Physics - Fluid Question with Solution | TestHub

Using the equation of continuity, the volume flow rate of water entering the pipe is equal to the volume flow rate of water leaving the sprinkler.

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

Here, the area of the main pipe is $A_1=\pi R^2$ and the speed of water is $v_1=v$.

The total area of the $n$ holes of the sprinkler is $A_2=n\pi r^2$ and let the speed of water leaving be $v_2=v^{\prime }$.

Substituting the values in the equation of continuity:

$\pi R^{2}v=n\pi r^2{v}^{\prime }$

$v^{\prime }=\frac{R^{2}v}{n{r}^2}$

Answer: $\frac{R^{2}v}{n{r}^2}$