Two capillaries of radii `r_(1)` and `r_(2)` and lengths `l_(1)` and `l_(2)` are set in series. A liquid of viscosity `eta` is flowing through the combination under a pressure difference p. The rate of flow of the liquid is :

Options

A. `(pip)/(8eta)[(l_(1))/(r_(1)^(4))+(l_(2))/(r_(2)^(4))]`
B. `(pip)/(8eta)[(l_(1))/(r_(1)^(4))+(l_(2))/(r_(2)^(4))]^(-1)`
C. `(pip)/(8eta)[(l_(1))/(r_(1)^(4))+(l_(2))/(r_(2)^(4))]^(2)`
D. `(pip)/(8eta)[(l_(1))/(r_(1)^(4))+(l_(2))/(r_(2)^(4))]^(-2)`

Answer

B

Explanation

`V=(pi(p_(1)-p_(2))r_(1)^(4))/(8etal_(1))=(pi(p_(2)-p_(3))r_(2)^(4))/(8etal_(2))`
`p_(1)-p_(2)=(8Vetal_(1))/(pir_(2)^(4))`
`p_(2)-p_(3)=(V8etl_(2))/(pir_(2)^(4))`
Adding `p_(1)-p_(3)=(8Veta)/(pi)[(l_(1))/(r_(1)^(4))+(l_(2))/(r_(2)^(4))]`
`p=(8Veta)/(pi)((l_(1))/(r_(1)^(4))+(l_(2))/(r_(2)^(4)))`
`V=(pip)/(8eta)((l_(1))/(r_(1)^(4)+(l_(2))/(r_(2)^(4)))`
`therefore` Correct choice is (b).