⚙️ Pelton Wheel Turbine
A virtual re-creation of the impulse-turbine experiment. Open the spear valve, let the jet spin the runner to maximum speed, then tighten the band brake step by step — from free runaway all the way to stall — recording speed, spring-balance forces, flow and inlet head to map the turbine's torque, power and efficiency characteristics. Then throttle the spear valve and see how the curves shift.
Purpose
To investigate the performance characteristics of an impulse turbine (Pelton wheel) and compare them with the ideal curves.
Theory
The nozzle converts the supply head into a high-velocity jet; the buckets turn the jet nearly 180°, and the change of momentum drives the runner. With the band brake providing the load:
Fb = F₁ − F₂ • T = Fb·r, r = 0.03 m • Pb = 2π·n·T • Ph = ρ·g·Q·Hi • η = Pb/Ph
Ideal theory predicts torque falling linearly from a maximum at stall to zero at runaway (bucket speed = jet speed), so power and efficiency are parabolas peaking near half the runaway speed — the classic operating point u ≈ Vjet/2.
Apparatus
Armfield hydraulic bench; F1-25 Pelton turbine demonstration unit (spear valve, jet deflector, band brake over the drum with two spring balances); tachometer; stopwatch; Bourdon inlet-pressure gauge.
Brake drum radius r = 0.03 m Collect 4 L per flow reading ≥ 6 load steps per spear setting, last one at stall
Procedure — perform it here
Observations & Computations
Collect ≥ 6 sets per spear setting from free speed down to stall. Fb = F₁ − F₂; T = Fb·r; Pb = 2πnT (n in rev/s); Ph = ρgQHi; η = Pb/Ph.
| No. | Spear | n (rpm) | F₁ (N) | F₂ (N) | Fb (N) | Q (L/s) | Hi (m) | T (N·m) | Pb (W) | Ph (W) | η (%) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| No sets yet — set the brake, collect 4 L, then press “Record set”. | |||||||||||
Characteristic curves — T, Pb and η vs speed
Your recorded points against the ideal curves (solid = spear fully open, dashed = partially open). Note where maximum torque, maximum power and maximum efficiency each occur.
Discussion
Comment on the shape of the graphs
Torque falls almost linearly with speed — maximum at stall, zero at runaway. Because Pb = 2πnT, the power curve is a parabola: zero at both extremes and peaking near half the runaway speed. Efficiency has the same parabolic shape since Ph is nearly constant for a fixed spear setting.
Where do maximum torque and maximum power occur — full vs partial opening?
Maximum torque is always at stall (n = 0); maximum power at roughly half the runaway speed. Throttling the spear valve reduces Q, so the whole torque line drops and the power parabola shrinks — but the runaway speed barely changes, because it is set by the jet velocity (≈√(2gHi)), not by the flow rate.
Is maximum efficiency at the same speed for both spear settings?
Very nearly, yes. Peak efficiency occurs where the bucket speed is about half the jet speed (u ≈ Vj/2). Since the jet velocity depends on the head — nearly the same at both openings — the optimum speed hardly moves, which is precisely why Pelton wheels regulate power by throttling flow with the spear valve while running at constant (synchronous) speed.
Optimum operating condition
Run the wheel at a speed ratio u/Vj ≈ 0.46–0.48 (just under half the runaway speed) — that is where the efficiency peaks; use the spear valve for load changes, and the deflector for sudden rejections to protect the penstock from water hammer.