Euler head for a centrifugal pump impeller from blade geometry and kinematics. Computes tip speed U₂, radial velocity Vr₂, whirl velocity Vu₂, and theoretical head.
Turbomachinery · PumpAngle from tangential — backward-curved blades 15°–35° are most common
Typical b₂/D₂ ratio: 0.03–0.10 — e.g. 15 mm for a 300 mm impeller
Euler turbomachinery equation (zero inlet swirl):
Where:
Blade angle effect on head:
| Blade type | β₂ | Head characteristic | Stability |
|---|---|---|---|
| Backward-curved | < 90° | H decreases with Q | Stable (most common) |
| Radial (straight) | = 90° | H constant with Q | Moderately stable |
| Forward-curved | > 90° | H increases with Q | Unstable (not recommended) |
The Euler head is the theoretical maximum. Actual pump head is reduced by slip (σ ≈ 0.85–0.95), hydraulic friction, and recirculation losses. The shaft power P = ρgQH/η where η is the overall pump efficiency including mechanical and volumetric losses.