Specific speed is the one index that takes a duty — a speed, a flow and a head — and hands back the SHAPE of impeller that does it well. $N_s = \dfrac{N\sqrt{Q}}{H^{0.75}}$, read aloud N-s equals N root Q over H to the three quarters. $N$ is the shaft speed, $Q$ the flow at the best efficiency point and $H$ the head per stage at that same point.

Now the honest headline, and it is the whole lesson: this number is not dimensionless and it is meaningless without its convention. The form printed on the curves you will actually meet is the US one — $N$ in rpm, $Q$ in US gallons per minute, $H$ in feet — and this lesson is authored in that convention throughout, which is why it is the one page in this chapter that is not metric. The European $n_q$, built from rpm, m³/s and metres, is about 51.6 times smaller for the same impeller. A figure of 40 read off a European chart and compared against the US bands makes a perfectly ordinary Francis impeller look impossible.

In the US convention the bands read: under about 1000, a radial-vane impeller — narrow, large in diameter, high head and modest flow. Roughly 1000 to 2500, a Francis-vane radial impeller, which is most of building services and process duty. Roughly 2500 to 5000, a mixed-flow impeller, its discharge already leaving at an angle. Above about 5000, an axial-flow propeller: all flow, almost no head.

Two arithmetic traps catch experienced people. Use the head per stage, not the total head of a multistage pump — a four-stage pump entered at full head reads about 2.8 times low and names the wrong impeller entirely. And for a double-suction impeller use HALF the flow, because each eye only sees half of it. Both figures belong at the best efficiency point: specific speed is a property of the impeller, not of whatever duty it happens to be throttled to this afternoon.