First slide

Fluid dynamics

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

Easy

A

$\frac{V R^{2}}{n^{3} r^{2}}$
B

$\frac{V^{2} R}{n r}$
C

$\frac{V R^{2}}{n^{2} r^{2}}$
D

$\frac{V R^{2}}{n r^{2}}$

Solution

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

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