The rate of flow of liquid through a capillary tube of radius r is V, when the pressure difference across the two ends of the capillary is p. If pressure is increased by 3p and radius is reduced to r/2, then the rate of flow becomes

Options

A. `(V)/(8)`
B. `(V)/(4)`
C. `(V)/(2)`
D. `(V)/(9)`

Answer

B

Explanation

According to Poiseuille.s equation
`V= (pi P r^(4))/(8 eta l)` …(i)
`V. = (pi (4P) ((r )/(2))^(4))/(8 eta l)` …(ii)
Divide (ii) by (i), we get `(V.)/(V) = (4)/(16) = (1)/(4) or V. = (V)/(4)`