A Pelton wheel converts the whole head into the speed of a single jet, about 0.98 times the square root of 2 × 9.81 × head, and runs best when its buckets move at half the jet speed. On 30 meters of head the jet leaves the nozzle at 23.8 m/s and a 40 cm wheel turns at about 568 RPM, close to the speed a generator wants.
Part of Micro-Hydro Turbine
An impulse turbine in which a nozzle fires a high-speed water jet at cup-shaped buckets on a wheel; it suits steep sites with little water.
High Head And Small Flow Suit A Jet
The carrier assigns the Pelton wheel to heads above 20 meters and quotes efficiency of 80 to 90%, the highest of any type. The wheel runs in air, not submerged, so the housing only has to catch spray. The nozzle does the pressure-to-speed conversion; the cups reverse the jet and take its momentum.
Method: Size The Jet And The Wheel From The Head
Step 1: Jet speed. v = 0.98 × √(2 × g × H), the nozzle coefficient of 0.98 being the one used on the Crossflow Turbine page. For H = 30 m: 2 × 9.81 × 30 = 588.6, whose square root is 24.26, so v = 0.98 × 24.26 = 23.8 m/s.
Step 2: Jet diameter. Jet area = flow ÷ jet speed. For the carrier’s 3 L/s stream (0.003 m³/s): 0.003 ÷ 23.8 = 0.000126 m², and d = √(4 × 0.000126 ÷ π) = 0.0127 m, a 12.7 mm jet. The carrier’s nozzle opening of 2 to 5 cm is therefore for larger flows: a 20 mm jet at 30 m passes 7.5 L/s and a 50 mm jet 46.7 L/s. For 3 L/s the tip must be near 13 mm.
Step 3: Wheel speed. Turbine Design sets the best runner speed at roughly half the jet speed, so bucket speed u = 23.8 ÷ 2 = 11.9 m/s. For a 40 cm wheel the speed is 11.9 ÷ (π × 0.4) = 9.47 turns per second, or 568 RPM. That sits inside the carrier’s 500 to 1,500 RPM range.
Step 4: Buckets. The carrier cuts a disc from 6-10 mm steel plate, 30-50 cm across, and welds 12-20 cups, each half a steel pipe, with a central splitter ridge. The Turbine Design page gives 15-25 cups; both figures are quoted rather than reconciled here, and any number in either range works if the cups do not overlap. Make each cup 3 to 4 times as wide as the jet, from that page: 3 × 12.7 = 38 mm to 4 × 12.7 = 51 mm. A pipe of 40-50 mm bore cut in half lengthwise gives that.
Step 5: Flow control. A needle (spear) valve in the nozzle changes the jet area while the jet speed stays the same, so efficiency holds across the load range. See Pelton Wheel for a longer build.
Worked Example: The Carrier’s 40 cm Wheel
- Hydraulic power: 9.81 × 3 L/s × 30 m = 883 W.
- At 85% turbine efficiency: 883 × 0.85 = 750 W at the shaft.
- Shaft speed 568 RPM is 568 × 2π ÷ 60 = 59.5 rad/s, so torque = 750 ÷ 59.5 = 12.6 N·m.
- The carrier’s shortcut of 3 × 30 × 7 = 630 W, less belts, wiring and generator, leaves its quoted 500 W of output.
Unloaded, A Pelton Runs Far Faster Than Its Best Speed
If the generator load is lost, the buckets stop pulling against the jet and the wheel accelerates until its bucket speed nears the jet speed. My recalled figure is that this free-run speed is roughly twice the best speed, which would be about 1,100 RPM here; confirm it by a low-flow test. Belts, bearings and the generator must tolerate it, and a dump load (Load Control) prevents it.
A 24 m/s jet cuts and a wheel cannot be stopped by hand
At 30 meters of head the jet leaves the nozzle at 23.8 m/s; at 100 meters it is 0.98 × √(2 × 9.81 × 100) = 43.4 m/s. Never put a hand, tool or face in the jet. Stop the wheel by closing the spear valve slowly, never suddenly, since a fast closure causes water hammer in the penstock. A jet deflector that swings the stream off the wheel without closing the pipe is standard practice (recalled, not from the corpus); fit one if you can. Name who can reach the valve and how long the wheel coasts down before anyone works near it.
Common Mistakes
- A nozzle too large for the flow — the stream cannot refill the pipe as fast as the nozzle empties it, so the forebay drains, air enters and the jet speed collapses.
- An off-centre splitter — the jet divides unequally and pushes the wheel sideways on its bearings.
- A wheel loaded until it runs well below half jet speed — the jet then overtakes the buckets and energy is wasted.
What’s Next
- Learn next: Generator Coupling (Belt vs Direct) for the drive to the alternator
- Combine with: Penstock Design & Materials for the high-pressure pipe feeding the nozzle