Two capillary tubes of same length but radii `r_(1) r_(2)` are arranged horizontally side by side to the bottom of a large vessel containing water. The radius of single tube of same length that can replaced them so that the rate of volume flow through it is equal to the total rate of volume flow through the two tubes is

Options

A. `r_(1)+r_(2)`
B. `(r_(1)+r_(2))^((1)/(4))`
C. `(r_(1)+r_(2))^(4)`
D. `(r_(1)^(4)+r_(2)^(4))^((1)/(4))`

Answer

4

Explanation

`(V)/(t)=(V_(1))/(t)+(V_(2))/(t),(piPr^(4))/(8etal)=(piPr_(1)^(4))/(8etal)+(piPr_(2)^(4))/(8etal)`