Question

The cylindrical tube of a spray pump has radius $R$. One end of the tube has $n$ fine holes each of radius $r$. If the speed of the liquid in the tube is $V$, then the speed of the ejection of the liquid through the holes is

• A. $\frac{V^{2}R}{nr}$
• B. $\frac{V{R}^2}{n^2{r}^2}$
• C. $\frac{V{R}^2}{n{r}^2}$
• D. $\frac{V{R}^2}{n^3{r}^2}$

Answer 1

The correct option is C $\frac{V{R}^2}{n{r}^2}$

Using equation of continuity, $Av=\text{constant}$
$A_1{v}_1=A_2{v}_2$
$\therefore \pi R^{2}V=\left(n\pi r^2\right)v^{\prime }$, where $n\pi r^2$ is the total area of $n$ fine holes and $v^{\prime }$ is the speed of ejection through each hole.
$\Rightarrow v^{\prime }=\frac{V{R}^2}{n{r}^2}$