When water flows through a tube of radius r placed horizontally, a pressure difference p develops across the ends of the tube. If the radius fo the tube is doubled and the rate fo flow halved, the pressure differnece will be

Options

A. `8p`
B. `p`
C. `(p)/(8)`
D. `(p)/(32)`

Answer

D

Explanation

Poiseuille's formula gives the quantity of liquid flowing through a capillary, `Q=(pi)/(8)(pr^(4))/(etal)`
i.e., `p-(8)/(pi)Q.(nl)/(r^(4)),if Q^(')=(Q)/(2),r^(')=2r`
`(p)/(n)=(8)/(pi)(Q)/(2).(nl)/((2r)^(4))=(8)/(p)(Q.nl)/(r^(4))xx(1)/(32)(becausen=32)`
i.e., pressure `p^(')=(p)/(32)`