Question

A venturimeter is installed in a horizontal pipe of $60mm$ diameter & throat diameter of $20mm$. A venturimeter is used to measure the velocity of water in a pipe. if pipe & thorat pressure difference is $50kPa$ then flow velocity $(inm/s$) is
(neglect frictional losses)

• A. $1.1$
• B. $5.1$
• C. $4.1$
• D. $3.1$

Answer 1

The correct option is A $1.1$

$Givendata,$

$\text{pipe diameter}{d}_1=60mm$
$\text{throat diameter}{d}_2=20mm$

$\Delta P=50kPa$

$\rho \text{=1000}\left(kg/m^3\right)\text{for water medium by continuity equation}$

${\rho }_1{A}_1{V}_1={\rho }_2{A}_2{V}_2$

As water is incompressible
${\rho }_1={\rho }_2$

$A_1{V}_1=A_2{V}_2$

$\frac{\pi }{4}{d}_1^2{V}_1=\frac{\pi }{4}{d}_2^2{V}_2$

$(60\times {10}^{-3}{)}^2{V}_1=(20\times {10}^{-3}{)}^2{V}_2$

$V_2=9V_1$ ... (1)

Now, by Bernoullie equation
$\frac{P_1-P_2}{\rho g}=\frac{V_2^2-V_1^2}{2g}...\left(2\right)$

Put $V_2$ from equation (1) to equation (2)

$\frac{P_1-P_2}{\rho }=\frac{\left(9V_1^2\right)-V_1^2}{2}$

$\frac{50\times {10}^3}{1000}=\frac{81V_1^2-V_1^2}{2}$

$50=\frac{80V_1^2}{2}$

$V_1=1.118\left(m/sec\right)$