Pump power affinity law
= Pump power affinity law
{title2=$P\propto\rho\omega^3D^5$}
If pump <power> depends only on fluid <mass density> $\rho$, impeller diameter $D$ and <angular velocity> $\omega$, <dimensional analysis> fixes $P=C_P\rho\omega^3D^5$, where $C_P$ is dimensionless. Comparing pumps with the same $C_P$ gives the displayed scaling. Geometrical or flow-regime changes can change $C_P$; the law is not a universal comparison of arbitrary pumps.