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

Options

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

Answer

D

Explanation

`A_(1)=10" cm"^(2)`

According to equation of continuity `A_(1)v_(1)=A_(2)v_(2)`
`:.v_(2)=(A_(1)v_(1))/(A_(2))=(10" cm"^(2)xx"1 m s"^(-1))/("5 cm"^(2))=2"m s"^(-1)`
For a horizontal pipe, according to Bernoulli.s theorem
`P_(1)+1/2pv_(1)^(2)=P_(2)+1/2pv_(2)^(2)`
`P_(2)=P_(1)+(1)/(2)rho(v_(1)^(2)-v_(2)^(2))`
`=2000+1/2xx10^(3)xx(1^(2)-2^(2))" "(because" Density of water", rho=10^(3)"kg m"^(-3))`
`=2000-1/2xx10^(3)xx3=2000-1500=500Pa`