Question

Water flows in a horizontal tube of variable cross section as shown. If the pressure difference of water between $X$ and $Y$ is $600N/m^2$, Area of cross section of pipe at $X$ and $Y$ are $3c{m}^2$ and $1.5c{m}^2$ respectively. Find the rate of flow of water through the tube. $($Assume density of water as $1000kg/m^3$ and $\frac{1}{\sqrt{10}}=0.316)$

• A. $169c{m}^3/s$
• B. $179c{m}^3/s$
• C. $189c{m}^3/s$
• D. $199c{m}^3/s$

Answer 1

The correct option is C $189c{m}^3/s$

Given
Area of cross section
$A_x=3c{m}^2$
$A_y=1.5c{m}^2$
Change in Pressure $P_x-P_y=600N/m^2$

By equation of continuity
$A_x{V}_x=A_y{V}_y$

$\frac{V_y}{V_x}=\frac{3c{m}^2}{1.5c{m}^2}=2$

By Bernoulli’s equation (as the pipe is horizontal)

$P_x+\frac{1}{2}\rho v_x^2=P_y+\frac{1}{2}\rho v_y^2$

$P_x-P_y=\frac{1}{2}\rho (v_y^2-v_x^2)=\frac{3}{2}\rho v_x^2$

$600=\frac{3}{2}\left(1000\right)v_x^2$
$v_x=\frac{2}{\sqrt{10}}$
$v_x=0.63m/s$

Rate of flow of water

$Q=A_x{v}_x=\left(3c{m}^2\right)\left(0.63m/s\right)=189c{m}^3/s$