Water is in streamline flow along a horizontal pipe with nonuniform cross-section. At a point in the pipe where the area of cross-section is 10 c`m^(2)`, the velocity of water is 1 `ms^(-1)` and the pressure is 2000 Pa. The pressure at another point where the cross-sectional area is 5 c`m^(2)` is :

Options

A. 1000Pa
B. 500Pa
C. 4000 Pa
D. 2000 Pa

Answer

B

Explanation

According to equation of continuity
`a_(1)v_(1)=a_(2)v_(2)`
`10xx10^(-4)xx1=5xx10^(-4)xxv_(2)`
`v_(2)=2m//s`
For horizontal pipe
`(P_(1))/p+1/2v_(1)^(2)=(P_(2))/p+1/2v_(2)^(2)`
`(2000)/(10^(3))+1/2.(1)^(2)=(P_(2))/(10^(3))+1/2.(2)^(2)`
`2+0.5=(P_(2))/(10^(3))+2`
`rArrP_(2)=500` pascals. So correct choice is (b).