Water is flowing streamline motion through a horizontal tube. The pressure at a point in a tube is P where the velocity of flow is v. At another point where the pressure is`p/2`, the velocity of flow is (density of water = `rho`)

Options

A. `sqrt""v^(2) +(p)/( rho)`
B. `sqrt""v^(2)-(p) /( rho)`
C. `sqrt""v^(2)+(2p) /( rho)`
D. `sqrt""v^2-(2p ) /( rho)`

Answer

A

Explanation

`P_(1) +(1)/(2) rho v_(1) ^(2) =P_(2) +(1)/(2) rho V_(2)^(2) `
`p+ (1)/(2) rho v^(2) =(P )/(2) +(1)/(2) rho V^(2)`
` (p-(p)/(2))+(1)/(2)rho V^(2)= (1)/(2) rho V^(2)`
`V^(f) = sqrt((P)/( rho )+v^(2))`