# Power Number

Written by Matt Milbury. Posted in Rotating Equipment

Power Number is a dimensionless number about the power used by fans, mixers and pump impellers at a specified rotational speed.

## Formula

$$N_p = \frac { P } { n^3 d^5 \rho}$$

Where:

$$N_p$$ = Power Number

$$P$$ = impeller power

$$n$$ = impeller rotational speed

$$\rho$$ = fluid density

$$d$$ = impeller diameter