Pelton Wheel Jet Impulse Turbine

Penstock & Nozzle

Head H 150 m

Nozzle diameter 10.0 mm

Runner & Generator

Bucket deflection angle β 20°

Generator load torque 20 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

Hydraulic efficiency: 0%peak 97%

How it works

A Pelton wheel is an impulse turbine: the entire pressure head is converted to jet velocity in a fixed nozzle before the water ever touches the runner, so the buckets work at atmospheric pressure and only redirect the jet's momentum.

Jet velocity:   v  = Cv·√(2gH)
Tangential force on bucket:
                F  = ρQ(v − u)(1 + cos β)
Runner dynamics:
                I·dω/dt = F·R − τ_load
Power delivered:
                P  = τ_load·ω
Hydraulic efficiency:
                η  = P / (½ρQv²)

Here u = ωR is the linear bucket speed, β is the small residual deflection angle (a real split bucket turns the relative flow through ≈180° − β), and Cv ≈ 0.98 is the nozzle velocity coefficient. Because the force term (v − u) vanishes as u → v, an unloaded wheel accelerates toward the jet speed itself — its runaway speed — rather than exploding; efficiency is exactly zero there since no torque reaches the shaft.

Head / nozzle — set the hydraulic power available (jet velocity and flow rate).
Bucket angle β — smaller β turns the flow through a wider angle and pushes the theoretical peak efficiency (1 + cos β)/2 higher.
Load torque — the generator's electromagnetic braking torque; the wheel spins up or down until F·R balances it.
Theory predicts peak efficiency exactly at the speed ratio u/v = 0.5 — use "Set load for peak η" to see the wheel settle there.

Water jet Split flow (deflected)

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