Pump Specific Speed (Dimensionless Index)
Pump Specific Speed (Dimensionless Index)
Specific speed is the single number pump engineers use to shorthand an impeller's geometry before they ever look at a curve or a drawing. It tells you at a glance whether a pump will be a slow radial-flow machine built for high head and low flow, or a fast axial-flow machine built for high flow and low head, which in turn drives impeller shape, casing design, and even susceptibility to cavitation.By long-standing US industry convention the index is computed from the plain numeric values of rotational speed in rpm, flow in gpm, and head in feet at the best efficiency point — not from unit-consistent quantities — so this worksheet intentionally treats N, Q, and H as bare numbers rather than pint quantities, matching how pump catalogs and selection charts report Ns.
The (US customary) pump specific speed is Ns = N*sqrt(Q)/H^0.75, using the numeric values of N in rpm, Q in gpm, and H in feet. where N_rpm is shaft speed, Q_gpm is flow rate at best efficiency point, and H_ft is the head developed at that flow, each treated as a plain number in its conventional unit.
Inputs
N_rpm := 1750=1750
Q_gpm := 500=500
H_ft := 100=100
Specific speed is defined from the raw numeric magnitudes in this mixed unit system, so no unit conversion or attachment is performed before combining them.
Ns_pump := N_rpm·sqrt(Q_gpm)/H_ft^0.75=1237.44
Results
A specific speed around 1,000-4,000 (US units) indicates a radial-flow centrifugal impeller suited to high head and modest flow, values in the low thousands to ~10,000 indicate mixed-flow impellers, and values above roughly 10,000 point toward axial-flow propeller pumps. Selecting an impeller whose specific speed matches the duty point keeps the pump operating near peak efficiency and away from the unstable, cavitation-prone region of its curve; a mismatch is a common root cause of premature wear or noisy operation in field troubleshooting.
Assumptions & limitations
- US customary convention: N in rpm, Q in gpm, H in ft, evaluated as plain numbers.
- Evaluated at the best efficiency point only — Ns changes elsewhere on the curve.
- Single-stage, single-suction assumption; double-suction impellers use a modified form.
- Does not by itself predict cavitation — that requires NPSH analysis.