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

Answer:

The power required to drive the pump is reduced in $\frac{1}{8}$.

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:

$\frac{\dot W_{B}}{\dot W_{A}} = \left(\frac{\dot n_{B}}{\dot n_{A}}\right)^{3}$ (Eq. 2)

If we know that $\frac{\dot n_{B}}{\dot n_{A}} = \frac{1}{2}$, then:

$\frac{\dot W_{B}}{\dot W_{A}} = \frac{1}{8}$

The power required to drive the pump is reduced in $\frac{1}{8}$.