Question

A venturimeter having a throat diameter of 0.1 m is used to estimate the flow rate of a horizontal pipe having a diameter of 0.2 m. For an observed pressure difference of 2 m of water head and coefficient of discharge equal to unity, assuming that the energy losses are negligible, the flow rate (in $m^3/s$) through the pipe is approximately equal to

• A. 0.500
• B. 0.150
• C. 0.050
• D. 0.015

Answer 1

The correct option is C 0.050

Diameter of throat,
d = 0.1 m
Diameter of pipe,
D = 0.2 m
Pressure difference,

$\frac{P_1-P_2}{w}=2m=h$


Coefficient of discharge,
$C_D=1$
Discharge,

$Q=\frac{C_D.A_1{A}_2\sqrt{2gh}}{\sqrt{A_1^2-A_2^2}}$

$A_1=\frac{\pi }{4}{\left(0.2\right)}^2$

$and{A}_2=\frac{\pi }{4}{\left(0.1\right)}^2$

$\Rightarrow Q=\frac{1\times {\left(\frac{\pi }{4}\right)}^2\times {\left(0.2\right)}^2{\left(0.1\right)}^2\sqrt{2\times 9.81\times 2}}{\left(\frac{\pi }{4}\right)\sqrt{(0.2{)}^4-(0.1{)}^4}}$

$=0.0508=0.050m^3/sec$