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 `(1.5 ms^(-1))` at a point where the diameter of the pipe is (in cm)

Options

A. 8
B. 16
C. 24
D. 32

Answer

B

Explanation

From equation of continuity ,
`a_1v_1 = a_2v_2 " "v_1 = 1 ms^(-1)`
`pi r_1^2 v_1 = pi r_2^2 v_2 " " v_2 = 1.5 ms^(-1)`
`(10 xx 10^(-2))^(2) xx 1 = r_2^2 xx 1.5 " " d_1 = 20 cm`
`r_2^2 = (100 xx 10^(-4))/(1.5) " " r_1 = (d_1)/2 =10 cm`
`:. r^2 = 8cm`
`:. d_2 = 16 cm`.