Calibration of Venturimeter

CALIBRATION OF VENTURIMETER AND ORIFICMETER Aim: To calibrate venturimeter and orifice plate for a given fluid and study the variation of coefficient of  discharge C d  d with Reynolds Number. Apparatus: Venturimeter, U-tube mercury manometer, stop watch, calibrated measuring tank, orificemeter, load cell and required accessories for mass measurement, Differential Pressure Transducer (DPT) to measure the rate of flow through through a pipe. Venturimeter consists consists of a Theory: Venturimeter is used to converging portion, throat and a diverging portion. The function of the converging portion is to increase the velocity of the fluid and temporarily lower its static pressure. The pressure difference between inlet and throat is developed. This pressure difference is correlated to the rate of flow. The expression for theoretical flow rate is obtained by applying the continuity equation and energy equation at inlet and throat section, and assuming the fluid to be ideal is given by:

Qth =

 A2

2 g h

⎡ ⎛  A  ⎞ 2 ⎤ ⎢1 − ⎜⎜ 2 ⎟⎟ ⎥ ⎢⎣ ⎝  A1  ⎠ ⎥⎦

where  A1 and  A2 are areas at inlet and throat & h static pressure difference between inlet and throat section in terms of m of water. Same equation for theoretical discharge holds good for orificemeter also. Construction of orificemeter is simplest amongst all the flowmeters in that it consists of a plate with a hole drilled in it. In principle, it is essentially similar to a venturi since it obstructs the flow of fluid, however, due to the absence of guiding passage on the downstream passage of the orificemeter, fluid comes out in the form of a free jet. This difference in the flow physics of the two flowmeters leads to difference in the value of discharge coefficient and irrecoverable pressure loss even when the area ratios for two are identical. Calibration of flowmetersEquations derived above relating flow rate to the differential pressure cannot be applied directly in practical applications. All the flowmeters need calibration a priori where a known quantity of fluid is passed through the flowmeter and the differential pressure across the flowmeter related to the actual mass flowrate through a discharge coefficient given as the ratio of actual to theoretical mass flowrate. Two methods of knowing the actual mass flowrate are- measurement of time for collection of a finite volume of fluid and measurement of mass collected in a certain amount of time. Procedure: Adjust the discharge. Note down the pressure difference hm. Calculate the theoretical discharge Qth. Note down the time for collection of 600 litres of water in the measuring tank and determine the actual discharge Qact . Also calculate the actual actual discharge by measuring measuring the mass collected in 300 sec. with the help of load cell and data acquisition software provided. Calculate the coefficient of  discharge C d  procedure for atleast ten mass mass flowrates for both both venturimeter venturimeter and orificemeter. d.  Repeat the procedure Observation Table: Diameter of the inlet section  D1 80mm Diameter of the throat section  D2 47mm 9810 N/m3 Specific weight of water γ  w 0.001 Pa.s Dynamic viscosity of water µ  3 Density of water ρ water  ρ 998 kg/m

Sl N o

Actual flowrate Vol. flowrate readings Volu me colle cted 3 (m )

Time (sec)

Orificemeter Readings Mass readings Mass colle cted (kg)

Q ac  t

(m 3  /s)

Venturimeter readings

flowrate

Time (sec)

Q act (m3 /s )

 D1

Man omet er Read ing (m of  Hg)

DPT Read ing (kPa )

Q th (m 3  /s)

C  d 

Man omet er Read ing (m of  Hg)

DPT Read ing (kPa )

Q th (m 3  /s)

C  d 

Specimen Calculations:

Qth =

 A2

2 g h

⎡ ⎛  A  ⎞ 2 ⎤ ⎢1 − ⎜⎜ 2 ⎟⎟ ⎥ ⎢⎣ ⎝  A1  ⎠ ⎥⎦

;

V 2th =

Qact 

⎛ π  2 ⎞ ⎜  D2 ⎟ ⎝  4  ⎠

; Re D1

V 1 D1

; C d  =

Qact  Qth

ISO 5167 specifies value of discharge coefficient for orificemeter as a function of diameter ratio  β  and Reynolds number Re D1-

⎛ 10 6 β  ⎞ 2 8 ⎟⎟ C d  = 0.5961 + 0.0261 β  − 0.216 β  + 0.000521⎜⎜  R e ⎝   D1  ⎠ where diameter ratio β  =

0. 7

Orifice diameter  D2

 Pipe diameter 

=

 Re

 D1

Calculate the value of discharge coefficient for the orificemeter according to ISO standard. Also note that the value of discharge coefficient for ventrimeter as specified by ISO 5167 is 0.984. Calculate uncertainty in estimation of the discharge coefficient for venturimrter and orificemeter for highest and lowest value of Reynolds number for volume flowrate and mass flowrate readings. Graphs: Compare the values of discharge coefficient obtained by volumetric flowrate measurement and mass flowrate measurement and comment on the result. Plot a graph of  C d  vs  Re D1 obtained by mass flowrate measurement, volume flowrate measurement and ISO 5167. Note- Mass measurement system has the following specification• Load cell used- Shear beam load cell, Stainless steel, IP68 grade • Platform scale capacity-5 tons • Platform scale accuracy- 1kg • Platform size- 1.5m × 1.5m Load cell is connected to a computer through a data acquisition system through RS 232 port.