The following dimensionless groups are often used to present data on centrifugal pumps: flow coefficient \(\varphi=\frac{Q}{\omega D^{3}}\), head coefficient \(\psi=\frac{g H}{\omega^{2} D^{2}}\), power coefficient \(\xi=\frac{\dot{W}}{\omega^{3} D^{5}}\), efficiency \(\eta=\) \(\frac{ho g Q H}{\dot{W}}\), specific speed \(N_{s}=\frac{\omega \sqrt{Q}}{(g h)^{3 / 4}}\), specific diameter \(D_{s}=\frac{\omega \sqrt{Q}}{(g h)^{1 / 4}}\). Show that the last three groups can be formed from combinations of the first three groups.