A pump motor is used to deliver water at a certain rate from a given pipe. To obtain 'n' times water from the same pipe in the same time by what amount (a) the force and (b) power of the motor should be increased ?

Options

A. `n^(2)` times
B. `n^(3)` times
C. `n` times
D. `n^(3//2)` times

Answer

B

Explanation

If a liquid of density `rho` is flowing through a pipe cross section `A` at speed `V`, the mass coming out per second will be `(dm//dt) = AV rho`
In order to get `n` time water in the same time.
`(dm//dt) = n(dm//dt)` i.e., `A'V' rho' = nAV rho`
But as pipe and liquid are same time, so rho' `rho.A' = A`
`V' = NV`.
So `(F')/(F) = (V' (dm//dt))/(V(dm//dt)) = (nV(n dm//dt))/(V(dm//dt)) = n^(2)`
or `F' = n^(2)F`
`(P')/(P) = (F'V')/(FV) = ((n^(2)F) (nV)/(FV) or P = n^(3)`.