Question

A horizontal pipe line carries water in a streamline flow. At a point along the pipe where cross sectional area is $10c{m}^2$, the water velocity is $1m{s}^{-1}$ and the pressure is $2000Pa$. The pressure of water at another point where the cross sectional area is $5c{m}^2$ is

• A. $1000Pa$
• B. $500Pa$
• C. $3500Pa$
• D. $1025Pa$

Answer 1

The correct option is B $500Pa$

As, the pipe is horizontal and applying Poiseuille's equation and Continuty eqution $\Rightarrow P_1+\frac{1}{2}P{V}^2=\frac{1}{2}P{V}_1^2+P_2$ and $A_1{V}_1=A_2{V}_2\Rightarrow 10\times 1=5\times x\to x=2$

$\Rightarrow 2000+\frac{1}{2}\left(1000\right)1^2=\frac{1}{2}10(2{)}^2+P_2$

$\Rightarrow 2500=500\times 4+P_2$

$\Rightarrow P_2=500Pa$