Question

Water flows in a horizontal tube as shown in figure. The pressure of water changes by $600N/m^2$ between x and y where the areas of cross section are $3c{m}^2$ and $1.5c{m}^2$ respectively. Find the rate of flow of water through the tube.

• 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 $189c{m}^3/s$

By equation of continuity
$\frac{v_y}{v_x}=\frac{3c{m}^2}{1.5c{m}^2}=2$
By Bernoulli’s equation
$p_x+\frac{1}{2}\rho v_x^2=p_y+\frac{1}{2}\rho v_y^2$
$p_x-p_y=\frac{3}{2}\rho v_X^2$
$v_x=0.63m/s$
$Q=A_x{v}_x=\left(3c{m}^2\right)\left(0.63m/s\right)=189c{m}^3/s$