Question

A venturimeter of 20 mm throat diameter is used to measure the velocity of water in a horizontal pipe of 40 mm diameter. If the pressure difference between the pipe and throat sections is found to be 30 kPa then, neglecting frictional losses, the flow velocity is

• A. 0.2 m/s
• B. 1.0 m/s
• C. 1.4 m/s
• D. 2.0 m/s

Answer 1

The correct option is D 2.0 m/s

Given data:
$d_2=20mm=0.02m,$
$d_1=40mm=0.04m$
$\Delta p=p_1-p_2=30kPa=30\times {10}^{3}Pa$

For continuity equation,We get
$A_1{V}_1=A_2{V}_2$
$V_2=\frac{A_1}{A_2}{V}_1=\frac{\frac{\pi }{4}{d}_1^2}{\frac{\pi }{4}{d}_2^2}\times V_1$
$={\left(\frac{d_1}{d_2}\right)}^2{V}_1={\left(\frac{0.04}{0.02}\right)}^2{V}_1$
$V_2=4V_1$
Applying Bernoulli's equation,We get
$\frac{p_1}{\rho g}+\frac{V_1^2}{2g}+z_1=\frac{p_2}{\rho g}+\frac{V_2^2}{2g}+z_2$
For horizontal pipe,
$z_1=z_2$
$\frac{p_1-p_2}{\rho g}=\frac{V_2^2-V_1^2}{2g}$
$\frac{\Delta p}{\rho }=\frac{1}{2}(V_2^2-V_1^2)$
$\frac{30\times {10}^3}{1000}=\frac{1}{2}\left[\right(4V_1{)}^2-V_1^2]$
$\frac{15V_1^2}{2}=30$
$V_1^2=4$
$V_1=2m/s$