Water flows steadily through a horizontal pipe of variable cross-section. If the pressure of water is P at a point where flow speed is v, the pressure at another point where the flow speed is 2v, is (Take density of water as `rho`):

Options

A. `P-(rhov^2)/(2)`
B. `P-(3rhov^2)/(2)`
C. `P-rhov^(2)`
D. `P-(3rhov^2)/(4)`

Answer

B

Explanation

According to Bernoulli's theorem,
`P+(1)/(2)rhov_(1)^(2)=P+(1)/(2)rhov_(2)^(2)`
Here, `P_(1)=P,v_(1)=v,P_(2)=?,v_(2)=2v`
`thereforeP+(1)/(2)rho(v)^(2)=P_(2)+(1)/(2)rho(2v)^(2)`
(or) `P_(2)=P+(1)/(2)rhov^(2)-(4rhov^2)/(2)`
`=P-(3rhov^2)/(2)`