Question

Water is flowing in a horizontal pipe in a streamline flow. It is given that the velocity of water is 2 m/s at a point A where the cross section area is ${10}^{-2}{m}^2$. The pressure at A is 8000 Pa. What will be the pressure at point B where the cross section area is $0.5\times {10}^{-2}{m}^2$?

• A. $4000Pa$
• B. $1000Pa$
• C. $2000Pa$
• D. $3000Pa$

Answer 1

The correct option is C $2000Pa$

Using equation of continuity, we can find the velocity at another point. we have
$a_1{v}_1=a_2{v}_2\Rightarrow {10}^{-2}\times 2=0.5\times {10}^{-2}\times v_2\Rightarrow v_2=4m/s$
according to Bernoulli's theoram, for water at same height
$\Delta P=\frac{\rho (v_1^2-v_2^2)}{2}\Rightarrow \Delta P=\frac{1000\times (2^2-4^2)}{2}=-6000Pa\Rightarrow P_2-P_1=-6000Pa\Rightarrow P_2-8000=-6000Pa\Rightarrow P_2=2000Pa$