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

Answer 1

Answer: (D)

$\frac{VR^2}{n r^2}$

Answer 2

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