Water flows steadily through a horizontal pipe of a variable cross-section. If the pressure of water is p at a point where the velocity of flow is v, what is the pressure at another point where the velocity of flow is 2v, `rho` being the density of water?

Options

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

Answer

A

Explanation

According to Bernoulli.s principle -
`P+1/2 rho v^2` = Constant
`implies P+1/2 rho v^2=P.+1/2 rho(2v)^2`
`implies P.=P-3/2 rho v^2`.