Archimedes Screw Pump Efficiency

Screw & Drive

Rotation speed 25 rpm

Tilt angle 30°

Intake water level 70%

Casing gap 6 mm

Live Readouts

Flow rate Q

0.0 L/s

Lift height H

0.0 m

Volumetric η

Overall η

Shaft power in

0 W

Hydraulic power out

0 W

How it works

An Archimedes screw traps water in helical chambers between the flights and lifts it as the screw rotates. Gravity keeps each pocket of water at the low point of its chamber, so the water advances axially roughly one pitch length per revolution without spinning with the screw.

Ideal flow:   Q_ideal = V_bucket · (N/60) · f_intake
Bucket vol:   V_bucket = π(R_o² − R_i²)·p
Leak flow:    q_leak = C_d · (gap·2πR_o) · sqrt(2·g·h_pitch)
Vol. eff.:    η_vol = 1 − q_leak / Q_ideal
Fill eff.:    η_fill = 1 (low N) → drops above ~35 rpm (splash/inertia)
Overall:      η_total = η_vol · η_fill · η_mech
Lift height:  H = L·sin(β)
Power:        P_out = ρ·g·Q_actual·H,   P_in = P_out / η_total

Rotation speed — faster turning shortens the time water has to leak backward through the casing gap each revolution (raises η_vol), but above roughly 35 rpm the buckets can't fully fill before they rotate past the intake, so splash losses cut η_fill.
Tilt angle — steeper screws lift water higher per unit length but increase the hydrostatic head driving gap leakage.
Intake water level — how deep the lower end sits in the sump; a shallow sump starves the buckets regardless of speed.
Casing gap — the manufacturing/wear clearance between flight tip and trough; a worn, wider gap leaks more at every speed.

Real-world relevance: this trade-off between leakage and fill/splash loss is exactly why hydropower Archimedes screws and agricultural screw pumps are run at a manufacturer-specified "rated speed" rather than as fast as the drive allows.

Water carried up Leakage droplets

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