A horizontal pipelline carries water in a streamline flow . At a point along the pipe , where the cross - sectional area is `10 cm^(2)` , the water velocity is 1 m/s and pressure is 2000 Pa . The pressure of water at another point where cross - sectional area is ` 5 cm^(2)` , is _______ (in Pa)

Options

A. 200Pa
B. 300Pa
C. 400Pa
D. 500Pa

Answer

D

Explanation

According to equation of continuity `A_(1)v_(1) = A_(2)v_(2), or v_(2) = (A_(1))/(A_(2)) v_(1) = (10)/(5) xx 1 =2 m//s`
Now according to Bernoulli.s equation,
`P_(1) + (1)/(2) rho v_(1)^(2) = P_(2) + (1)/(2) rho v_(2)^(2)`
`2000 + (1)/(2) xx 10^(3) xx 1^(2) = P_(2) + (1)/(2) xx 10^(3) xx 2^(2)`
On solving we get `P_(2) = 500`Pa