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

Options

A. 1000 Pa
B. 500 Pa
C. 3500 Pa
D. 1625 Pa

Answer

B

Explanation

Using equation of continuity,
`A_(1)v_(1)=A_(2)v_(2)`
`10xx1=5xxv_(2)rArrv_(2)=2`m/s
Now by Bernoulli.s theorem,
`(P_(1))/p+1/2v_(1)^(2)=(P_(2))/p+1/2v_(2)^(2)`
`rArrP_(2)=P_(1)+1/2p(v_(1)^(2)-v_(2)^(2))`
`=2000+1/2xx10^(3)(1^(2)-2^(2))`
= 2000 - 1500 = 500 pascals.
Thus correct choice is (b).