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Two capillary tubes of the same length b...

Two capillary tubes of the same length but different radii r1 and r2 are fitted in parallel to the bottom of a vessel. The pressure head is P . What should be the radius of a single tube that can replace the two tubes so that the rate of flow is same as before

A

`r_(1)+r_(2)`

B

`(r_(1)r_(2))/(r_(1)+r_(2))`

C

`(r_(1)+r_(2))/(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
When the tubes are fitted in parallel
`V=V_(1)+V_(2)`
`implies (pi p r^(4))/(8etal)=(p r_(1)^(4))/(8 eta l)+(pi p r_(2)^(4))/(8) implies r^(4)=r_(1)^(4)+r_(2)^(4)`
`therefore r=(r_(1)^(4)+r_(2)^(4))^(1//4)`
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