Question

A pipe having an internal diameter $D$ is connected to pipe of same size. Water flows into the second pipe through $n$ holes, each of diameter $d$. If the water in the first pipe has speed $v$, the speed of water leaving the second pipe is :

• A. $\frac{D^{2}v}{n{d}^2}$
• B. $\frac{n{D}^{2}v}{d^2}$
• C. $\frac{n{d}^{2}v}{D^2}$
• D. $\frac{d^{2}v}{n{D}^2}$

Answer 1

The correct option is A $\frac{D^{2}v}{n{d}^2}$

Since equal amount of water flows per second through each pipe,

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

$⟹\pi \frac{D^2}{4}v=n\pi \frac{d^2}{4}{v}^{\prime }$

$⟹v^{\prime }=\frac{D^2}{n{d}^2}v$