Power Plant - Tutorial Sheets

Power Plant Engineering TUTORIAL

Ker erba bala la Univ Univer ersi sity ty College of Engineering Mechanical Engineering Department Academic Year

2012 - 2013

Class

4th Year Class

Subject

Power Plant Engineering

Lecturer

Dr. Raoof M. Radhi

Kerbala University Power Plant Engineering College Sheet No. 01 th Mech. Eng. Dept. – 4 year class 2012 – 2013 -----------------------------------------------------------------------------------------------------------Thermodynamic Review ----------------------------------------------------------------------------------------------------------1 – Explain the Temperature – entropy ( T-s ) diagram, defining defining all lines of significance, and state its use in dealing with a thermodynamic problems. 2 – Repeat Q.1 for Enthalpy – entropy ( h – s ) diagram . 3 - Repeat Q.1 for for Pressure – enthalpy ( P – h ) diagram . 4 – Define the following thermodynamic processes and terms : A - adiabatic - isentropic – isothermal – isobaric - polytropic B - saturation temperature temperature – saturation line line – latent heat – specific heat – critical point – interpolation 5 – Define each of the followings, and state the differences between them A – nozzle – diffuser – throttle B – pump – compressor – fan – turbine 6 – Explain briefly the four laws of thermodynamics

All groups required to answer the following questions : 7 – convert the following units : lbm to kg - Btu to Joule - calorie to Joule - feet to meter - ft/s to m/s inch to centimeter - psi to atm - Btu/lbm to kJ/kg - Btu/hr to kw - cu.ft to liter – 8 – relate each of the following temperature units to each others : Deg. C - deg. F - deg. K - deg. R

Kerbala University Power Plant Engineering College Sheet No.02 th Mech. Eng. Dept. – 4 year class 2012 – 2013 -----------------------------------------------------------------------------------------------------------

1 – define the following terms: Reversibility Irreversibility Isothermal process Adiabatic process Isentropic process Isobaric process Polytropic process 2 – explain briefly with the aid a simple schematic and T-s diagram the principle of Carnot cycle. 3 - explain briefly with the aid a simple schematic and T-s diagram the principle of Rankin cycle. 4 - explain briefly with the aid a simple schematic and T-s diagram the principle of Brayton cycle. 5 - explain briefly with the aid a simple schematic diagram the principles of hydro-power station. 6 - explain briefly with the aid a simple schematic diagram the principles of nuclear power generation.


The followings are general methods of power plant classification, discuss each one in details. Groups should answer the question number that corresponds to the group number: 1. 2. 3. 4. 5.

Status Fuel type Capacity Operation Prime mover

6 - Classify a specific power plant according to above methods and discuss in brief.

Kerbala University Power Plant Engineering College Sheet No. 04 th Mech. Eng. Dept. – 4 year class 2012 – 2013 -----------------------------------------------------------------------------------------------------------

Explain with a simple diagram the function of the following components of a power plant : 1 – coal handling system. 2 – ash handling system. 3 – steam generating plant. 4 – plant deaerating methods. 5 – plant cooling arrangements. 6 – flue gas expelling system.

Kerbala University Engineering College Mech. Eng. Dept. – 4th year class

Power Plant Sheet No.05 2012 – 2013

A - PROBLEM STATEMENT:

Indicate whether the following states for water are in the liquid, saturation, or superheated region. Specify the quality of the states in the saturation region:

State

P (kPa)

T (°C)

v (m3/kg)

1

1700

200

--

2

1200

--

0.0010

3

--

75

3.0

4

500

202

--

5

350

--

0.005

6

10000

311

---

B – SOLVE THE FOLLOWINGS : 1 - At the beginning of a process, the thermometer reads 15 °F. You want to

stop the experiment when the absolute temperature has ha s doubled. What is the final temperature in degrees Celsius? 2 - Determine the SI values for the following energy-related quantities: 1

Btu/(ft2-hr), 13,000 Btu/lbm, and 50,000 Btu/h.

3 - The numerical values of the properties x, y are given. Linearly interpolate

and obtain the specified property. x

y

110 1.2074 115 1.031

Find: y for x = 112.3 4 - The numerical values of the properties x, y, and z are given. Linearly interpolate and obtain the specified property. x = 10 y

z

x = 50 y

z

150 19.513 150 3.8894 200 21.820 200 4.3561

Find: z for x = 27 and y = 150

5 - water at P = 0.08 MPa and h = 1000 kJ/kg. Find: T and v 6 - Find the efficiency of an ideal engine working between the steam point and the ice point.

Kerbala University Power Plant Engineering College Sheet No.06 th Mech. Eng. Dept. – 4 year class 2012 – 2013 ----------------------------------------------------------------------------------------------------------1 – Power plant actual output is ( 648000 MWhr ) , if the rated full capacity is (1000 MW). Find the plant capacity factor (CF) for plant operation of (30)days. ( anws : 0.9 ) 2 – A wind farm consists of (10) wind turbines , each of (2)MW full rated capacity. If the wind farm produces (43416)MWhr under certain operating conditions. Calculate the farm (CF) for a period of one year. ( anws : 0.25 ) 3 – A /A hydro-power station uses (26) main generators of full rated output of (700)MW each, (2) auxiliary generators of (50)MW each. Find the plant (CF) if the actual output for one year was (79,47)TWhr. ( anws : 0.4957 ) B / What is the maximum power output of a plant if it’s annual actual actua l generating power averaging (4.2)TWhr, and the capacity factor is (0.23). ( anws : 2080 MW ) 4 – The peak load on a power plant is (60 MW). The load having maximum demand of (30 , 20 , 10 , 14 )MW are connected to the plant. The capacity of the plant is (80 ) MW and the annual load factor is (0.5). Estimate : a / the average load on the plant. b / energy supplied per year . c / the demand factor . d / the diversity factor . ( anws : 30MW , 262.8MW , 0.811 , 2.466 ) 5 – A / A plant having a rated capacity of (200MW) (200MW) and maximum load is (100MW) . Find the plant utility factor factor if it’s load load factor averaging (80 %) . ( anws : 0.4) B / Calculate the availability factor and the the capacity factor of a plant operating under the following conditions : i – ready to operate during a particular week but held as stand-by. ii – operate at half rated power for one month . ( anws : ( 1.0 – 0.0 ) , ( 1.0 – 0.5 ) 6 – A hydro power plant is to be used as peak load plant at an annual load factor of 5 (30 % ). The electrical energy obtained during the year is ( 750 x 10 )KWhr. Determine : i – max demand ii – reserve capacity of the plant if the plant capacity factor is (24 %) (Anws : 28530 kW , 7137 kW )

Kerbala University Power Plant Engineering College Sheet No. 07 th Mech. Eng. Dept. – 4 year class 2012 – 2013 ----------------------------------------------------------------------------------------------------------1 – The maximum (peak) load on a thermal power plant of (60 MW) capacity is (50MW) at an annual load factor of (50 %) . The load having maximum demand of (25,20,8,5) MW are connected to the power plant . Determine : i – average load on the power plant iii – demand factor ii – energy generated per year . iv – diversity factor 6 ( anws : 25 MW , 219 x 10 kWhr , 0.86 , 1.16 ) 2 – A steam power plant has an installed capacity of ( 120 MW) and maximum demand of ( 100 MW) . The coal consumption is ( 0.4 kg/kWhr), and cost of coal is (80 PU). 5 The annual expenses of salaries and overhead charges are ( 50 x 10 PU). The power 5 plant works at a load factor of ( 0.5) , and the capital cost of the plant is ( 4 x 10 PU) where interest rate and depreciation is ( 10 %) of capital cost . Determine the cost generation per kWhr . ( anws : 0.0435 PU ) 3 - 15 electrical power consumption units each require (60)kW to operate, if (5 units, 10 units , and 6 units) groups to operate for a period of (2hrs) in various time of the day. Determine : I – the connected load ii – maximum demand Iii – demand factor iv – daily load factor. ( anws : 900kW , 600kW , 66.67 % , 17.5 % ). 4 - A power station has a maximum demand of (15)MW , a load factor of (0.7), a plant capacity factor of (0.525) , and a plant use factor of (0.85) . Find : i – the daily energy produced . ii – the reserve capacity of the plant . 3 ( anws : 252 x 10 kWhr , 5000kW ) 5 – The annual load on a (30)MW power plant is (25)MW. The PP supplies load having maximum demand of (10 , 8.5 , 5 , 4.5)MW . The annual load factor is (0.45) . Find: i – average load ii – energy supplied per year. iii – diversity factor iv – demand factor 6 ( anws : 11.25 MW , 98.55 x 10 kWhr , 1.12 , 0.893 ) 6 - The maximum demand of generating station is (100)MW. The annual capital charge 6 6 of transmission & distribution are (2.5 x 10 , 2 x 10 )PU , their diversity factor is (1.3), and efficiency is (90 %).The generating station capital cost is (100)PU/annum/ kW demand , plus (0.05)PU / kWhr supplied. Determine : i – yearly cost / kW demand ii – cost / kWhr supplied ( anws : 111.538 PU , 0.0522 PU )


1. Find the efficiency of the Carnot’s engine working between the steam point and the ice point. (answ. : 26.81% ) 2. A Carnot’s engine whose temperature of the source is 400K takes 200 calories of heat at this temperature and rejects 150 calories of heat to the sink. What is the temperature of the sink? Also calculate the efficiency of the engine. (answ. : 300K) 3. A Carnot engine operates between 227°C and 127°C .If it absorbs 60* 10 calorie at high temperature, how much work per cycle can the engine 4 perform? ( answ.: 50.4*10 J

4

4. A Carnot engine absorbs 100J of heat from a reservoir at127°C and rejects 600J of heat during the cycle. Calculate (i) the efficiency of the engine (ii) the temperature of the sink and (iii) the amount of useful work done during each cycle?

(answ. : 40% , 240 k , 400J )

5 - A Carnot cycle is performed by air initially at 327°C.Each satge represents a compression or expansion in the ratio 1:6.Calculate(i) the lowest temperature (ii) efficiency of the cycle, given γ = 1.4? (answ. : 293K , 51.2% ) 6. A Carnot heat engine device receives a heat transfer of 100 kJ of heat from a source at 100°C. If there is a heat transfer to 20°C, calculate the work produced and the thermal efficiency of the Carnot engine. ( answ. : 21.45 kJ , 21.4 % )

Kerbala University Power Plant Engineering College Sheet No.09 th Mech. Eng. Dept – 4 year. 2012 – 2013 ----------------------------------------------------------------------------------------------------------q.1- A Carnot cycle running on a closed system . The temperature limits are 300 K and 1000 K. If the work done by the system is (39.61 kJ) . Determine (a) the efficiency, (b) the heat supplied and heat rejected of the system . (ans:70% , 56.58kJ , 16.97 kJ) q.2 - A Carnot heat engine with an efficiency of 60% receives heat from a source at a rate of 3000 kJ/min, and rejects the waste heat to a medium at 300 K. Determine (a) the power that is generated by the engine, (b) the heat source temperature.(ans:30kw,750K)

q.3 - What is the highest possible theoretical efficiency of a heat engine operating in a

closed system with (1.5 kg) working fluid. The h eat source is from hot reservoir of furnace gases at (2000 ºC) when the cooling water available at (10 ºC) . Also find the heat energy supplied and rejected , and the actual work done if the engine (η m ) is ( 85 %) . (ans:87.54%,3426.5 , 560 , 2549.62 kJ) q.4 - A Carnot cycle operates between the temperature limits (140 , 500) ºF , if the heat

supplied is (300 Btu/min) . Determine : a/thermal eff. b/ work & horsepower c/ heat rejected d/ ΔS during isothermal expansion. (ans: 37.5%, 112.5- 2.65 , 187.5Btu/min , 0.3125 Btu/R.min )

q.5 – A hot reservoir at (800 ºC) and cold reservoir at (15 ºC) , if Pmax is (210 bar) and

Pmin is (1 bar). Assuming air is the working fluid. Calculate : i – the net work. ii – gross work. iii - the work ratio of the cycle iv – cycle efficiency (ans : 168 kJ/kg , 793.2 kJ/kg , 0.212 , 73.2 % ) q.6 A Carnot cycle running on a closed system has 1.5 kg of air. The temperature limits are 300 K and 1000 K, and the pressure limits are 20 and 1900 kPa. Determine (a) the efficiency, (b) the net work output. (ans : 70% , 101.85 kJ )

Kerbala University Power Plant Engineering College Sheet No. 10 th Mech. Eng. Dept – 4 year . 2012 – 2013 ----------------------------------------------------------------------------------------------------------Q.1 – A Carnot engine has a low temperature sink of (10 ºC) and max theoretical efficiency of (38 %). By how much does the temperature of the high temperature source need to be increased to raise the efficiency to (50 %) . ( ans : T h1 = 183 ºC , Th2 = 293 ºC , ΔT h = 110 ºC ) Q.2 - Find the efficiency of the Carnot engine working between the steam point and the ice point . ( ans : 26.81 % ) Q.3 – An inventor claims to have an engine that receives (100 Btu) of heat and produce (25 Btu) of useful work when operating between a source at (140 ºF)) and a receiver ( 0 ºF) . Is the claim a valid claim . Q.4 – In a Carnot cycle, the steam pressure varies between (30) and (0.04)bar . Calculate the net (heat & work ) transferred and the cycle efficiency . Discuss your results . ( ans : 725 kJ/kg , 725 kJ/kg , 40.0 % ) Q.5 – A steam power plant operates between boiler pressure of (42) bars and condenser pressure of (0.035)bar . Calculate the max theoretical efficiency of the plant . ( ans : 43.2 % ) Q.6 – One kg of steam at (7)bar , entropy (6.5 lJ/kg.K) is heated reversibly at constant pressure until temperature is (250 ºC) . Calculate the heat supplied and show on T-s diagram the area which represent the heat flow . ( ans : 283 kJ/kg )

Kerbala University Power Plant Engineering College Sheet No. 11 th Mech. Eng. Dept. – 4 year 2012 – 2013 ----------------------------------------------------------------------------------------------------------q.1 – Steam enters a turbine superheated at (6 MPa) and (680 ºK) , after expansion it exit the turbine at (0.1 MPa) with quality of (0.89) . The steam flow rate is (12) kg/s . Determine the power delivered by the turbine. ( ans : 9756 KW ). q.2 – Determine the flow rate required to produce (25 MW) of shaft power from a steam turbine in which the steam enters at (10 MPa & 720 ºK) , and exit at (5 kPa ) for the following cases : i – ideal turbine . ii – turbine with η is = 96 % ( ans : 19.53 kg/s , 20.34 kg/s ) q.3 – If steam enters a turbine at (10 MPa & 800 ºK) , and exit at a quality of (0.91) and (100 kPa) . Determine the isentropic efficiency of the turbine . ( ans : 0.935 ) q.4 – Consider a steam turbine in which the steam enters as superheated vapor at (800 ºK & 6 MPa) and exit at (0.1 MPa) . The flow rate of the steam is (15 kg/s), and the isenptropic efficiency of the turbine is (90 %) . Determine : i – the outlet state of the steam ii – the power produced by the turbine . ( ans :{T 2 = 372.76 K , h 2 = 2623.4 kJ/kg , s 2 = 6.2207 kJ/kg.K , x = 0.9772} , 12949KW) q.5 – Steam enters a turbine as saturated vapor at (2MPa) , and exit at (101 kPa) with steam quality of (0.92). Determine : i – turbine isentropic efficiency . ii – how does the ( η ( ans : 0.6 , 0.71 )

is

) change if the exit pressure is decreased to (35 kPa) .

q.6 – State the Rankine cycle assumption , and determine it’s efficiency if the operating conditions are steam to the turbine at (40 bar & 400 ºC) , condenser pressure (0.05 bar). Draw the plant schematic and T-s diagrams . ( ans : 37.8 % )

Kerbala University Power Plant Engineering College Sheet No. 12 th Mech. Eng. Dept. 4 year 2012 – 2013 -----------------------------------------------------------------------------------------------------------

Describe in details the power plant represented by each of the following schematic diagrams , then draw it’s expected operation On a ( T-s ) diagram .

1 – power plant ( A )


2 – power plant ( B )


3 – power plant ( C )

Describe in details the power plant represented by each of the following schematic diagrams , then draw it’s expected operation On a ( T-s ) diagram . 4 – power plant ( D )

Describe in details the power plant represented by each of the following schematic diagrams , then draw it’s expected operation On a ( T-s ) diagram . 5 – power plant ( E )

------------------------------------------------------------------------------------------------------------


6 – power plant ( F )

Kerbala University Power Plant Engineering College Sheet No.13 Mech. Eng. Dept. 2012 – 2013 ----------------------------------------------------------------------------------------------------------General Question : Study the diagrams below, and then give detailed description of what it might represent in terms of : a – overall view b – components shown c – flow lines d – operation 1–

2–

3–

4-

5–

6–

7 –

8–

Kerbala University Power Plant Engineering College Sheet No. 14 Mech. Eng. Dept. 2012 – 2013 -----------------------------------------------------------------------------------------------------------

Q.1/ In a steam power cycle, the steam supply is at (15 bar), and dry & saturated. The condenser pressure is (0.4 bar). Calculate : Carnot and rankine efficiencies ( neglect pump work) Q.2/ In a steam PP, pressure and temperature at turbine inlet are (20 bar and 360 deg.C) respectively. Steam expand in the turbine to (0.08 bar), then enter the condenser, where it condenses to saturated liquid water. The pump feeds back the water into the boiler. Assume ideal process, find per kg of steam : I – net work ii- cycle efficiency Q.3/ A Rankine cycle operates between pressure (80 bar) and (0.1 bar). The max cycle temperature is (600 deg.C). If the turbine and pump efficiencies are (0.9 and 0.8) respectively. Calculate the specific work and cycle efficiency. Q.4/ A simple Rankine cycle works between pressures (28 bar and 0.06 bar). The initial conditions of steam being dry saturated. Calculate : i- cycle eff. ii – work ratio iii- specific steam consumption Q.5/ The adiabatic enthalpy drop across the prime mover of the Rankine cycle is (840 kJ/kg). The enthalpy of the steam supplied is (2940 kJ/kg). If the back pressure is (0.1 bar). Find the ( SSC , thermal eff.). Q.6/ A (35 kw) IP system engines consumes (284 kg/hr) at (15 bar) and (250 deg C). If condenser pressure is (014 bar), determine: i- final condition of steam. ii- Rankine eff. iii- relative eff.

Kerbala University Power Plant Engineering College Sheet No. 15 th Mech. Eng. Dept. – 4 year 2012 – 2013 ----------------------------------------------------------------------------------------------------------1 – A steam power plant operates between boiler pressure of ( 42 bar ) and condenser pressure of ( 0.035 bar ). Calculate for these limits : i – cycle efficiency. ii – work ratio. iii – specific steam consumption. Do the above calculation for each of the following cases : a – carnot cycle using wet steam. ( anws : 0.432 , 0.739 , 4.9 kg/kw.hr ) b – rankine cycle with dry saturated steam at entery to turbine. (anws :0.368, 0.996 , 3.64) c – rankine cycle of ( b ) when expansion process has isentropic efficiency of ( 80% ). ( anws : 0.294 , 0.995 , 4.56 kg/kw.hr ). d – comments on your results . 2 – Compare the Rankine cycle performance of ( Q.1b ) with that obtained when the steam is Superheated to ( 500° C ), neglecting the feed water pump work . ( anws : Q.1 b : η = 36.8% , ssc = 3.64 kg/kw.hr Q.2 : η = 39.9% , ssc = 2.71 kg/kw.hr ). 3 – Calculate the thermal efficiency and specific steam consumption if re-heat is added to the plant of ( Q.2 ), where steam is just dry saturated at end of the first stage expansion, reheated to the intial temperature ( 500° C ) at the start of the second expansion stage . ( anws : Q.1b : 36.8% , 3.64 kg/kw.hr Q.2 : 39.9% , 2.71 kg/kw.hr Q.3 : 41% , 2.14 kg/kw.hr ) 4- The Rankine cycle of ( Q.1b ) is modified to include one feedwater heater , calculate the thermal efficiency and specific steam consumption. ( anws : 39.6% , 4.12 kg/kw.hr ). 5- A feedwater heater of the open type is supplied with condensate at (0.1 bar) , and extracted steam from the turbine at ( p = 30 bar and x = 0.95). Calculate the flow rate of the extracted steam needed to just produce saturated feed water at heater outlet. ( ans : 0.414 kg ). 6- Steam enters a turbine with isentropic efficiency of (0.78) at (12MPa) (400 ºC) , and (0.3 kg/s), and exit at (0.15 MPa) . Determine : i- actual power output. (ans : 187.1 KW) ii- actual outlet temperature. (ans : 111.37 ºC) iii-actual outlet fluid phase . (ans : x = 0.881)

Kerbala University Power Plant Engineering College Sheet No. 16 th Mech. Eng. Dept. – 4 year 2012 – 2013 -----------------------------------------------------------------------------------------------------------

1 – In a regenerative steam cycle with two closed feedwater heater, steam supplied to the Turbine at ( P = 40 bar ) and ( T = 500° C ), steam is exhausted to the condenser at ( P=0.035 Bar ). Steam conditions at the intermediate bleed points ( Pa = 10 bar , Ta = saturated ) And ( Pb = 1.1 bar and Tb = saturated ) . Calculate : I – steam rates at the bleeding point ( a and b ). Ii – plant work output. Iii – plant thermal efficiency. ( anws : 0.147 kg/kg steam , 0.124 kg/kg steam , 1134.5 kj/kg , 42.3% ). 2 – A steam turbine is used to drive a feed – water pump of a large utility boiler. A ( 17.78 kg/s ) of supercritical steam enters the turbine at ( 808.3 ° K ) and ( 23.26 MPa ). The steam exit the turbine at ( 5.249 kPa ) with quality of ( 0.9566 ) . Determine : i – the power produced by the turbine. ii – the turbine isenptropic efficiency . ( anws : 15.2 kw , 60% ). 3 – Consider a steam power plant operating on the ideal regenerative Rankine cycle with OFWH . Steam enters the turbine at ( 15 MPa and 600° C ), and is condensed in the condenser at a pressure of ( 10 kPa ) . Some steam leaves the turbine at a pressure of ( 1.2 MPa ) and enters the OFWH. Determine : i – the fraction of steam extracted fron turbine. ii – cycle thermal efficiency. ( anws : 0.227 , 46.3% ). 4 – A steam power plant operating on the ideal Rankine cycle. The steam enters the turbine at ( 3 MPa and 350° C ), and is condensed in the condenser at pressure of ( 10 kPa ). Determine : i – thermal eff. of the power plant. ii – thermal eff. if steam is superheated to ( 600° C ) instead of ( 350° C ). iii – thermal eff. if the boiler pressure is raised to ( 15 MPa ) , while tuerbine inlet temperature remains at ( 600° C ). ( anws : 0.335 , 0.373 , 0.43 ) 5 - Consider a steam power plant that operates on an ideal reheat-regenerative Rankine cycle with one open feedwater heater, one closed feedwater heater and one reheater. Steam enters the turbine at ( 15 MPa ) and ( 600 C ) and is condensed in the condenser at a pressure of ( 10 kPa ) . Some heat extracted from the turbine at ( 4 MPa ) for the closed feedwater heater and the remaining steam is reheated at the same pressure to ( 600 C ). The extracted steam is completely condensed in the heater and is pumped to ( 15 MPa ) before it mixes with the feedwater at the same pressure. Steam for the open feedwater heater is extracted from

the low-pressure turbine at a pressure of ( 0.5 MPa ). ( 35 marks ) i– draw the power plant schematic diagram . ii – draw the system Ts diagram . iii –determine the fraction of steam extracted from the turbine each time . iv –calculate cycle thermal efficiency. v- evaluate the boiler efficiency if the fuel mass rate is (350 kg/hr) and HHV is (338 00kJ/kg). vi –calculate the steam specific consumption (kg/kw.hr) . vii – if (90 % ) generator efficiency, calculate the OPPHR when the site auxiliary power consumption is (3 ) of that totally generated.

6 - 1 kg/s of hot superheated steam at 300 C is fed into the steam turbine at 2.5MPa. The turbine is adiabatic. The exiting stream is at 0 .1MPa, and is a saturated vapor at 100 C (just about to contain some condensed water). If 70% of the turbine rotational energy is used to drive a generator to convert to electrical energy, calculate the electrical output of this system.

Kerbala University Engineering College. Mech. Eng. Dept.- 3 rd year

Power Plant Sheet No. 17 2012 – 2013

----------------------------------------------------------------------------------------------------------Q.1 - Steam at a pressure of (15 bar) and (250 deg C) is expanded through a turbine at first to a pressure of (4 bar). It is then reheat a t constant pressure to the initial temperature of (250 deg C) and is finally expanded to (0.1 bar). Using Mollier chart, estimate the work done per kg of steam flowing through the turbine and amount of heat supplied during the process of reheat Assume all expansion processes to be isentropic.

Q.2 - A steam power plant operates on a theoretical reheat cycle. Steam from boiler at (150 bar) and (550 deg C) expands through the high pressure turbine. It is reheated at a constant pressure of (40 bar) to (550 deg C) and expands through low pressure turbine to a condenser at (0.1 bar). Draw the (T-s ) and (h-s) diagrams of the cycle . Find : I – quality of steam at turbine exhaust. Ii – cycle efficiency Iii –steam rate in kg/kw.hr

Q.3 - A turbine is supplied with steam at a pressure of (32 bar) and a temperature of (410 deg C). The steam then expands isentropically to a pressure of (0.08 ba r). Find the dryness fraction at the end of expansion and thermal efficiency of the cycle. If steam is reheated at (5.5 bar) to a temperature of (395 deg C) and then expanded isentropically to a pressure of (0.08 bar), what will be the dryness fraction and thermal efficiency of the cycle.

Q.4 - In a (15 MW) steam power plant operating on ideal reheat cycle, steam enters the HP turbine at (150 bar) and (600 deg C). The condenser is maintained at a pressure of (0.1 bar), if the moisture content at the exit of the LP turbine is (10.4%), assume steam to be reheated to the initial temperature, determine: i- reheat pressure. ii- thermal efficiency iii- specific steam consumption iv-rate of pump work

Q.5 – Study the shown diagram and answer the questions below using the given data find : a – the value of (m1) b – the plant thermal efficiency s.point P 1 1 5 MPa 2 4 MPa 3 ? 4 10 kPa U

U

Q.6 -

T 600ºC ? ? ?



----------------------------------------------------------------------------------------------------------Q.1 - A steam turbine is fed with steam hav ing an enthalpy of (3100 kJ/kg). It moves out of the turbine with an enthalpy of (2100 kJ/kg). Feed heating is done at a pressure of (3.2 bar) with steam enthalpy of (2500 kJ/kg). The condensate from a condenser with an enthalpy of (125 kJ/kg) enters into the feed water. The quantity of bled steam is (11200 kg/hr). Find the power developed by the turbine . Assume that the water leaving the feed heater is saturated liquid at (3.2 bar) and the heater is direct mixing type. Neglect pump work. -------------------------------------------------------------------------------------------------Q.2 - In a single heater regenerative cycle the steam enters the turbine a t (30 bar), and (400 deg.C), and the exhaust pressure is (0.10 bar). The feedwater he ater is adirect contact type which operates at ( 5 bar). Neglect pump work, Find : I – the efficiency and the steam rate of the cycle. ii- the increase in mean temperature as compared to the Rankine cycle with out regeneration of : a - heat addition b – efficiency c – steam rate

Q.3 - Steam is supplied to a turbine at a pressure of (30 bar), and a temperature of (400 deg.C), and is expanded adiabatically to a pressure of (0.04 bar). At a stage of turbine where pressure is (3 bar) a connection is made to a surface heater in which the feed water is heated by bled steam to a temperature of (130 deg.C). The condensed steam from the feed heater is cooled in a drain cooler to (27 deg.C). The feed water passes through the drain cooler before entering the feed heater. The cooled drain water combines with the condensate in the well of the condenser. Assume no heat losses in the steam, calculate : i - mass of steam used for feed heating per (1 kg) of steam entering the turbine. ii - thermal efficiency of the cycle. ---------------------------------------------------------------------------------Q.4 - Steam is supplied to a turbine at (30 bar) and (350 deg.C). The turbine exhaust pressure is (0.08 bar). The main condensate is heated regeneratively in two stages by steam bled from the turbine at (5 bar) and (1 bar) respectively. Calculate the masses of steam bled off at each pressure per kg of steam entering the turbine, and the theoretical thermal efficiency of the cycle. ----------------------------------------------------------------------------------------------------

Kerbala University Power Plant Engineering College Sheet No.19 Mech. Eng. Dept. 2012 – 2013 -----------------------------------------------------------------------------------------------------------

Q.1 –

Q.2 –

Q.3 -

Q.4 –

Q.5 –

Q.6 – Answer the followings : A - What is the relationship between water drum and super heater in regards to pressure? B - Name 8 considerations of installing an economizer? C - How do power plants practice reduced fuel consumption? D - Why do we have chemical treatment of feed water? E - What is high heating value and how is it different than low heating value. F - What do you find in flue gas analysis? Explain. G - Describe what is on a Mollier chart



----------------------------------------------------------------------------------------------------------Q.1 - A steam power plant with inlet steam to the HP turbine at (90 bar , 500 º C) and condensation at (40 º C) produces (500 MW). It has one stage of reheat optimally placed which raises the steam temperature back to (500 º C). One closed feedwater heater with drains cascaded back to the condenser receives bled steam at the reheat pressure, and the remaining steam is reheated and then expanded in the LP turbine. The HP and LP turbines have isentropic efficiencies of (92%, 90%) respectively. The isentropic efficiency of the pump is (75%). Use (TTD = - 1.6 º C), calculate : i – the mass flow rate of steam at turbine inlet in (kg/s) ii – the cycle efficiency iii – the cycle work ratio --------------------------------------------------------------------------Q.2 - An ideal steam power plant operates between (70 bar , 550 º C), and (0.075 bar). It has (7) feedwater heaters. Find the optimum pressure and temperature at which the heaters operate.

Q.3 - In a power plant, the efficiencies of the electric generator, turbine (mechanical), boiler, cycle and the overall plant are (0.97, 0.95, 0.92, 0.42, and 0.33) respectively. What percentage of the total electricity generated is consumed in running the auxiliaries.

Q.4 - A steam generator comprises a boiler, a superheater, an economizer, and an air preheater. The feewwater enters the economizer at (140 º C) and leaves as saturated liquid. Air is preheated from a temperature of (25 º C) to (250 º C). Steam leaves the boiler drum at (60 bar , 0.98 dry) and leaves the superheater at (450 º C). When using coal with CV of (25.2 MJ/kg) the rate of evaporation is (8.5 kg steam per kg coal and the AF ratio is (15) by mass. Neglecting heat losses and pressure drops, estimate the heat transfer per kg fuel in each component and the efficiency of the steam generator. What are the percentages of the total heat absorption taking place in the economizer, boiler, and superheater respectively. Assume Cp of air and water as (1.005 and 4.2) kJ/kg.k respectively.

Q.5 - Steam at (150 bar , 550 º C) is expanded in an HP turbine to (20 bar) when it is reheated to (500 º C) and expanded in LP turbines to condenser pressure of (0.075 bar). There are (5) feedwater heaters, one extraction from HP turbine at (50 bar), (3) FWH from LP turbine at (10 , 5 , 3 )bar, and one from LP turbine at (1.5 bar). The middle heater is the dearator and all others are closed heaters. Assume ideal conditions, take (TTD = 0) for all heaters, determine : i – the cycle efficiency ii – the feedwater temperature at inlet to the steam generator iii – the steam rate iv – the heat rate v – the quality of steam at turbine exhaust vi – the power output if the steam flow rate is (300 t/h)

Q.6 - A textile factory requires (10 t / h) of steam for process heating at (3 bar) saturated and (1000 kw) of power, for which a back pressure turbine of (70%) internal efficiency is to be used. Find the steam condition required at inlet of the turbine. ---------------------------------------------------------------------------------------



----------------------------------------------------------------------------------------------------------Q.1 - Steam at (40 bar , 500 º C) flowing at the rate of (5500 kg/hr) expands in a HP turbine to (2 bar) with isentropic efficiency 0f (83%). A continuous supply of steam at (2 bar). (0.87) quality and a flow rate of (2700 kg/hr) is available from a geothermal energy source. This steam is mixed adiabatically with the HP turbine exhaust steam and the combined flow then expands in a LP turbine to (0.1 bar) with an isentropic efficiency of (78%). Determine the power output and the thermal efficiency of the plant. Assume that (5500 kg/hr) of steam is generated in the boiler at (40 bar , 500 º C) from saturated feedwater at (0.1 bar). Had the geothermal steam not added, what would have been the power output and efficiency of the plant. Neglect pump work. Q.2 - In a cogeneration plant, the power load is (5.6 MW) and the heating load is (1.163 MW). Steam is generated at (40 bar , 500 º C) and is expanded isentropically through a turbine to a condenser at a (0.06 bar). The heating load is supplied by extracting steam from the turbine at (2 bar) which condensed in the process heater to saturated liquid at (2 bar) and then pumped back to the boiler. Neglecting pump work, compute : i – the steam generation capacity of the boiler in ( t/h) ii – the heat input to the boiler in (kW). iii – the fuel burning rate of the boiler in (ton/hr) if a coal of CV (25 MJ/kg) is burned and the boiler efficiency is (88%). iv – the heat rejected to the condenser. v – the rate of flow of cooling water in the condenser if the temperature rise of water is (6 º C). Q.3 - In a combined power and process plant the boiler generates (21000 kh/hr) of steam at a pressure of (17 bar) and temperature (230 º C). A part of the steam goes to a process heater consumes (132.56 kW), the steam leaving the process heater (0.957 dry) at (17 bar) being throttled to (3.5 bar). The remaining steam flows through an HP turbine which exhausts at a pressure of (3.5 bar). The exhaust steam mixes with the process steam before entering the LP turbine which develops (1337.5 kW). At the exhaust, the pressure is (0.3 bar) and the steam is (0.912 dry). Draw the line and T-s diagrams of the plant and determine : i – the steam quality at the exhaust of the HP turbine. ii – the power developed by the HP turbine iii – the isentropic efficiency of the HP turbine.

Q.4 - A mercury cycle is superposed on the steam cycle operating between the boiler outlet conditions at (40 bar and 400 ºC) and the condenser temperature (40 ºC). The heat released by mercury condensing at (0.2 bar) is used to impart the latent heat of vaporization to the water in the steam cycle. Mercury enters the mercury turbine as saturated vapor at (10 bar). Compute : i – Kg of mercury per Kg water. ii – the efficiency of the combined cycle. Q.5 - Calculate the ideal efficiency of a binary vapor cycle. The steam cycle operates between pressures (30 and 0.04) bar, and uses a superheat temperature of (450 deg.C). The mercury (Hg) cycle works between pressures (14 and 0.1) bar. The (Hg) entering the turbine in a dry saturated conditions. -----------------------------------------------------------------------------------------------------------Q.6 - A binary vapour cycle operates on mercury and steam. Standard mercury vapour at (4.5 bar) is supplied to the mercury turbine, from which it exhausts at (0.04 bar). The mercury condenser generates saturated steam at (15 bar) which is expanded in a steam turbine to (0.04 bar). i- determine the overall efficiency of the cycle. ii- if (48000 kg/hr) of steam flows through the steam turbine, wha t is the flow through the mercury turbine. iii- assuming that all processes are reversible, what is the useful work done in the binary vapour cycle for the specific steam flow. iv- if the steam leaving the mercury condenser is superheated to a temperature of (300 deg C) in a superheater located in the mercury boiler and if the internal efficiencies of the mercury and steam turbines are (0.84 & 0.88) respectively. Calculate the overall efficiency of the cycle. ------------------------------------------------------------------------------------------------------------

ALL TUTORIAL GROUPS SHOULD ATTEMPT TO SOLVE PROBLEM Q.7 Q.7 – In a cogeneration binary cycle, superheated steam enters the turbine with a mass flow rate of (5 kg/s) at (40 bar & 440 ºC) and expands isentropically to (1.5 bar). Half of the flow is extracted at (1.5 bar) and used for industrial process heating. The remaining steam passes through a heat exchanger which serves as the boiler of the refrigerant-R12 cycle and as the condenser for the steam cycle. The condensate leaves the heat exchanger as saturated liquid at (1 bar), where it is combined with the return flow from the industrial process at (60 ºC) and (1 bar), before being pumped isentropically back to the steam generator. The refrigrenet-R12 cycle is an ideal Rankine cycle with refrigerant entering the turbine at (16 bar & 100 ºC) and the saturated liquid leaving the condenser at (9bar). Determine : i – the rate of heat transfer in the steam generator. ii – the net power output of the binary cycle. iii – the rate of heat transfer to the industrial process.



----------------------------------------------------------------------------------------------------------Q.1 - To provide a natural draught a chimney of height (16 m) is used. Take ambient temperature as (20 deg C), calculate : I – the draught in mm of water when the temperature of the chimney gases is such that the mass of the gases discharged is maximum. II- If the temperature of flue gases does not exceed (350 deg C) find air suppled per kg of fuel, when discharge is maximum. [ ans. : (9.638 mm) , (15.87 kg/kg coal) ] Q.2 - With a chimney of height (45 m), the temperature of flue gases with natural draught was (370 deg C). The same draught was developed by induced draught fan and the temperature of the flue gases was (150 deg C). Mass of the flue gases formed is (25) kg/kg of coal fired. The boiler house temperature is (35 deg C). Assuming (Cp=1.004 kJ/kg.K) for the flue gases determine the efficiency of the chimney. [ ans. : (0.2 %) ] Q.3 - Determine the height and diameter of the chimney used to produce a draught for a boiler which has an average coal consumption of (1800 kg/hr) and flue gases formed per kg of coal fired are (14 kg). The temperature of ambient air and flue gases are (35 and 310) deg.C respectively. Assume actual draught is (80 %) of theoretical. The pressure losses through the system are given below : Pressure loss in fuel bed = 7 mm of water Pressure loss in boiler flues = 7 mm of water Pressure loss in bends = 3 mm of water Pressure loss in chimney = 3 mm of water Pressure head equivalent to velocity of flue gases passing through the chimney = 1.3 mm of water. [ ans. : (53.88 m) , (1.478 m) ] Q.4 - A chimney has a height of (24 m). The ambient temperature is (25 deg C). Temperature of flue gases passing through the chimney is (300 deg C). If the air flow through the combustion space is (20 kg/kg fuel burnt), find the followings : I – the theoretical draught in mm of water. II – velocity of the flue gases passing through the chimney if (50 %) of the theoretical draught is lost in friction at the grate and passage. [ ans. : (12.9 mm H2O) , (13.99 m/s) ]

Q.5 - Calculate power of a motor required to drive a fan which maintains a draught of (54 mm) of water under the following conditions for (i) induced draught fan, (ii) forced draught fan : Temp. of flue gases leaving the boiler in each case (Tg) = 240 deg C Temp. of air in the boiler house (Ta) = 20 deg C Air supplied per kg of fuel in each case (ma) = 18.5 kg Mass of coal burnt per hour (M) = 1820 kg Efficiency of the fan (ƞ f ) = 82 % [ ans. : (8.78 kW) , (5.014 kW) ] Q.6 - How much air is used per kg of coal burnt in a boiler having chimney of (32.3 m) height to create a draught of (19 mm) of water column when the temperature of the flue gases in the chimney is (370 deg C) and the temperature of the boiler house is (29.5 deg C). [ ans. : 18.52 kg/kg coal ]


Power Plant Sheet No.23 2012 – 2013

----------------------------------------------------------------------------------------------------------Q.1 - The following readings were obtained during a boiler trial of (6 hrs) duration : Mean steam pressure = 12 bar ; Mass of steam generated = 40000kg ; Mean dryness fraction = 0.85 ; Mean feed water temperature = 30 C ; Coal used = 4000 kg ; Coal CV = 33400 kJ/kg Calculate : i – factor of equivalent evaporation ii – equivalent evaporation from and at (100 C) iii – efficiency of the boiler. [ans . : (1.045) , (10.45 kg steam/kg fuel) , (70.65 %) ] °

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Q.2 - A steam generator evaporates (18000 kg/hr)of steam at (12.5 bar) and a quality of (0.97) from feed water at (105 C), when coal is fired at the rate of (2040 kg/hr). If the higher CV of the coal is (27400 kJ/kg), find : i – the heat rate of the boiler in kJ/hr ii – the equivalent evaporation iii – the thermal efficiency. [ans . : (4.1146 x 10**7 kJ/hr) , (8.936 kg steam/kg fuel) , (73.61 %) ] °

Q.3 - The following data refer to a boiler plant consisting of an economizer, a boiler and a super-heater..: Mass of water evaporated per hour = 5940 kg Mass of coal burnt per hour = 675 kg L.C.V of coal = 31600 kJ/kg Pressure of steam at boiler stop valve = 14 bar Temperature of feed water entering the economizer = 32 C Temperature of feed water leaving the economizer = 11 C Dryness fraction of steam ( leaving boiler- entering super-heater) = 0.96 Temperature of steam leaving super-heater = 260 C Specific heat of superheated steam = 2.33 kJ/kg.K Determine : i – percentage of heat in coal utilized in economizer, boiler, and super-heater ii – overall efficiency of boiler plant. [ans. : (9.66 ; 65.7 ; 6.34)% , 81.79 % ] °

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Q.4 - The following observations were made during the trial of a boiler plant consisting of a battery of (6) Lancashire boiler and an economizer : CV of coal/kg (29915 kJ); mass of feed water/kg dry coal (9.1 kg); equivalent evaporation from and at (100 C) per kg of dry coal (9.6 kg); temp. of feed water to economizer (12 C); temp. of feed water to boiler (105 C); air temp.(13 C); temp. of flue gas entering economizer (370 C); mass of flue gas entering economizer (18.2 kg/kg coal); mean specific heat of flue gas (1.046 kJ/kg.C); Find : i – the efficiency of the boiler alone ii - the efficiency of the economizer alone iii- the efficiency of the whole boiler plant. [ ans . : (72.4 %) , (52.1 %) , (84.2 %) ] °

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Q.5 - An oil fuel with a lower calorific value of (44700 kJ) is burnt in a boiler with air/fuel ratio of (20). Neglecting ash, calculate the maximum temperature attained in the furnace of the boiler. Assume that whole of the heat combustion is given to the products of combustion and their average specific heat is (1.08). Take boiler room temperature as (38 C). [ans. : (2009 °C) ] °

Q.6 - In a boiler test (1250 kg) of coal are consumed in (24 hrs). The mass of water evaporated is (13000 kg) and mean effective pressure is (7 bar). The feed water temperature was (40 C), heating value of coal is (30000 kJ/kg). The enthalpy of (1 kg) of steam at (7 bar) is (2570.7 kJ). Determine : i - equivalent evaporation per kg of coal. ii - efficiency of the boiler. [ ans. : (11.075 kg) , (83.3 %) ] °

Kerbala University Power Plant Engineering College Sheet No.24 Mech. Eng. Dept. – 4th class 20012 – 2013 ----------------------------------------------------------------------------------------------------------1 – The velocity of steam leaving the nozzles of an impulse turbine is ( 900 m/s ) and the nozzle angle is ( 20° ). The blade velocity is ( 300 m/s ) and the blade velocity coefficient is ( 0.7 ) . Calculate for a mass flow of ( 1 kg/s ) and symmetrical blading : i – blade inlet angle. ii – the driving force on the wheel. iii – the axial force . iv - – the diamgram horsepower . v – the diagram efficiency. ( anws : 29.24° , 927.7 N , 92.3 N , 278.3 KW , 68.7% ) 2 – In an impulse steam turbine , steam is accelerated through the nozzle from rest. It enters the nozzle at ( 9.8 bar ) dry saturated. The height of the blade is ( 10 cm ) and the nozzle angle is ( 15° ). The mean blade velocity is ( 144 m/s ), and the blade velocity ratio is (0.48), the blade velocity coefficient is ( 0.97 ), nozzle efficiency is ( 92% ), blade angles at inlet and outlet are equal, and the wheel rotational speed is ( 3000 rpm ). Find : i – isentropic heat drop. ii – energy lost in the nozzle and moving blade due to friction. iii – energy lost due to finite velocity of steam leaving the stage . iv – mass flow rate. v – power developed per stage . vi – diagram efficiency. vii – stage efficiency . ( anws : 48.9 KJ/kg , 0.83 KJ/kg , 3.2 KJ/kg , 112.95 kg/s , 4682 KW , 92.16% , 84.78% ) 3 – An impulsive stage of a steam turbine is supplied with dry saturated steam at ( 14.7 bar ). The stage has a single row of moving blades running at ( 3600 rpm ), the mean diameter of the blade disc is ( 0.9 m ). The nozzle angle is ( 15° ), and the axial component of the absolute velocity leaving the nozzle is ( 93.42 m/s ), the height of the nozzle at their exit is ( 100 mm ). The nozzle efficiency is ( 0.9 ), and the blade velocity coefficient is ( 0.966 ). The exit angle of the moving blade is ( 2° ) greater than the inlet. Determine : i – blade inlet and outlet angles . ii – isentropic heat drop in the stage . iii - stage efficiency. iv – power developed by the stage. ( anws : 29.5° , 31.5° , 196.82 KJ/kg , 0.66.2 , 17579.4 KW ) 4 – In a simple steam impulse turbine, steam leaves the nozzle with a velocity of ( 1000 m/s ) at an angle of ( 20° ) to the plan of rotation. The mean blade velocity is ( 60% ) of velocity of maximum efficiency. If the diagram efficiency is ( 7 0% ), and the axial thrust is ( 39.24 N per kg/s steam ). Calculate : i – blade angles . ( graphical solution ). ii – blade velocity coefficient. iii – heat lost due to friction in KJ/kg. ( anws : measured from V.diagram , .89 , 55.94 KJ/kg/s )

5 – The data for steam turbine operating conditions are given as follows : turbine speed steam mass flow inlet steam is saturated at inlet pressure of outlet steam pressure nozzle velocity coefficient blade inlet angle α i V b / V ai blade velocity coefficient KE of steam leaving last stage is blade velocity blading is mean diameter fo all stages ( windage + leakage ) losses

1800 6 0.5 x 10 6.9 2.76 0.97 13 2 (cos α i ) / 2 0.92 lost 70 symmetrical constant 3.5 %

rpm kg/hr MPa MPa degree

m/s

Determine : i – blading efficiency ii – stage efficiency iii – number of stages iv – actual power output ( ans : 0.9137 , 0.828 , 16 , 19.36 ) 6 – Draw a scale velocity diagram for a steam turbine having the following conditions : αi βe blade velocity coeff. blade velocity turbine speed Nozzle velocity coeff. V b / V ai

15 deg. 22 deg 0.91 350 m/s 3600 rpm 0.96 2 (cos α i ) / 2

Determine the followings by making your own assumption : i – stage efficiency ii – stage power iii – flow cross section area iv – friction losses.

Kerbala University Power Plant Engineering College Sheet No. 25 th Mech. Eng. Dept. – 4 year 2012 – 2013 -----------------------------------------------------------------------------------------------------------

1 – At a particular ring of a reaction turbine, the blade speed is ( 67 m/s ), and the rate of steam flow is ( 4.54 kg/s ). The steam is dry saturated at ( 1.373 bar ). Bothe fixed and moving blades have inlet and exit angles of ( 35° & 20° ) respectively. Determine : i – power developed by the pair of rings. ii – heat drop if the steam expands with efficiency of ( 80% ) . ( anws : 64.47 KW , 80.58 KJ/kg )

2 – Stage of a reaction turbine blading delivers dry saturated steam at ( 2.7 bar ) from a fixed blades at ( 90 m/s ). The mean blade height is ( 40 mm ), and the moving blade exit angle is ( 20 ° ). The axial velocity of the steam is ( ¾ ) of the blade velocity. Steam is supplied to the stage at the rate of ( 9000 kg/hr ). Calculate : i – the wheel speed ii – the diagram power. iii - The diagram efficiency. iv - Enthalpy drop of the steam in the stage . ( answ : 1822.8 rpm , 13.14 KW , 78.7% , 5.26 KJ/kg ) 3 – Steam at ( 15 bar ) and ( 350° C ) is expanded through ( 50% ) reaction turbine to a pressure ( 0.14 bar ). The stage efficiency is ( 78% ) for each stage, where expansion is carried out in ( 20 ) stages. The diagram power is ( 12000 KW ), and assuming that the stages all develop equal work. At a specified stage , [ the pressure is ( 1 bar ), steam is dry saturated, exit blade angles is ( 20° ), blade speed ratio is ( 0.7 ), and the blade height is ( 1/12 ) of the blade diameter ] . Calculate : i – flow of steam. ii – blade diameter. iii – rotor wheel speed . ( anws : 75790 kg/hr , 0.895 m , 2779.43 rpm )

4- A 50% reaction turbine having inlet steam entry angle is (20º), the absolute steam inlet speed is (240 m/s) and the blade mean velocity is (210 m/s), assuming diagram symmetry , i- draw scaled velocity diagram. ii- calculate power developed. iii- find the blade efficiency. 5- 12 successive stages of a reaction turbine have blades relative inlet and outlet angle of (80º and 20º )respectively. The mean diameter of the blade row is (1.2 m), and the speed of rotation is (3000 rpm). If the axial velocity is constant throughout the stages. The steam inlet conditions are (10 bar, 250º C), and the outlet pressure is (0.2 bar). Find : i- enthalpy drop per stage ii- the overall efficiency (ans. : 40.4 kJ/kg , 0.731 ) 6- A reaction turbine runs at (300 rpm) and it’s steam consumption is ( 16500 kg/hr). The pressure of steam at certain pair is (1.765 bar), and it’s dryness fraction Is (0.9) and the power developed by the pair is (3.31 kW). The discharge blade tip Angle both for fixed and moving blade is (20º) and the axial velocity of flow is (0.72) of the mean moving blade velocity. Find the drum diameter and the blade height. Take the tip leakage as (8%), but neglect area blocked by blade thickness. ( ans. : 1.03 m , 0.1 m )

Kerbala University Power Plant Engineering College Sheet No. 26 th Mech. Eng. Dept. 4 class 2012 – 2013 ----------------------------------------------------------------------------------------------------------1 – In a gas turbine unit, air is drawn in at ( 1.02 bar ) and ( 15° C ), and is compressed to ( 6.12 bar ). If maximum temperature is limited to ( 800° C ). Calculate for the ideal constant pressure cycle : i - thermal efficiency ii – work ratio. ( anws : 0.402 , 0.55 ) 2 – Calculate the thermal efficiency and the specific work output of a simple gas turbine plant operating on the Joule cycle. The max and min temperatures of the cycle are ( 1000°K) and ( 288° K ) respectively. The pressure ratio is ( 6 ) and the isentropic efficiency o f the compressor and turbine are ( 0.85 and 0.9 ) respectively. ( anws : 27.7% , 135 KJ/kg ) 3 – A gas turbine uses Joule cycle principles. The inlet pressure and temperature to the compressor are ( 1 bar ) & ( -10 ºC) respectively. After constant pressure heating, the pressure and temperature are ( 7 bar & 700 ºC) respectively. The flow rate of air is ( 0.4 ) kg/s . Calculate : i – cycle efficiency ii – heat transfer into the heater iii – net power output. ( ans. : 0.427 , 206.7 kW , 88.26 kW ) 4 – A gas turbine uses Brayton cycle. The pressure ratio is (6). The inlet temperature to the compressor is (10 ºC). The flow rate of air is (0.2 k g/s). The temperature at inlet to turbine is (950 ºC) . Calculate : i – the cycle efficiency ii – heat transfer into heater iii – net power output ( ans. : 0.4 , 150.95 kW , 60.38 kW ) 5 - A gas turbine expands gas from (1 MPa) pressure and (600 ºC) to (100 kPa ) pressure. The isentropic efficiency is (0.92). The mass flow rate is ( 12 kg/s). Calculate the exit temperature and the power output. ( ans.: 485.6 deg.K , 4672 kW ) 6 - A compressor stage working on air at (1 bar & 25 ºC) has a work output of (17 kJ/kg), and an isentropic efficiency of (0.9). Calculate the pressure at compressor outlet. ( ans. : 1.21 bar )

Kerbala University Power Plant Engineering College Sheet No. 27 th Mech. Eng. Dept. 4 class 2012 – 2013 -----------------------------------------------------------------------------------------------------------

1 - An air standard Brayton cycle operates between temperature limits (T 1 , T3 ) minimum and maximum temperature respectively. Show that the optimum pressure ratio for maximum specific output is given by

r p = (T3 /T 1 )γ/ (2 ( γ -1 )) 2 – An air standard Brayton cycle operates between temperature limits (T 1 , T3 ) minimum and maximum temperature respectively. Show that heating of compressed air by exhaust gas from the turbine will not be possible when

r p > (T3 /T 1 )γ/ (2 ( γ -1 )) 3 – Drive an expression for the work input to a two stage compression with complete inter-cooling, stating the condition that must be applied to achieve the required results . 4 – In a gas turbine cycle with reheating, show for maximum work output that :

rpi = √ rp.total

5 - A gas turbine plant consist of two compressor stages with perfect inter-cooling between the stages. The pressure ratio is the same for both stages, and the overall pressure ratio is (r p ). The temperature of air at inlet to the compressor is (T1). If the maximum temperature of the cycle is (T3). The expansion is carried out in a single stage turbine, show that the specific output will be maximum when

r p = (T3 /T 1

)⅔(γ/ ( γ -1 ))

6 – Do a complete comparison of the following cycles with the ideal Brayton cycle in-terms of thermal efficiency and specific work output : I - gas turbine cycle with regeneration. ii – gas turbine cycle with reheating . iii – gas turbine cycle with inter-cooling .


1 – A gas turbine unit working on standard Brayton cycle. The pressure ratio is (6.5), 2 air enters compressor at ( 1.03 kg/cm ) and (25 ºC). The maximum cycle temperature is (850 ºC). Calculate : i – specific output ii – cycle efficiency iii – power output for mass flow rate of (8 kg/s) ( ans : 256.2 kJ/kg air , 41.5% , 2049.6 kW ) 2 – A gas turbine used for electrical power generation plant. The shaft power supplied to the generator is ( 34.46 KW ). Combustion products enters turbine at ( 1530° K ) and exit at ( 720° K ) with a flow rate of ( 122.2 kg/s ). Approximating combustion products to air properties , estimate the fraction of turbine power used to generate electricity. Comments on your results . ( anws : 30% ) 3 – A gas turbine uses pressure ratio of (7.5). The inlet temperature and pressure are (10 ºC and 105 kPa). The temperature after heating in the combustion chamber is (1300 ºC). Assuming isentropic compression and expansion . For unit mass rate, calculate the ideal efficiency if no regenerator is used, and compare it to the thermal efficiency when regenerator of (0.88) effectiveness is used. Consider ( Cpa = 1.005kJ/kg.k ), (Cpg = 1.15 kJ/kg.k), ( γ = 1.4 for air ), and ( index k = 1.33 for exhaust gas ) . ( ans.: 0.438 , 0.693 ) 4 - A gas turbine power plant operates on a simple Brayton cycle with air as the working fluid. The air enters the turbine at 1 MPa and 1000 K and leaves at 125 kPa, 610 K. Heat is rejected to the surroundings at a rate of 8000 kW and air flow rate is 25 kg/s. Assuming a compressor efficiency of 80%, determine the net power output. How would the net power be affected if the compressor efficiency dropped to 75%? ( ans. : 3310 kW , 2594 kW )

5 - A Brayton cycle with regeneration and air as the working fluid operates on a pressure ratio of (8 ) . The minimum and maximum temperatures of the cycle are 300 and 1200 K. The adiabatic efficiencies of the turbine and the compressor are 80% and 82% respectively. The regenerator effectiveness is 65%. Determine ( a) the thermal efficiency, (b) net power output , and (c) how would the answers change if the regenerator effectiveness were increased to 75%? (ans. : 148.8 kW , 28.2 % , 148.8 kW , 29.5 % ) 6 – A gas turbine draws in air from atmosphere at ( 1bar & 10º ) and compresses it to (5bar) With an isentropic efficiency (80%). The air is heated to (1200 k)at constant pressure and then expand through two stages in series back to (1 bar). The HP turbine is connected to the compressor and produces just enough power to drive it. The LP turbine is connected to external load and Produces (80 kW) of power. Both turbines have isentropic efficiency of (85%). Calculate : i- air mass rate. ii- inter-stage pressure of turbine iii-cycle thermal efficiency (ans. : 0.423 kg/s , 2.29 bar , 23.2% )

Kerbala University Power Plant Engineering College Sheet No. 29 th Mech. Eng. Dept. 4 class 2012 – 2013 ----------------------------------------------------------------------------------------------------------1 – A gas turbine draws air from atmosphere at (1bar & 15 ºC) an d compresses it to (4.5 bar) with an isentropic efficiency 0f (0.82). The air is heated to (1100 ºK) at constant pressure and then expanded through two stages in series back to (1 bar). The HPT drives the compressor and the LPT produces (100 kW) for external use. The isentropic efficiencies for both turbines are (0.85). Neglecting the increase in mass due to the addition of fuel. Calculate : i– air mass rate ii – cycle thermal efficiency. ( ans. : 0.642 kg/s , 20.1% ) 2 –A gas turbine power generating plant has two turbines, one to drive the compressor and the other to drive the generator. The compressor takes in air at (27 ºC) and compresses it according to a pressure ratio of (6). Compressed air is then passed through the combustion chamber where its temperature is raised to (1050 ºK). Pressure ratios for both turbines are (6). If only sufficient hot gases is passed through the turbine to drive the compressor, and the isentropic efficiencies for both the compressor and the turbines are (0.85). Calculate : I – the fraction of hot gases passing through the compressor’s turbine. Ii – power output of the turbine driving the generator per kg of air. Iii – plant efficiency. (Ans. : 0.66 , 122.3 kW , 23.69% ) 2

3 – A gas turbine operating on Brayton cycle between pressure range of ( 0.098 and 0.49 MN/m ). Compressor takes in air at (300 ºK) and c ompresses it to the maximum pressure limits with isentropic efficiency of (82%). If (0.013 kg) of fuel ha ving LHV of ( 42000 kJ/kg) is supplied per (kg of air ). If the turbine isentropic efficiency is ( 8 6%) , calculate : i – power output per kg of air ii –the ideal thermal efficiency of the unit iii – the actual thermal efficiency of the plant iv – the unit relative efficiency (ans. : 125 kJ/kg air , 37% , 22.5% , 60.8% ) 4 – A gas turbine unit has a pressure ratio of ( 6 ) and max cycle temperature of ( 600° C ). The isentropic efficiency of the compressor and turbine are ( 0.82 and 0.85 ) respectively. air enter the compressor at ( 15° C ) and ( 15 kg/s ). Calculate: i - the power output in ( KW ) of an electric generator geared to the turbine. ii - the plant thermal efficiency iii – the work ratio of the plant ( anws : 920 KW , 15.8% , 0.206 ).

2

5 – In a gas turbine plant the air pressure and temperature before co mpression are ( 1.01 kg/cm and 28 ºC). The ratio of max to min pressures is (3.5), and the temperature of gas before expansion in the turbine is ( 700 ºC). If the isentropic efficiencies of the compressor and the turbine are ( 80% & 85%) respectively. Calculate : i – turbine exhaust temperature. ii – cycle thermal efficiency iii – percentage change in plant thermal efficiency if regenerator of (0.7) effectiveness is added to the plant. (ans. : 724 ºK , 17% , 56.47% increase ) 6 – A gas turbine unit takes in air at ( 17° C) and ( 1.01 bar ), the pressure ratio is ( 8 ). The compressor is driven by the HP turbine , and the LP turbine drives a separate power shaft. The isentropic efficiencies of the compressor, the HP turbine and the LP turbine are ( 0.8 , 0.85 , and 0.83 ) respectively. Considering max temperature (650° C) Calculate : i – pressure and temperature of the gases entering the power turbine. ii – the net power developed by the unit per kg/s mass flow. iii – the work ratio. iv – the thermal efficiency. ( anws ; 620.5°K , 1.65 bar , 74.5 KW , 0.201 , 19.1% )


DRAW THE SCHEMATIC AND T-s DIAGRAMS OF THE

FOLLOWING GAS TURBINE

CYCLES :

1 – Closed cycle with separate power turbine , two combustion chambers and regeneration. The hot gases flows in series through the turbines .

2 – Closed tandem cycle having two stages of compression and expansion with reheating , regeneration and inter-cooling.

3 – Open cycle with separate power turbine , two combustion chamber and regeneration. The hot gases flows in parallel through the turbines.

4 – Single shaft closed cycle constant pressure combustion with reheat and regeneration.

5 – Closed compound two stages of compression and expansion with regeneration and inter-cooling.

6 – Single shaft closed cycle constant pressure combustion with multi stage compression and inter-cooling.

Kerbala University Power Plant Engineering College Sheet No. 31 th Mech. Eng. Dept. 4 year 2012 – 2013 --------------------------------------------------------------------------------1 – Estimate the flow rate of air and specific fuel consumption (gm/kW.hr) of a gas turbine plant when it is developing (410 kW) out put with a ( r p = 4). The isentropic efficiency of the compressor and turbine are both (84%). The fuel LHV of (42000kJ/kg ). The gas leaves the turbine at (580 ºC). Atmospheric conditions are ( 1bar and 25ºC). Assume [Cp = 1.005 kJ/kg.k and

γ = 1.4] for air Into compressor , and {Cp = 1.108 kJ/kg.k and γ = 1.39} for gas

In combustion chamber. i- estimate air flow rate ii- specific fuel consumption (gm/kW.hr) iii- plant efficiency (Ans. : 2.228 kg/s , 363.8 gm/kW.hr , 23.6 %) 2 – An open cycle gas turbine plant consists of a compressor , combustor, turbine and regenerator. Air is compressed from ( 1.01 2 2 kg/cm and 20 ºC) to (6.5 kg/cm ). Heat is added to increase the temperature to (770 ºC). Expansion takes place in the turbine after which the gas passes through the regenerator. Pressure loss in the air side of the regenerator together with the combustion chamber is 2 2 (0.07 kg/cm ), and the gas side of the regenerator is (0.05 kg/cm ). If the regenerator thermal ratio is (0.6), and the gas leave the 2 regenerator at pressure of (1.05 kg/cm ). The process in the compressor and turbine assumed isentropic, and [Cp = 1.005

kJ/kg.k and γ = 1.4]. Calculate the plant specific output and efficiency. Ans. : 208.73 kJ/kg air , 44.6 %

3- A gas turbine plant of (800 kW) capacities, takes the air at ( 1.01 bar and 15ºC). The pressure ratio of the cycle is (6), and the max temperature is limited to (700 ºC). A regenerator of (75%) effectiveness is added in the plant to increase the overall efficiency of the plant. The pressure drop in the combustion chamber is (0.15 bar), as well as in the regenerator is also (0.15 bar). Assuming the isentropic eff. of the compressor and turbine are ( 0.80 and 0.85) respectively. Determine the plant thermal eff. and neglecting the mass of the fuel. ( ans. : 19.6 % ) 4- In an open cycle regenerative gas turbine plant, the air enter the compressor at ( 1 bar and 32 ºC) and leaves at (6.9 bar). The temp. at the end of the combustion end is (816 ºC). The isentropic eff. of compressor and turbine are respectively (.84 & 0.85). combustion eff. is (90%) and regenerator effectiveness is (60%). Determine : i- thermal eff. ii- air rate (kg/kw.hr) iii-. Work ratio (ans. : 25.48% , 28.56 kg/kW.hr , 0.32 ) 5- In a gas turbine plant, air is compressed through a pressure ratio of (6) from (15 ºC). It is then heated to the max permissible temp. of (750 ºC) and expanded in two stages, each of expansion ratio of ( √6 ). The air being reheated between the stages to (750 ºC). A heat exchanger allows the heating of the compressed gas through (75%) of the max range possible. The isentropic eff. of the compressor and turbine are (0.8 & 0.85). Calculate : i- cycle eff. ii- work ratio iii- work/kg air (ans. : 0.324 , 0.385 , 152 kJ/kg air ) 6- A simple open cycle gas turbine plant operates with a pressure ratio (5) and the ratio of max to min cycle temp. {(T3/T1) = 3}. If the isentropic eff. of turbine is (0.87), and inlet temp. to compressor is (300k). Calculate the minimum isentropic eff. of the compressor for which the unit will produce power. (ans. 0.62)

Kerbala University Power Plant Engineering College Sheet No. 32 th Mech. Eng. Dept. – 4 2012– 2013 ----------------------------------------------------------------------------------------------------------1- Air enters the compressor of a simple gas turbine at 0.1 MPa, 300 K. The pressure ratio is 9 and the maximum temperature is 1000 K. The turbine process is divided into two stages each with a pressure ratio of 3, with intermediate reheating to 1000 K. Determine (a) the cycle efficiency and (b) net output. (c) What would the answers be if the reheat were eliminated? Answers: (a) 39.15%, (b) 277.8 kJ/kg, (c) 46. 65%, 204.8 kJ/kg

=============================================================== 2- Repeat problem (1) for the net output per kg of air, assuming the pressure ratio of the first stage turbine before reheat to be (a) 7, (b) 5, (c) 3, (d) 2. (e) Use a T-s diagram to explain why the output increases and then decreases. Answers: (a) 234.6 kJ/kg, (b) 262.2 kJ/kg, (c) 277.8 kJ/kg, (d) 268.0 kJ/kg =============================================================== Air enters the compressor of an ideal air standard Brayton cycle at 100 kPa, 290 K, with a mass flow rate of 6 kg/s. The compressor pressure ratio is 10. The turbine inlet temperature is 1500 K. If a regenerator with an effectiveness of 70% is incorporated in the cycle, determine (a) the thermal efficiency of the cycle. (b) What would the thermal efficiency be if the regenerator effectiveness increased to 9 0% ? 3-

Answers: (a) 57.50%, (b) 60.83%

=============================================================== A Brayton cycle with regeneration and air at 100 kPa as the working fluid operates on a pressure ratio of 8. The minimum and maximum temperatures of the cycle are 300 and 1200 K. The adiabatic efficiencies of the turbine and the compressor are 80% and 82% respectively. The regenerator effectiveness is 65%. Determine (a) the thermal efficiency and (b) net power output. (c) What would the thermal efficiency be if the regenerator effectiveness increased to 75%? 4-

Answers: (a) 27.12%, (b) 133.5 kW, (c) 28.1 1% =============================================================== Air is compressed from 100 kPa, 310 K to 1000 kPa in a two stage compressor with intercooling between stages. The intercooler pressure is 350 kPa . The air is cooled back to 310 K in the intercooler before entering the second compressor stage. Eac h compressor stage is isentropic. Determine (a) the temperature at the exit of the second compressor stage and (b) the total compressor work in kJ/kg. 5-

Answers: (a) 417.3 K, (b) 242.6 kJ/kg

===============================================================

o

Air enters the compressor of an ideal air standard Brayton cycle at 100 kPa, 25 C with 3 a volumetric flow rate of 8 m /s and is compressed to 1000 kPa. The temperature at the o inlet to the first turbine stage is 1000 C. The expansion takes place isentropically in two o stages, with reheat to 1000 C between the stages at a constant pressure of 300 kPa. If a regenerator having an effectiveness of 100% is incorporated in the cycle, determine (a) the thermal efficiency of the cycle. 6-

Answers: (a) 62.1%

Kerbala University Power Plant Engineering College Sheet No. 33 th Mech. Eng. Dept. – 4 class 2012 – 2013 ----------------------------------------------------------------------------------------------------------1 – In a marine gas turbine unit a HP stage turbine drives the compressor, and a LP stage turbine drives the propeller through suitable gearing. The overall pressure ratio is (4) and the maximum temperature is (650 deg.C). The isentropic efficiency of the compressor, HP turbine, and LP turbine are ( 0.8 , 0.83 , 0.85 ) respectively, and the mechanical efficiency of both shafts is (98%). The air intake conditions are (1.01 bar and 25 deg.C) . Neglecting all other losses. Calculate : i – the pressure between turbine stages. ii – thermal efficiency iii - shaft power when the mass flow is (60 kg/s). v – plant thermal efficiency when heat exchanger of (0.75) thermal ratio is fitted (ans : 1.57 bar , 14.9% , 4560 kW, 23.4% ) 2 – In a gas turbine generating station the overall compression ratio is (12), performed in three stages with pressure ratios of ( 2.5 , 2.4 , 2 ) respectively. The air inlet temperature to the plant is (25 deg.C), and inter-cooling between stages reduces the temperature to (40 deg.C). The HP turbine drives the HP & IP compressor stages. The LP turbine drives the LP compressor and the generator. The gases leaving the LP turbine are passed through a heat exchanger which heats the air leaving the HP compressor. The temperature a t inlet to the HP turbine is (650 deg.C), and reheating between turbine stages raises the temperature to (650 deg.C). The gases leaving the heat exchanger at temperature of (200 deg.C). The isentropic efficiency of each compressor stage is (0.83), and the isentropic efficiencies of the HP & LP turbines are (0.85 & 0.88 ) respectively. Take the mechanical efficiency of each shafts (98%). The air mass flow is (140 kg/s). Calculate : i – the power output (kW) ii – plant thermal efficiency. iii – the heat exchanger thermal ratio. ( ans : 25300 kW , 33.7% , 0.825 ) 3 – A (5000 kW) gas turbine generating set operates with two compressor stages with inter-cooling between stages. The overall pressure ratio is (9). A HP turbine is used to drive the compressors, and a LP turbine drives the generator. The temperature of the gas at entry to the HP turbine is (650 ºC), and the gases are reheated to ( 650 ºC) after expansion in the first turbine. The exhaust gases leaving the LP turbine are passed through a heat exchanger to heat the air leaving the HP stage compressor. The compressors have equal pressure ratios and inter-cooling is complete between stages. The air inlet temperature to the unit is (15 ºC). The isentropic efficiency of each compressor stage is (0.8), and the isentropic efficiency of e ach turbine stage is (0.85). The heat exchanger thermal ratio is (0.75). A mechanical efficiency of (98%) can be assumed for both the power shaft and the compressor turbine shaft. Neglecting all pressure losses and changes in KE, calculate for the plant i – thermal efficiency ii- work ratio iii – air mass flow rate ( neglect fuel mass rate ) (Ans. : 0.288 , 0.358 , 32.6 kg/s )

4 – In a gas turbine generating set two stages of compression are used with an intercooler between stages. The HP turbine drives the HP compressor, and the LP turbine drives the LP compressor and the alternator.. The exhaust from LP turbines passes through a heat exchanger which transfers heat to the air leaving the HP compressor. There is a reheat combustion cha mber between turbine stages which raises the gas temperature to ( 600 deg. C), which is also the gas temperature at entry to the HP turbine. The overall pressure ratio is (10), each compressor having the same pressure ratio, and the air temperature at entry to the unit is (20 deg.C). Assuming isentropic efficiencies of (0.8) for both compressor stages, and (0.85) for both turbine stages, and that (2 %) of the work of each turbine is used in overcoming friction. The he at exchanger thermal ratio is (0.7), and inter-cooling is complete between compressor stages. Neglecting all other losses. Calculate : I – the power output (kw) for mass flow rate of (115 kg/s) Ii – the overall thermal efficiency of the plant. ( ans. : 14460 kW , 25.7 % )

5 – A gas turbine unit has two compressors in series giving overall pressure ratio of (6). The air leaving the HP compressor passes through a heat exchanger before entering the combustion chamber. The heat exchanger thermal ratio is (0.65). The expansion is in two turbine stages, the first stage driving the compressors, and the second stage driving the generator. The gases leaving the LP turbine pass through the heat exchanger before exhausting to atmosphere. The HP turbine inlet temperature is (800 deg.C) and the air inlet temperature to the system is (15 deg.C). The isentropic efficiency of each compressor is (0.8), and that of each turbine is (0.85). The mechanical efficiency of each shaft is (98%). Neglecting all othe r losses, calculate : I – the overall thermal efficiency Ii – the power developed when air mass flow is (0.7 kg/s ) Iii – specific fuel consumption of fuel having calorific value of (42000kJ/kg), and the combustion efficiency is (97%). (Ans : 28.7% , 94.3 kW , 0.303 kg/kW.hr) 6 – A gas turbine draws in air from atmosphere t ( 1 bar and 10 ºC) and compresses it to (5 bar) with an isentropic efficiency of (80%). The a ir is heated to (1200 ºK) at constant pressure and then expanded through two stages in series back to ( 1 bar). The HP turbine is connected to the compressor and produces just enough power to drive it. The LP turbine stage is connected to an external load and produces (80 kW) of power. The isentropic efficiency is (85%) for both turbine stages. Neglecting the increase in mass due to the addition of fuel for combustion. Calculate : I – the mass flow of air. Ii – the inter-stage pressure of the turbines. Iii – the cycle thermal efficiency. ( ans. : 0.423 kg/s , 2.29 bar , 23.2% )

7. A gas turbine is to be used in a CHP plant, the maximum cycle temperature is (1000 ºK) and the air suction temperature is (288 ºK). The pressure ratio is (6), and the isentropic efficiencies of the compressor and turbine are (0.85 & 0.90) respectively. γ = 1.4 and Cp = 1.005 kJ/kg K for air and gas. The exhaust from the gas turbine is to be used to generate 15 bar, 350 ºC steam in a boiler which is supplied to a steam turbine where it exhausts at 0.04 bar. The gas and steam turbines are used to generate electrical power. The exhaust gas leaves the boiler at 170 ºC. The isentropic efficiency of the steam turbine is 0.85. If the gas turbine output power is 100 MW, what is the output power of the combined cycle and what is the combined cycle efficiency? (Approx. 140 MW, and 40 %)

( Cp = 1.005 kJ/kg.k , γ = 1.4 )for compression and for expansion Cp=1.15 kJ/kg.k and γ=1.333.

Kerbala University Power Plant Engineering College Sheet No. 34 Mech. Eng. Dept. 2012– 2013 -----------------------------------------------------------------------------------------------------------

1- The volumetric rate of water in a hydro-electric scheme is (50 m³/s). The overall efficiency of the plant is (72 %). If the electric power output is to be (150 MW). What head of water is required. ( ans. : 14.4 m ) 2- The mean height of the feeder reservoir in a hydro-electric power scheme is (568 m). At rated load the overall efficiency is (86 %). If the plant operates for (5 hrs), delivering (1750 MW). What mass of water : i – passed through the turbine ii – has been the flow rate. 6 3 (ans. : 6.5 x 10 m , 365 kg/s ) 3- A hydro-electricity supply system has an overall efficiency of (82 %). If the effective head is ( 500 m), calculate the volumetric flow rate needed to generate (300 MW) of electrical power. (ans. : 74.59 %) 4- A hydro-power plant produces (100kW) from water fall of (50m). What is the flow velocity if water wheel instead of water turbine is to be used in an identical plant. (ans. : 31.38 m/s ) 3 5- Water falls at (2.5 m /s)from a large reservoir through the penstock to a hydro-turbine. The reservoir surface is (30 m) above the turbine water exit location. Determine : i- the ideal power produced from this system. ii- assuming overall losses is equivalent to (1 m ) head, what will be the turbine efficiency in this case. iii- if the electrical generator efficiency is (95 %) of the turbine efficiency, calculate the effective power of the electrical generator. (ans.: 735.75 kW , 96.7 % , 653.63 kW ) 6- Water turbine produces ideal hydro-power of (100kW) from water fall of (51m) above turbine exit pipe at (3 m/s) velocity. Determine : i- water mass rate ii- exit pipe diameter (ans. : 199.8 kg/s , 29.13 cm )



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1 - The following data relate to a proposed hydro-electric station: Available head (28 m); catchment area (420 sq. km); rainfall (140 cm/yr); percentage of rainfall utilized (68 %); penstock efficiency (94 %); turbine efficiency (8) %); generator efficiency (84 %); load factor (44 %). i - Calculate the power developed. ii – suggest suitable machines and specify the same. [ ans. : 2186 kW , 2 machines each of 2957 kW rating] 2 - The following data is available for a hydro-power plant: Available head (140 m); catchment area (2000 sq. km); annual average rainfall (145 cm); turbine eff. (85 %); generator eff. (90 %); percolation and evaporation losses (16 %). Determine : i-Power developed ii-Suggest type of turbine to be used if runner speed is to be below (240 rpm) [ ans. : 8111 kW , Pelton] 3 - A hydroelectric station is to be designed to operate at a mean head of (205 m) and supplied from a reservoir lake having catchment area of (1000 sq. km) with average annual rain fall of (125 cm) of which (80 %) is available for power generation. The expected load factor at the plant is (75 %). Allowing a head loss of (5 m) and assuming efficiency of the turbine and generator to be respectively (90 % , 95 %). I - Calculate suitable MW rating of the station. Ii – comment on the type of turbine to be installed. [ans . : 70.9 MW , Francis ]

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