Find Power ?

Question

A pump is used to pump a liquid of density D continuously through a pipe of cross section area A.If liquid is flowing with speed v,then power of pump is
(a) (DAv^2)/3
(b) (DAv^2)/2
(c) 2DAv^2
(d) (DAv^3)/2

Answer 1

W_dot = power

 

F = force

 

p = dynamic pressure = (1/2) D v^2

 

W_dot = Fv = (pA)v = [(1/2) D v^2 * A] * v = (D A v^3) / 2

 

The correct answer is (d)