Question

thermaldynamics and fluid mechanics

Question 4 An orifice plate flow meter, as shown in figure Q4, is situated in a horizontal pipe of 95 cm diameter (d) in which water flows. The pressure difference between the vena contracta and flow upstream at point 1 is measured using a differential manometer. The diameter of the sharp-edged orifice (d.) is 35 cm. The coefficient of discharge for the flow meter is 0.7, and the coefficient of contraction is 0.62. Assume the density of mercury to be 13600 kg/ml. (i) Determine the pressure difference between points 1 and 2 [5 marks] Determine the equation for the ideal (theoretical) volumetric flow rate. [5 marks] Calculate the cross-sectional areas of the pipe and vena contracta. (5 marks] (iv) Evaluate the value for the ideal (theoretical) volumetric flow rate of the water in the pipe. (5 marks] (v) Evaluate the value for actual (real) mass flow rate of the water in the pipe and find the coefficient of velocity for the orifice plate flow meter. (5 marks) Water Flow - Streamlines Vena Contracta Differential manometer Mercury Figure Q4: Flow through an orifice plate flow meter.

Answer 1

Oy onfuce Plate floometer. die gsem du: 35cm coefterorent of discharge Ca=0.4 Weffeverent of comboection, 6c70.62 Density of mercry, m= 136o@kglm} water density, P.1000 I3 m3 dvezda 1 a I Bazocm a H mereury. Head difference of U-tube manometer h. 20cm of Hg In terms of water Haths - 1720 of me -12 2252cm = 2. 52m 42252m. (1) Bessure difference, AP: IgH 1000x 9.81x2.52 224721.2 Da T AP=24121.2 P9] Calculate Equation of volumetric flowsate. het Pipp and Vina be the pressure and velvotes respectively at sections ® and . Then by applying Bernoull's equation, 2122, (Herizontal), Ho difference between prezometic heads. V2-]39H+ VIZ s 9f 91,90,92 be the area of cross-section at Section ☺ ☺ and crisferee respectively, Discharge, Q- Q,Mg = R0 V2 vij V2 = a J 2sh His this, cua coefficient of reality,

The section is the section of minimum arca (vena -conbauta). It is related to ao by goscila ell cp coeffercient of compaction. Bern eq, d), and db. Vea cu __2944 JI- Cu? ce? S9372 Q = Q0 V2 = 6692.12 Cc C cd Cel: cuischarge weftimento Therefore, az ca al Jagn So-cat (12) a=canai Jagh Jarraz? (li) Cross-section area of pipe ay and vene- cenbente an 9. ore y 60,55)2=0.4083 m2 90+ Cext da? 20 = 0.6277 .3514 Tai? o. todam? 199=0.0556 m2) % Calculate 2227,700,353 92=0,0562 m² theertercal fellowrate la GX 91 92 Jagh . Sapa-azz cl= 0.7% 0.4083X 0.0962 J 249.81x2. 52 v (0.7086)2-(0.056252 1 Q20,4745 m/s )

♡ Calculate Oetual mass fallero date. misa mm 160 x 0.4449 .474.38 ksts coefficient of velocity, Gdaccou G= 1, 129 Cu71 Case case)