Pelton Wheel Jet Impulse Turbine (2D)

Jet & Nozzle

Jet velocity v 32 m/s

Nozzle diameter 10.0 mm

Bucket & Generator

Bucket deflection angle β 20°

Generator load torque 10 N·m

Live Readouts

Jet velocity v

0.0 m/s

Flow rate Q

0.0 L/s

Bucket speed u

0.0 m/s

Speed ratio u/v

0.00

Wheel speed

0 rpm

Power output

0.00 kW

Fraction of theoretical peak: 0%peak at u/v = 0.50

How it works

A Pelton wheel is an impulse turbine: the jet's momentum, not its pressure, does the work. Each curved bucket reverses the relative flow through nearly 180°, so the force on the bucket depends only on the relative velocity between jet and bucket, v − u.

Tangential force:   F  = ρQ(v − u)(1 + cos β)
Wheel dynamics:     I·dω/dt = F·R − τ_load
Bucket speed:       u = ωR
Extracted power:    P  = F·u = ρQ(v − u)(1 + cos β)·u

P(u) is a downward parabola in u (everything else held fixed): it is zero when the bucket is stationary (u = 0, no work done per unit time despite maximum force) and zero again when the bucket runs away to jet speed (u = v, force vanishes). Setting dP/du = 0 gives v − 2u = 0, i.e. the power curve always peaks at u = v/2 — regardless of flow rate, deflection angle or nozzle size. The live plot below sweeps u from 0 to v at the current settings and marks that peak; the wheel's own dynamics settle near it only when the load torque is tuned to match ("Set load for peak power").

Jet velocity / nozzle diameter — set the available hydraulic power (jet speed and flow rate).
Bucket angle β — smaller β turns the flow through a wider angle, raising the peak of the (1 + cos β) factor.
Load torque — the generator's braking torque; the wheel spins up or down until F·R balances it.

Incoming jet Deflected flow

optimal u/v = 0.500 ✓