Hydroelectric Power Plant — Dam, Penstock & Turbine

Plant Controls

Reservoir head H 80 m

Gate opening 60%

Turbine efficiency η 90%

Turbine units online

Live Output

Power output0.0 MW

Penstock velocity0.0 m/s

Total flow rate0.0 m³/s

Turbine speed0 RPM

How it works

Water stored behind the dam holds gravitational potential energy proportional to the head H (the height it falls). Opening the intake gate lets it accelerate down the penstock, and the discharge through an orifice-like gate follows a Torricelli-style relation:

Q = Cd · A(gate) · √(2gH)
v = Q / A(penstock)

The falling water spins the turbine runner, which drives the generator. The electrical power delivered is the classic hydropower equation:

P = η · ρ · g · Q · H
ρ = 1000 kg/m³ (water density)
g = 9.81 m/s² (gravity)
η = turbine + generator efficiency

Head H — raises the reservoir level and the pressure driving flow; power scales linearly with H at fixed flow, but flow itself also grows with √H.
Gate opening — throttles the intake area, controlling flow rate Q and penstock velocity.
Efficiency η — losses in the turbine runner, bearings and generator windings; real plants run 85–95%.
Turbine units — large dams split flow across several parallel turbines so each can be serviced independently; total power scales with units online.

Real-world relevance: this is the same P = ηρgQH relation used to size every hydroelectric station, from small run-of-river plants to the Three Gorges Dam.

Reservoir / penstock flow Generator output

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