Pump Specific Speed (Ns)

Specific speed answers a question the duty point alone cannot: what shape of impeller does this job want? Combine speed, flow and head into one index at the best efficiency point and the geometry falls out. Below about Ns = 1500 you want a radial impeller: narrow, large-diameter, high head, low flow. Between roughly 2000 and 5000 the impeller becomes mixed-flow, and above about 9000 it is an axial propeller, all flow and almost no head. A 1750 rpm pump making 100 ft at 500 gpm has $\mathrm{Ns} = 1750 \times \sqrt{500} / 100^{0.75} \approx 1237$: a classic end-suction radial machine.

Ns as written is not dimensionless despite being quoted as a bare number: the value depends entirely on the units, and the US convention (rpm, gpm, ft) that this page evaluates gives numbers roughly 51.6 times the metric (rpm, m³/s, m) convention. Always state which you mean. There is also a sibling worth knowing: suction specific speed, $S = N\sqrt{Q}/\mathrm{NPSHr}^{0.75}$, where values above about 11 000 flag a pump that will be unstable and cavitation-prone away from its best efficiency point, a lesson the refining industry learned expensively in the 1970s.