Question

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

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

Answer 1

Answer: (D)

Let the speed of the ejection of the liquid
through the holes be v. Then according to the
equation of continuity
$\pi R^{2}V=n\pi r^{2}vorv=\frac{\pi R^{2}V}{n\pi r^2}=\frac{V{R}^2}{n{r}^2}$