The cylinderical 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 :

Options

A. `(VR^(2))/(n^(3)r^(2))`
B. `(V^(2)R)/(nr)`
C. `(VR^(2))/(n^(2)r^(2))`
D. `(VR^(2))/(nr^(2))`

Answer

D

Explanation

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= (pi R^(2) V)/(n pi r^(2)) = (VR^(2))/(nr^(2))`