Water flows steadily through a horizontal pipe of a variable cross-section. If the pressure of the water is p at a point , where the speed of the flow is v. What is the pressure at another point , where the speed of the flow is 2 v ? Let the density of water be `1 g cm ^(-3)`.

Options

A. `P- (3rho 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 theorem `P_(1) + (1)/(2) rho v_(1)^(2) = P_(2) = (1)/(2) rho v_(2)^(2)`
Here, `P_(1) = P, v_(1) = v, P_(2) =?, v_(2) = 2v`
`:. P + (1)/(2) rho (v)^(2) = P_(2) + (1)/(2) rho (2v)^(2)`
or `P_(2) = P + (1)/(2) rho v^(2) - (4rho v^(2))/(2) = P - (3 rho v^(2))/(2)`