In a horizontal pipe of non-uniform cross-section, water flows with a velocity of `1 ms^(-1)` at a point where the diameter of the pipe is 20 cm. The velocity of water (in `ms^(-1)`) at a point where the diameter of the pipe 5 cm is

Options

A. 64
B. 24
C. 8
D. 16

Answer

D

Explanation

Diameter of pipe at first point `(d_(1)) = 20 cm = 0.2 m`
Radius of pipe at first point
`(r_(1)) = (0.2)/(2) = 0.1 m`
Velocity of water at first point
`(v_(1)) = 1 ms^(-1)`
Diameter of pipe at second point
`(d_(2)) = 5cm = 0.05 m`
Radius of pipe at second point,
`(r_(2)) = (0.05)/(2) = 0.025 m`
According to equation of continuity,
`A_(1)v_(1) = A_(2)v_(2)`
`pi r_(1)^(2)v_(1) = pi r_(2)^(2)v_(2)`
`v_(2) = ((r_(1))/(r_(2)))^(2) xx v_(1)`
`v_(2) = ((0.1)/(0.025))^(2) xx 1`
`v_(2) = 16 ms^(-1)`