is defined as the absolute pressure head at the inlet to pump, minus the vapour pressure head (in absolute units) plus the velocity head. NPSH = Absolute pressure head at inlet of the pump – vapour pressure head (absolute units) + velocity head 4.23) What is meant by NPSH?

[AU, Nov / Dec - 2014]

The Negative Positive Suction Head (NPSH) is defined as the absolute pressure head at the inlet to pump, minus the vapour pressure head (in absolute units) plus the velocity head. NPSH = Absolute pressure head at inlet of the pump – vapour pressure head (absolute units) + velocity head 4.24) Write the equation for specific speed for pumps and also for turbine. [AU, Nov / Dec - 2005] Specific speed of pump

𝑁𝑠 =

𝑁√𝑄 𝐻𝑚 3/4

N

= Speed of the pump

Q

= Discharge of the pump

Hm

= Manometric head

Specific speed of turbine



𝑁𝑠 = N

= Speed of the turbine

P

= Power developed

H

= Head

𝑁√𝑃 𝐻 5/4

4.25) Define specific speed as applied to pumps.

[AU, May / June - 2009]

The specific speed of a centrifugal pump is defined as the speed of a geometrically similar pump which would deliver one cubic meter of liquid per second against a head of one meter. 4.26) Define specific speed.

[AU, Nov / Dec - 2007]

The specific speed of a centrifugal pump is defined as the speed of a geometrically similar pump which would deliver one cubic meter of liquid per second against a head of one meter. 4.27) What is specific speed of a pump? How are pumps classified based on this number?

[AU, Nov / Dec - 2009]

The specific speed of a centrifugal pump is defined as the speed of a geometrically similar pump which would deliver one cubic meter of liquid per second against a head of one meter. Pump

Speed N

Specific speed

Slow

10 – 30

Medium

30 – 50

High

50 – 80

Mixed flow

-

80 – 160

Axial flow

-

100 – 450

Radial flow

4.28) Define manometric efficiency and mechanical efficiency of a centrifugal pump.

[AU, April / May - 2015] Manometric efficiency is the ratio of the manometric head to the head

imparted by the impeller to the water 𝜂𝑚𝑎𝑛 =

𝑀𝑎𝑛𝑜𝑚𝑒𝑡𝑟𝑖𝑐 ℎ𝑒𝑎𝑑 ℎ𝑒𝑎𝑑 𝑖𝑚𝑝𝑎𝑟𝑡𝑒𝑑 𝑏𝑦 𝑖𝑚𝑝𝑒𝑙𝑙𝑒𝑟 𝑡𝑜 𝑤𝑎𝑡𝑒𝑟



Mechanical efficiency is the ratio of the power available at the impeller to the power at the shaft of the centrifugal pump 𝜂𝑚𝑒𝑐ℎ =

𝑃𝑜𝑤𝑒𝑟 𝑎𝑡 𝑡ℎ𝑒 𝑖𝑚𝑝𝑒𝑙𝑙𝑒𝑟 𝑃𝑜𝑤𝑒𝑟 𝑎𝑡 𝑡ℎ𝑒 𝑠ℎ𝑎𝑓𝑡

4.29) What do you mean by manometric efficiency and mechanical efficiency of a centrifugal pump?

[AU, Nov / Dec - 2007]

Manometric efficiency is the ratio of the manometric head to the head imparted by the impeller to the water 𝜂𝑚𝑎𝑛 =

𝑀𝑎𝑛𝑜𝑚𝑒𝑡𝑟𝑖𝑐 ℎ𝑒𝑎𝑑 ℎ𝑒𝑎𝑑 𝑖𝑚𝑝𝑎𝑟𝑡𝑒𝑑 𝑏𝑦 𝑖𝑚𝑝𝑒𝑙𝑙𝑒𝑟 𝑡𝑜 𝑤𝑎𝑡𝑒𝑟

Mechanical efficiency is the ratio of the power available at the impeller to the power at the shaft of the centrifugal pump 𝜂𝑚𝑒𝑐ℎ =

𝑃𝑜𝑤𝑒𝑟 𝑎𝑡 𝑡ℎ𝑒 𝑖𝑚𝑝𝑒𝑙𝑙𝑒𝑟 𝑃𝑜𝑤𝑒𝑟 𝑎𝑡 𝑡ℎ𝑒 𝑠ℎ𝑎𝑓𝑡

4.30) What are operating characteristics curves of centrifugal pump? [AU, April / May - 2015] The curves which are plotted while the pump is running at a constant design speed. These curves show the relation between efficiency, brake power, head and discharge. 4.31) What is meant by pump?

[AU, Nov / Dec - 2009]

The hydraulic machines which convert the mechanical energy into hydraulic energy are called as pump 4.32) Under what conditions would you suggest use of double-suction pump and a multistage pump?

[AU, Nov / Dec - 2010]

 If the need of continuous delivery of fluid  If uniform discharge of fluid is needed  If the required discharge of the fluid is more  If the space is limited to use single suction pump for the higher capacity. 4.33) What are roto dynamic pumps? Give examples.

[AU, Nov / Dec - 2009]

The centrifugal pump is the common type roto dynamic pump in which the rotating impeller of a pump impresses a centrifugal head or pressure on the liquid which leaves the impeller at a high velocity. This pressure enables the liquid to raise to higher level. CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 58


4.34) Why the reciprocating pump is called a positive displacement pump? [AU, April / May - 2011] It discharges a definite quantity of a liquid during the displacement of its piston, therefore it is called as positive displacement pump. 4.35) How are reciprocating pumps classified?

[AU, Nov / Dec - 2011]

According to fluid being contact with piston  Single acting pump  Double acting pump According to number of cylinders  Single cylinder pump  Double cylinder pump  Triple cylinder pump  Duplex double acting pump  Quantiplex pump 4.36) What are the materials used for manufacturing reciprocating pumps? [AU, Nov / Dec - 2014]  Stainless steel  Aluminum  Brass  Bronze  Nickel – alloy 4.37) When will you select a reciprocating pump?

[AU, Nov / Dec - 2005]

For obtaining high pressure or head and low discharge, a reciprocating pump is selected. 4.38) List the advantages of double acting reciprocating pump. [AU, Nov / Dec - 2014]  Both suction and delivery strikes takes place simultaneously  Discharge is continuous and more uniform  Rate of discharge is almost twice that of single acting pump 4.39) Draw the relationship between discharge and crank angle for a single acting pump.

[AU, Nov / Dec - 2013]



4.40) What is the function of non – return valve in a reciprocating pump? [AU, May / June - 2012] The function of non – return valve in reciprocating pump to allow the water to flow only in one direction, the suction non return valve allows water from sump to cylinder and the delivery non – return valve allows water from cylinder to delivery pipe. 4.41) Distinguish between centrifugal pump and reciprocating pump. [AU, Nov / Dec – 2005, 2012] Centrifugal pump  The discharge is continuous and

Reciprocating pump  The discharge is fluctuating and

smooth.

pulsating.

 Starting torque is more

 Staring torque is less

 Action on fluid is dynamic

 Action on fluid by the pump is due to positive displacement.

 Used for lower heads and large

 Used for high heads and low

discharge

discharge

 Efficiency is high

 Efficiency is low

 It is compact

 It is comparatively large

 Smooth operation without noise

 Not smooth in operation and noisy

 Maintenance cost is low

 Maintenance cost is high

 Priming is necessary

 Priming is not necessary

4.42) Mention the significance of 'back leakage'.

[AU, Nov / Dec - 2013]



As the rotor of rotary positive displacement pump rotates the trapped oil is carried to the pressure side through the clearance which is known as back leakage. The maximum operating pressure is controlled by the back leakage 4.43) Define slip of reciprocating pump. [AU, April / May - 2010, Nov / Dec - 2012] Slip is defined as the difference between the theoretical discharge and actual discharge of the pump. 4.44) When does negative slip occur?

[AU, Nov / Dec - 2008]

Negative slip occurs when the delivery pipe is short and suction pipe is long and the pump is running at high speed 4.45) What is negative slip in a reciprocating pump? What are the causes for it? [AU, May / June - 2013] Slip is defined as the difference between the theoretical discharge and actual discharge of the pump. If actual discharge is more than the theoretical discharge the slip of the pump is negative. In that case the slip of the pump is known as negative slip. Negative slip occurs when the delivery pipe is short and suction pipe is long and the pump is running at high speed 4.46) Define slip, negative slip in reciprocating pump.

[AU, May / June - 2014]

Slip is defined as the difference between the theoretical discharge and actual discharge of the pump. If actual discharge is more than the theoretical discharge the slip of the pump is negative. In that case the slip of the pump is known as negative slip. 4.47) Define slip of a pump. When does negative slip occur? [AU, Nov / Dec - 2003] Slip is defined as the difference between the theoretical discharge and actual discharge of the pump. Negative slip occurs when the delivery pipe is short and suction pipe is long and the pump is running at high speed.



4.48) Define slip and percentage of slip of a reciprocating pump. [AU, Nov / Dec – 2008, 2010] Slip is defined as the difference between the theoretical discharge and actual discharge of the pump. The ratio between slip and theoretical discharge is called as percentage of slip. 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝑠𝑙𝑖𝑝 =

𝑄𝑡ℎ − 𝑄𝑎𝑐𝑡 ∗ 100 𝑄𝑡ℎ

4.49) Define slip and percentage slip.

[AU, Nov / Dec - 2011]

Slip is defined as the difference between the theoretical discharge and actual discharge of the pump. The ratio between slip and theoretical discharge is called as percentage of slip. 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝑠𝑙𝑖𝑝 =

𝑄𝑡ℎ − 𝑄𝑎𝑐𝑡 ∗ 100 𝑄𝑡ℎ

4.50) What is the % of slip in reciprocating pump? [AU, Nov / Dec – 2006, May / June– 2012] The ratio between slip and theoretical discharge is called as percentage of slip. 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝑠𝑙𝑖𝑝 = 4.51) Discuss – slip.

𝑄𝑡ℎ − 𝑄𝑎𝑐𝑡 ∗ 100 𝑄𝑡ℎ [AU, April / May - 2011]

Slip is defined as the difference between the theoretical discharge and actual discharge of the pump. If actual discharge is more than the theoretical discharge the slip of the pump is negative. In that case the slip of the pump is known as negative slip. Negative slip occurs when the delivery pipe is short and suction pipe is long and the pump is running at high speed 4.52) Define slip in reciprocating machines.

[AU, Nov / Dec - 2011]

Slip is defined as the difference between the theoretical discharge and actual discharge of the pump. 4.53) Distinguish between pumps in series and pumps in parallel. [AU, April / May - 2005] CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 62


Pumps In Series

Pumps In Parallel

 When two (or more) pumps are

 When two or more pumps are

arranged in serial their resulting

arranged

pump

is

resulting performance curve is

obtained by adding their heads at

obtained by adding their flow

the same flow rate as indicated in

rates at the same head as

the figure below.

indicated in the figure below.

performance

curve

 Centrifugal pumps in parallel are used to overcome larger volume flows than one pump can handle alone.

in

parallel

their

 Centrifugal pumps in parallel are used to overcome larger volume flows than one pump can handle alone.

4.54) Can actual discharge be greater than theoretical discharge in a reciprocating pump?

[AU, Nov / Dec - 2009] Sometimes the actual discharge of a reciprocating pump is more than the

theoretical discharge. It happens when the delivery pipe is short and suction pipe is long and the pump is running at high speed. It cause the delivery valve to open even before the suction stroke is completed. It results into pushing some quantity of water into the delivery pipe before the commencement of delivery stroke. Thus the actual discharge become more than the theoretical discharge. 4.55) Which factors determine the maximum speed of reciprocating pump? [AU, Nov / Dec - 2009] The maximum speed of the reciprocating pump is governed by the maximum allowable vacuum pressure or minimum absolute pressure so that the separation of flow does not takes place.



Maximum vacuum pressure of the head which occurs at θ = 0 It also depends on atmospheric head, acceleration head, suction head and delivery head. 4.56) What factors govern the speed of reciprocating pump? [AU, May / June - 2012] The maximum speed of the reciprocating pump is governed by the maximum allowable vacuum pressure or minimum absolute pressure so that the separation of flow does not takes place. Maximum vacuum pressure of the head which occurs at θ = 0 It also depends on atmospheric head, acceleration head, suction head and delivery head. 4.57) Brief on acceleration head.

[AU, Nov / Dec - 2011]

When the piston moves outward at the beginning of the stroke, a negative pressure is created which is equal to the suction head (hs). In addition to this, the fluid or liquid will also be accelerated in the suction stroke. Due to acceleration head (has), the total negative pressure head at the beginning of the stroke is equal to hs + has denoted by the ordinate EA' shown in Figure. So, the absolute pressure at the ordinate A' is equal to A'S. At the same time, the absolute pressure should not fall below the vapour or vacuum pressure and the separation should not take place. At the beginning of delivery pipe, the liquid is accelerated but it is decelerated or retarded while at the end of delivery pipe. Here also, the absolute pressure should not fall below the vacuum pressure to avoid separation. CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 64


4.58) What are rotary pumps? Give examples


Rotary pumps resemble like a centrifugal pumps in appearance. But, the working method differs. Uniform discharge and positive displacement can be obtained by using these rotary pumps. So, we can clearly say, it has the combined advantages of both centrifugal and reciprocating pumps. The examples for rotary pumps are  External pump.  Internal gear pump.  Lobe pump.  Vane pump. 4.59) What is a rotary pump? Give its classification.


Rotary pumps resemble like a centrifugal pumps in appearance. But, the working method differs. Uniform discharge and positive displacement can be obtained by using these rotary pumps. So, we can clearly say, it has the combined advantages of both centrifugal and reciprocating pumps. The various types of rotary pumps are  External pump.  Internal gear pump.  Lobe pump.  Vane pump. 4.60) What is the function of air vessel? [AU, Nov / Dec – 2008, May / June - 2009, April / May - 2010] The main functions of air vessels are  To obtain a continuous supply of liquid at a uniform rate  To save a considerable amount of work in overcoming the frictional resistance in the suction and delivery pipe  To run the pump at a high speed without separation 4.61) What is an air vessel in reciprocating pump?

[AU, May / June - 2006]

An air vessel is a closed chamber containing compressed air in the portion and liquid at the bottom of the chamber. At the base of the chamber there is an opening through which the liquid may flow into the vessel or out from the vessel.



When the liquid enters the vessel the air gets compressed and when leaves the vessel the air will expand in the chamber. 4.62) Mention the working principle of an Air-vessel.


An air vessel is a closed chamber containing compressed air in the portion and liquid at the bottom of the chamber. At the base of the chamber there is an opening through which the liquid may flow into the vessel or out from the vessel. When the liquid enters the vessel the air gets compressed and when leaves the vessel the air will expand in the chamber. Pump has two air vessel each fitted to suction pipe and delivery pipe 4.63) What is an air vessel? List the objectives that would be fulfilled by the use of air vessels.

[AU, Nov / Dec - 2010]

An air vessel is a closed chamber containing compressed air in the portion and liquid at the bottom of the chamber. At the base of the chamber there is an opening through which the liquid may flow into the vessel or out from the vessel. When the liquid enters the vessel the air gets compressed and when leaves the vessel the air will expand in the chamber. The main objectives of air vessels are  To obtain a continuous supply of liquid at a uniform rate  To save a considerable amount of work in overcoming the frictional resistance in the suction and delivery pipe  To run the pump at a high speed without separation 4.64) What is an air vessel? What are its uses?

[AU, May / June - 2012]

An air vessel is a closed chamber containing compressed air in the portion and liquid at the bottom of the chamber. At the base of the chamber there is an opening through which the liquid may flow into the vessel or out from the vessel. When the liquid enters the vessel the air gets compressed and when leaves the vessel the air will expand in the chamber. The uses of air vessels are  To obtain a continuous supply of liquid at a uniform rate  To save a considerable amount of work in overcoming the frictional resistance in the suction and delivery pipe  To run the pump at a high speed without separation CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 66


4.65) What are the advantages of air vessel?

[AU, May / June - 2013]

 To obtain a continuous supply of liquid at a uniform rate  To save a considerable amount of work in overcoming the frictional resistance in the suction and delivery pipe  To run the pump at a high speed without separation 4.66) State the advantages of fitting air vessels in reciprocating pumps. [AU, May / June - 2009]  To obtain a continuous supply of liquid at a uniform rate  To save a considerable amount of work in overcoming the frictional resistance in the suction and delivery pipe  To run the pump at a high speed without separation 4.67) What are the uses of air vessels?

[AU, May / June - 2014]

The uses of air vessels are  To obtain a continuous supply of liquid at a uniform rate  To save a considerable amount of work in overcoming the frictional resistance in the suction and delivery pipe  To run the pump at a high speed without separation 4.68) Define indicator diagram.


Indicator diagram is the graph between the pressure head in the cylinder and distance travelled by piston from inner dead center for one complete revolution of the crank. 4.69) What is indicator diagram?

[AU, May / June - 2009]

Indicator diagram is the graph between the pressure head in the cylinder and distance travelled by piston from inner dead center for one complete revolution of the crank. 4.70) Draw the ideal indicator diagram.




4.71) A single acting reciprocating pump, running at 50rpm. The diameter of piston = 20cm and length = 40cm. Find the theoretical discharge of the pump. [AU, April / May - 2011] Given: N = 50 rpm

D = 0.2m

L = 0.4m

Solution: 𝑄𝑡ℎ = 𝑄𝑡ℎ 𝑄𝑡ℎ

𝐴∗𝐿∗𝑁 60

𝜋 ∗ 𝐷2 ∗ 𝐿 ∗ 𝑁 = 4 ∗ 60

𝜋 ∗ 0.22 ∗ 0.4 ∗ 50 = 4 ∗ 60

𝑄𝑡ℎ = 0.0104 𝑚3 /𝑠 4.72) A centrifugal pump delivers 20 litres/s of water against a manometric head of 850 mm at 900 rpm. Find the specific speed of pump. [AU, April / May - 2010] Given: Q = 20*10-3 m3/s

Hm = 0.850m

N = 900rpm

Solution:

𝑁𝑠 =


900√20 ∗ 10−3 𝑁𝑠 = 0.8503/4 𝑁𝑠 = 143.778 𝑟𝑝𝑚 4.73) The following data refer to a centrifugal pump which is designed to run at 1500 rpm. D1 = 100 mm, D2 = 300 mm, B1 = 50 mm, B2 = 20 mm, Vf1= 3 m/s. Find the velocity of flow at outlet.


Given: N = 1500 rpm

D1 = 0.1m

B2 = 0.02m

Vf1= 3 m/s

D2 = 0.3m

B1 = 0.05m

Solution:

Discharge CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 68


𝑄 = 𝜋𝐷1 𝐵1 𝑉𝑓1 𝑄 = 𝜋 ∗ 0.1 ∗ 0.05 ∗ 3 𝑄 = 0.0471 𝑚3 /𝑠 Velocity of flow at outlet

𝑄 = 𝜋𝐷2 𝐵2 𝑉𝑓2 0.0471 = 𝜋 ∗ 0.3 ∗ 0.02 ∗ 𝑉𝑓2 𝑉𝑓2 = 2.5 𝑚/𝑠 4.74) A pump is to discharge 0.82 m3/s at a head of 42 m when running at 300 rpm. What type of pump will be required?

[AU, Nov / Dec - 2011]

Given: Q = 0.82 m3/s

Hm = 42m

N = 300rpm

Solution:

𝑁𝑠 = 𝑁𝑠 =


300√0.82 423/4

𝑁𝑠 = 16.466 Specific speed lies between 10 to 30, so slow speed radial flow pump is recommended



UNIT – V – TURBINES PART - A 5.1) Classify Hydrodynamic machines.


 Power producing machines (Hydraulic turbines)  Impulse turbine  Reaction turbine  Power absorbing machines (Hydrodynamic pumps)  Mixed flow pumps  Axial flow pumps 5.2) How are hydraulic turbines classified [AU, May / June - 2009, 2014, Nov / Dec - 2009 April / May - 2011] According to the type of energy at inlet  Impulse turbine  Reaction turbine According to the direction of flow through runner  Tangential flow turbine  Radial flow turbine  Axial flow turbine  Mixed flow turbine According to the head at the inlet of the turbine  High head turbine  Medium head turbine  Low head turbine According to the specific speed of the turbine  Low specific speed turbine  Medium specific speed turbine  High specific speed turbine



5.3) What is a pump turbine? Is it the same as turbine pump? [AU, April / May - 2015] There are applications in which the same turbo machine is used as both a pump and turbine; these devices appropriately called as Pump Turbine. Pump turbine is not as the same as turbine pump, turbine pump is meant only for pumping of liquids.

5.4) What are high head turbines?

[AU, Nov / Dec - 2009]

The turbines operating head is above 250m then the turbines are called as high head turbines. 5.5) List the range of head for various turbines. S.No

Head based Turbine

1

Low head

2

Medium head

3

High head

4

Very High head

Head (m) 2–5

Discharge

[AU, April / May - 2015] Type of Turbine

High

Kaplan or Propeller

16 – 70

High or Medium

Kaplan or Francis

71 – 500

Medium or Low

Francis or Pelton

Low

Pelton

> 500

5.6) State and concise on Euler turbine equation.

[AU, Nov / Dec - 2014]

The Euler turbine equation relates the power added to or removed from the flow, to characteristics of a rotating blade row. The equation is based on the concepts of conservation of angular momentum and conservation of energy. CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 71


The above Equation is called the Euler Turbine Equation. It relates the temperature ratio (and hence the pressure ratio) across a turbine or compressor to the rotational speed and the change in momentum per unit mass. Note that the velocities used in this equation are what we will later call absolute frame velocities (as opposed to relative frame velocities). If angular momentum increases across a blade row, then 𝑇𝑇𝑐 > 𝑇𝑇𝑏 and work was done on the fluid (a compressor). If angular momentum decreases across a blade row, then 𝑇𝑇𝑐 < 𝑇𝑇𝑏 and work was done by the fluid (a turbine). 5.7) State the principles on which turbo-machines are based. [AU, Nov / Dec - 2010] Turbo machines are based on the principle of fluid momentum. The fluid momentum is gradually changed into rotation motion of the mechanical member. 5.8) Explain specific speed.

[AU, Nov / Dec - 2005]

It is defined as the speed of a turbine which is identical in shape, geometrical dimensions, blade angles, gate opening etc., with the actual turbine but of such a size that it will develop unit power when working under unit head. The specific speed of the turbine is used in comparing the different types of turbines as every type of turbine has different specific speed. 5.9) Define specific speed.

[AU, Nov / Dec - 2009]

It is defined as the speed of a turbine which is identical in shape, geometrical dimensions, blade angles, gate opening etc., with the actual turbine but of such a size that it will develop unit power when working under unit head. 5.10) Define specific speed of a turbine.

[AU,

Nov / Dec – 2003, 2008, 2009, May / June–2007, 2009, April / May –2010, 2011] It is defined as the speed of a turbine which is identical in shape, geometrical dimensions, blade angles, gate opening etc., with the actual turbine but of such a size that it will develop unit power when working under unit head. 5.11) Define specific speed of a turbine. What is its usefulness? [AU, Nov / Dec - 2007] CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 72


It is defined as the speed of a turbine which is identical in shape, geometrical dimensions, blade angles, gate opening etc., with the actual turbine but of such a size that it will develop unit power when working under unit head. The specific speed of the turbine is used in comparing the different types of turbines as every type of turbine has different specific speed. 5.12) How is specific speed of a turbine defined?

[AU, May / June - 2006]

It is defined as the speed of a turbine which is identical in shape, geometrical dimensions, blade angles, gate opening etc., with the actual turbine but of such a size that it will develop unit power when working under unit head. 5.13) What is meant by specific speed of a turbine?


It is defined as the speed of a turbine which is identical in shape, geometrical dimensions, blade angles, gate opening etc., with the actual turbine but of such a size that it will develop unit power when working under unit head. 5.14) Define specific speed and unit speed of a turbine.


Specific speed is defined as the speed of a turbine which is identical in shape, geometrical dimensions, blade angles, gate opening etc., with the actual turbine but of such a size that it will develop unit power when working under unit head. Unit speed is the speed of the turbine under unit head. 5.15) Write the equation for specific speed for pumps and also for turbine. [AU, Nov / Dec - 2012] Specific speed of pump

𝑁𝑠 =


N

= Speed of the pump

Q

= Discharge of the pump

Hm

= Manometric head

Specific speed of turbine

𝑁√𝑃 𝑁𝑠 = 5/4 𝐻 N

= Speed of the turbine

P

= Power developed

H

= Head



5.16) Why not the specific speed of a hydraulic turbine is calculated using watts, instead of metric horse power?


A metric horsepower-hour (hp·h) is an outdated unit of energy, not used in the SI system of units. The unit represents an amount of work a horse is supposed capable of delivering during an hour. 1 metric hp·h = 2.65 MJ. 5.17) What is hydraulic turbine?

[AU, May / June - 2006]

Hydraulic turbines are the machines which convert the energy of flowing water into mechanical energy 5.18) Classify turbines according to flow.

[AU, Nov / Dec - 2005]

According to the direction of flow through runner  Tangential flow turbine  Radial flow turbine  Axial flow turbine  Mixed flow turbine 5.19) Explain the working of impulse turbine.


Impulse turbine works on the principle of impulse. In these turbines, the head or pressure energy of water is first converted into kinetic energy by means of a nozzle or set of nozzles kept close to the runner. This high velocity jet produced by nozzle is allowed to impinge on the set of buckets fixed on the outer periphery of the wheel or runner. The direction of the jet is changed by buckets. The change of momentum of water causes the wheel to rotate, thus the mechanical energy is produced. It should be noted that the pressure of water is atmospheric and remains constant while passing over the runner. Examples: Pelton wheel, Girard turbine, Turgo turbine 5.20) What is reaction turbine? Give examples


In reaction turbines, a part of pressure energy is first converted into kinetic energy before supplied to the runner. Therefore, the water enters the runner having partly the pressure energy and partly the kinetic energy and both these energies are reduced simultaneously while passing over the runner and produce mechanical energy. Hence, these turbines work on the principle of impulse reaction. The runner of these being under pressure above atmospheric, it requires the blades of turbine to run in closed passages which are completely filled with water in all conditions. CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 74


Examples: Francis, Kaplan and Propeller turbines 5.21) Differentiate between reaction turbine and impulse turbine. [AU, Nov / Dec - 2003, April / May - 2008, 2015, May / June - 2012] Impulse turbine

Reaction turbine

 All the potential energies are

 Only a portion of fluid energy are

converted into kinetic energy by

converted into kinetic energy

nozzle before entering to turbine

before entering to turbine runner

runner  Blades are only action when they

 Blades are action at all time

are i.e in front of nozzle  Water may be allowed to enter a part or whole of the wheel

 Water is admitted over the circumference of the wheel

circumference.  Wheel does not run full and air has free access to the buckets

 Water completely fills the vane passage throughout the operation of the turbine

 Unit is installed above the tail race

 Unit is kept entirely submerged in water below the tail race.  Flow regulation is possible with

 Flow

regulation

is

possible

without loss

loss  Flow is regulated by means of

 Flow is regulated by needle valve

guide vane assembly.

fitted into the nozzle 5.22) What is a ‘breaking jet’ in Pelton wheel/turbine? [AU, May / June - 2007, Nov / Dec – 2007, 2012] When the nozzle is completely closed by moving the spear in the forward direction the amount of water striking the runner reduces to zero. But the runner due to inertia goes on revolving for a long time. To stop the runner in a short time, a small nozzle is provided which directs the jet of water on the back of the vanes. This jet of water is called breaking jet.



5.23) Draw velocity triangle diagram for Pelton wheel turbine. [AU, Nov / Dec - 2008]

5.24) Define the flow ratio of reaction radial flow turbine. [AU, Nov / Dec - 2012] The ratio of the velocity of flow at inlet (Vf1) to the velocity given √2𝑔𝐻 is known as flow ratio. 𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑖𝑜 =

𝑉𝑓1 √2𝑔𝐻

5.25) List the main parts of Kaplan turbine.

[AU, Nov / Dec - 2012]

 Scroll casing  Guide vanes mechanism  Hub with vanes or runner of the turbine  Draft tube 5.26) What is draft tube?

[AU, Nov / Dec - 2012]

Draft tube is a pipe of gradually increasing area which connects the outlet of runner to the tail race. It is used for discharging water from the exit of the turbine to tail race. 5.27) What is draft tube? In which type of turbine is mostly used? [AU, Nov / Dec - 2003] Draft tube is a pipe of gradually increasing area which connects the outlet of runner to the tail race. It is used for discharging water from the exit of the turbine to tail race. It is mostly used in reaction turbine.



5.28) Write the function of draft tube in turbine outlet? [AU, April / May - 2005, 2008, Nov / Dec - 2011]  It permits a negative head to be established at the outlet of the runner and thereby increase the net head on the turbine. The turbine may be placed above the tail race without any loss of net head and hence turbine may be inspected properly.  It converts a large proportion of the kinetic energy (V2/2g) rejected at the outlet of the turbine into useful pressure energy. Without the draft tube, the kinetic energy rejected at the outlet of the turbine will go waste to the tail race.  Hence by using draft-tube, the net head on the turbine increases. The turbine develops more power and also the efficiency of the turbine increases. 5.29) What is the function of draft tube? [AU, May / June– 2007, Nov / Dec - 2009]  It permits a negative head to be established at the outlet of the runner and thereby increase the net head on the turbine. The turbine may be placed above the tail race without any loss of net head and hence turbine may be inspected properly.  It converts a large proportion of the kinetic energy (V2/2g) rejected at the outlet of the turbine into useful pressure energy. Without the draft tube, the kinetic energy rejected at the outlet of the turbine will go waste to the tail race.  Hence by using draft-tube, the net head on the turbine increases. The turbine develops more power and also the efficiency of the turbine increases. 5.30) What are the different types of draft tubes?

[AU, Nov / Dec - 2009]

 Conical draft tube  Simple elbow tubes  Moody spreading tubes  Elbow draft tubes with circular inlet and rectangular outlet



5.31) Why does a Pelton wheel not possess any draft tube? [AU, May / June - 2012] In case of Pelton wheel the available head is converted into kinetic energy before entry to runner buckets and the turbine operate under atmospheric pressure conditions. The velocity of the water leaving at the turbine exit is small, therefore the exit of the runner is above the tail race level and there is no need for draft tube. 5.32) Mention the importance of Euler turbine equation.

[AU, Nov / Dec - 2011]

Euler’s turbine equation plays a central role in turbo machinery as it connects the specific work and geometry and velocities in the impeller 5.33) What are the different efficiencies of turbine to determine the characteristics of turbine?

[AU, Nov / Dec - 2006 May / June– 2012]

Mechanical Efficiency =

Volumetric Efficiency =

Power at the shaft of the turbine Power delivered by water to the runner

Volume of Water or steam actually striking the runner Volume of water supplied to the turbine

Overall Efficiency =

Shaft Power at turbine Power supplied at the inlet of the turbine

5.34) Define -volumetric efficiency of turbine. Volumetric Efficiency =

[AU, Nov / Dec - 2014]

Volume of Water or steam actually striking the runner Volume of water supplied to the turbine

5.35) Define hydraulic efficiency and jet ratio of a Pelton wheel. [AU, Nov / Dec - 2010] Hydraulic efficiency is the ratio between work done per second to kinetic energy of jet per second. 𝜂ℎ =

𝑤𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 𝑝𝑒𝑟 𝑠𝑒𝑐𝑜𝑛𝑑 𝑘𝑖𝑛𝑒𝑡𝑖𝑐 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝑗𝑒𝑡 𝑝𝑒𝑟 𝑠𝑒𝑐𝑜𝑛𝑑

5.36) Define hydraulic efficiency and axial thrust of a roto-dynamic hydraulic machine.

[AU, May / June - 2013]



5.37) What is meant by hydraulic efficiency of turbine? [AU, Nov / Dec – 2012, 2013] Hydraulic efficiency is the ratio of the power produced by the turbine runner and the power supplied by the water at the turbine inlet. 5.38) Define hydraulic efficiency and overall efficiency of a turbine. [AU, Nov / Dec - 2012] Hydraulic efficiency is the ratio of the power produced by the turbine runner and the power supplied by the water at the turbine inlet. Overall efficiency is the ratio of power available at the turbine shaft to the power available from the water jet 5.39) Define overall efficiency and plant efficiency of turbines. [AU, May / June– 2007, 2012] Overall efficiency is the ratio of power available at the turbine shaft to the power available from the water jet Plant Efficiency of a plant is the percentage of the total energy content of a power plant's fuel that is converted into electricity. 5.40) What is the difference between a turbine and a pump? [AU, Nov / Dec – 2010, May / June - 2012] Turbine  Turbines

convert

Pump hydraulic

 Pump convert mechanical energy

energy into mechanical entry

into hydraulic entry

 It is energy producing machine

 It is energy absorbing machine

 Flow takes place from high

 Flow takes place from low

pressure side to low pressure side

pressure side to high pressure side

 Flow is decelerated

 Flow is accelerated

5.41) Differentiate between pumps and turbines. [AU, May / June, Nov / Dec – 2007, 2008] Turbine  Turbines

convert

Pump hydraulic

energy into mechanical entry

 Pump convert mechanical energy into hydraulic entry



 It is energy producing machine

 It is energy absorbing machine

 Flow takes place from high

 Flow takes place from low

pressure side to low pressure side

pressure side to high pressure side

 Flow is decelerated

 Flow is accelerated

5.42) A shaft transmits 150 Kw at 600 rpm. What is the torque in Newton – meters?


Given: P = 150 *103 W

N = 600rpm

Solution: Power 2𝜋𝑁𝑇 60 2 ∗ 𝜋 ∗ 600 ∗ 𝑇 150 ∗ 103 = 60 𝑃=

𝑇 = 1989.436 𝑁 − 𝑚

5.43) The mean velocity of the buckets of the Pelton wheel is 10 m/s. The jet supplies water at 0.7 m3/s at a head of 30 m. The jet is deflected through an angle of 160° by the bucket. Find the hydraulic efficiency. Take CV = 0.98. [AU, April / May - 2010] Given: u = 10m/s

Q = 0.7 m3/s

H = 30m

jet is deflected through an angle of 160° Solution: Assume speed ratio

𝐾𝑢 = 0.45 Velocity of jet

𝑉1 =

𝑢 12 = 𝐾𝑢 0.45

𝑉1 = 26.67 𝑚/𝑠 Blade angel CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 80


𝛷 = 180 − 160 = 20°

Hydraulic efficiency 𝜂ℎ =

2𝑢 (𝑉1 − 𝑢 )(1 + 𝑐𝑜𝑠𝛷 ) 𝑉1 2

2 ∗ 12 (26.67 − 12 )(1 + 𝑐𝑜𝑠20°) 𝜂ℎ = 26.672 𝜂ℎ = 0.96 = 96 % 5.44) A water turbine has a velocity of 8.5m/s at the entrance of draft tube and velocity of 2.2m/s at exit. The frictional loss is 0.15m and the tail race water is 4m below the entrance of draft tube. Calculate the pressure head at entrance. [AU, April / May - 2011] Given: Velocity at inlet,

V1 = 8.5 m/s

Velocity at outlet,

V2 = 2.2 m/s

Frictional Loss

hf = 0.1 m/s

Vertical Height Between tail race and inlet of draft – tube = 4m Let y = Vertical Height Between tailrace and outlet of draft – tube Applying Bernoulli’s Equation at the inlet and outlet of draft-tube and taking reference line passing through section 2- 2, we get

𝑃1 𝑉1 2 𝑃2 𝑉2 2 + + 𝑍1 = + + 𝑍2 + ℎ𝑓 𝜌𝑔 2𝑔 𝜌𝑔 2𝑔 Where CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 81


Z1 = 4 + y 𝑃2 𝜌𝑔

= Atmospheric pressure head + y =

𝑃𝑎 𝜌𝑔

+𝑦

Z2 = 0

𝑃1 8.52 𝑃𝑎 2.22 + + (4 + 𝑦) = ( + 𝑦) + + 0 + 0.1 𝜌𝑔 2 ∗ 9.81 𝜌𝑔 2 ∗ 9.81 Taking the atmospheric pressure head as zero

𝑃1 8.52 2.22 + + (4 + 𝑦) = (0 + 𝑦) + + 0 + 0.1 𝜌𝑔 2 ∗ 9.81 2 ∗ 9.81 𝑃1 = −7.3357 𝑚 𝜌𝑔 The negative sign means vacuum pressure head


FLUID MECHANICS & MACHINERY NOTES WITH QUESTION BANK AND TWO MARK QUESTION ANSWERS

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