Presets
Playback
Plant
Reservoir height and the pipe that carries the water to the turbine.
Nozzle and wheel
Jet size, bucket shape and how fast the wheel is allowed to turn.
Layers
Model checks
The science
From reservoir to jet
Water falls through the gross head H but the penstock (length L, diameter D, Darcy friction factor f) wastes part of it. With pipe speed v = Q / A_p the net head at the nozzle is H_n = H - (f L/D + K) v^2 / (2g). The nozzle turns it into a free jet of speed V_j = C_v sqrt(2 g H_n) and flow Q = C_v A_n sqrt(2 g H_n). Because H_n depends on Q and Q on H_n, the page solves the pair by bisection every time a slider moves.
Pelton wheel
Buckets split the jet and turn it back through the deflection angle beta (180 degrees would be a full reversal). Momentum balance gives the mechanical power P = rho Q u (V_j - u) (1 - k cos beta), where u = omega R is the bucket speed and k < 1 the relative-speed loss in the bucket. P is largest at u = V_j / 2. The hydraulic efficiency is eta_h = P / (rho g Q H_n), and the overall efficiency also includes the pipe loss and a mechanical loss factor eta_m.
Specific speed
The dimensionless specific speed N_s = omega sqrt(P / rho) / (g H_n)^(5/4) tells which turbine family fits: low values (about 0.05 to 0.4 for one jet) point to impulse wheels like this one, higher values to Francis and Kaplan runners.
Simplifications
Steady flow (no water hammer), constant friction factor, one jet, no splash or windage loss, constant k. The 3D page shares the same turbine family but is a visual scene; the numbers here are the engineering relations, not data of a specific plant.
What to try
- Move the speed ratio slider to 0.5 and watch the power peak, then to 0.95 and see the wheel almost free-running with almost no power.
- Make the penstock long and narrow: the energy line drops steeply and the net head, jet speed and power fall.
- Open the nozzle: flow rises, but friction loss grows with Q squared, so power gains flatten out.
- Compare the presets Alpine and Lowland to see how head and flow trade against each other.