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 prop pr^4 " " (eta " and l are constants")`
`therefore V_2/V_1 = (p_2/p_1)(r_2/r_1)^4 = 2xx(1/2)^4 = 1/8`
`rArr V_2 = Q/8`