A horizontal pipeline carries water in a streamlime flow, At a point along the pipe, where the cross-sectional area is `10cm^(2)`, the water velocity is `1ms^(-1)` and the pressure is `2000 Pa`. The pressure of water at another point where the cross-sectional area is `5cm^(2)`, is .....Pa. (Density of water `=10^(3)kg-m^(3))`.

Options

A. 100Pa
B. 300 Pa
C. 500 Pa
D. 700 Pa

Answer

C

Explanation

From continuity equation
`A_(1)v_(1)=A_(2)v_(2)`
`:. v_(2)=((A_(1))/(A_(2)))v_(1)=(10/5) (1) =2 m//s`
Applying Bernoulli's theoram at 1 and 2
`P_(2)+1/2 rhov_(2)^(2) =P_(1) +1/2 rhov_(1)^(2)`
`:. P_(2)=P_(1)+1/2 rho(v_(1)^(2)-v_(2)^(2))`
`=(2000+1/2xx10^(3)(1-4))`
`:. P_(2)=500 Pa`