Two capillary tubes of lengths in the ratio `2 : 1` and radii in the ratio `1 : 2` are connected in series. Assume the flow of the liquid through the tube is steady. Then, the ratio of pressure difference across the tubes is

Options

A. `r_(1)+r_(2)`
B. `(r_(1)r_(2))/(r_(1)+r_(2))`
C. `(r_(1)+r_(2))/(2)`
D. None of these

Answer

D

Explanation

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)`