Hydroelectric Power Calculator

How it works

P = η × ρ × g × Q × H_net (ρ = 1,000 kg/m³, g = 9.81 m/s²) · H_net = H_gross × (1 − penstock loss) · annual energy = P × 8,760 h × capacity factor · quick estimate: P(kW) ≈ 8.3 × Q(m³/s) × H(m) at 85%

Falling water carries potential energy ρ·g·H per cubic metre, so the power available is that energy times the flow rate. A turbine and generator convert most of it — about 85–92% in large plants and less in small ones — after friction in the penstock has taken a few percent of the head. Annual energy depends on how much of the year the flow is available, expressed as a capacity factor. High heads with little flow suit impulse turbines (Pelton, Turgo); medium heads suit Francis turbines; and low heads with large flows suit Kaplan or propeller turbines.

Worked example

A stream delivering 2 m³/s with a 50 m gross head and 5% penstock losses has a net head of 47.5 m. The water power is 1,000 × 9.81 × 2 × 47.5 = 931.6 kW, and at 85% efficiency the plant produces 791.9 kW (1,062 hp). At a 50% capacity factor that is 3,468,465 kWh a year, worth $277,477.20 at 0.08 per kWh. A Francis or crossflow turbine suits this head.

Sources: US DOE — Types of hydropower turbines and how hydropower works · Wikipedia — Hydroelectricity (power calculation)

Frequently asked questions