Water flows in a streamline manner through a capillary tube of radius a. The pressure difference being P and the rate of flow is Q . If the radius is reduced to `a//2` and the pressure difference is increased to 2P, then find the rate of flow.

Options

A. 4Q
B. Q
C. `(Q)/(4)`
D. `(Q)/(8)`

Answer

D

Explanation

`"As" V=(pipr^(4))/(8etal)`
`therefore V alpha pr^(4)[eta and l "are constant")`
`therefore (V_(2))/(V_(1))=((p_(2))/(p_(1)))((r_(2))/(r_(1)))^(4)=2xx((1)/(2))^(4)=(1)/(8) RightarrowV_(2)=(Q)/(8)`