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A liquid is flowing in a horizontal unif...

A liquid is flowing in a horizontal uniform capillary tube under a constant pressure difference P . The value of pressure for which the rate of flow of the liquid is doubled when the radius and length both are doubled is

A

`P`

B

`(3P)/(4)`

C

`(P)/(2)`

D

`(P)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
D
From `V=(Ppir^(4))/(8etal)implies P=(V8etal)/(pir^(4))implies (P_(2))/(P_(1))=(V_(2))/(V_(1))xx(l_(2))/(l_(1))xx((r_(1))/(r_(2)))^(4)=2xx2xx((1)/(2))^(4)=(1)/(4)`
`impliesP_(2)=(P_(1))/(4) = (P)/(4)`
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