Question

For a given centrifugal pump, if the speed of rotation of the impeller is cut in half, how does the power required to drive the pump change

Answer 1

The power required to drive the pump is reduced in
`(1)/(8)`.

Step-by-step explanation:

From Turbomachinery, we find that power required to drive the pump (
`\dot W`) is directly proportional to the cube of the speed of rotation of the impeller (
`\dot n`). That is:

`\dot W \propto \dot n^(3)`

`\dot W = k\cdot \dot n ^(3)` (Eq. 1)

Where
`k` is the proportionality constant.

And now we eliminate the proportionality constant by constructing the following relationship:

`(\dot W_(B))/(\dot W_(A)) = \left((\dot n_(B))/(\dot n_(A))\right)^(3)` (Eq. 2)

If we know that
`(\dot n_(B))/(\dot n_(A)) = (1)/(2)`, then:

`(\dot W_(B))/(\dot W_(A)) = (1)/(8)`

The power required to drive the pump is reduced in
`(1)/(8)`.