TAHA Engineering Toolsby TAHA Knowledge Lab

Energy & Renewables

Hydropower Output Calculator

Hydraulic and electrical power from water flow and net head (P = ρ g Q H η), and the energy per day, month and year.

Inputs

A reservoir, a sloping penstock to a turbine, the tailwater, and the gross head between the water levels.intake water levelpenstock: flow Q,friction lossesTP(el)tailwater levelgross headH(net) = H(gross) − lossesP = ρ g Q H(net) η
Water flows from the intake through the penstock to the turbine (T). The gross head is the difference between the intake and tailwater levels; friction and fitting losses in the penstock reduce it to the net head available at the turbine. Diagram not to scale.

Gross head (difference between intake water level and tailwater level) minus the losses in the intake, penstock and valves.

Turbine × generator (× drive) efficiency at this flow, from the equipment data.

1000 kg/m³ for fresh water (about 998 at 20 °C).

Result

Estimated electrical power
83.3565
Hydraulic power (ρ g Q H)
98.0665
Flow rate
0.5
Net head used
20
Energy per day
2,000.56
Energy per month (average)
60,850.3
Energy per year
730,203
Capacity factor used
100%
Working
P_hyd = ρ × g × Q × H = 1,000 × 9.80665 × 0.5 × 20 = 98.0665 kW P_el = P_hyd × η = 98.0665 × 0.85 = 83.3565 kW Energy per day = P_el × 24 h = 2,000.56 kWh

The water carries 98.0665 kW of hydraulic power; with the efficiency entered the generator gives about 83.3565 kW, or 730,203 kWh per year on this basis.

  • An estimate only. Real output depends on the seasonal flow (the flow you can rely on, after any environmental release), head losses that change with flow, the turbine’s operating range and part-load efficiency, and downtime.
  • Use the net head: the gross head minus the friction and fitting losses up to the turbine. The full gross head is never available at the turbine.

Educational estimate — check the assumptions below.

About this calculator

Water falling through a height gives up energy. The hydraulic power is the weight of water flowing per second times the height it falls: P = ρ g Q H. A turbine and generator turn part of it into electricity (overall efficiency η).

The height to use is the net head — the gross head (difference between the intake water level and the tailwater level) minus the friction and fitting losses in the intake and penstock. This calculator works from the net head, or from the gross head and a head loss, and estimates the energy from operating hours or a capacity factor (one basis only).

Formula

Hnet = Hgross − hloss    Phyd = ρ × g × Q × Hnet    Pel = ρ × g × Q × Hnet × η

Eday = Pel × t (hours per day)   or   Eday = Pel × 24 h × CF    Eyear = 365 × Eday

ρ = water density (kg/m³, default 1000), g = 9.80665 m/s², Q = flow (m³/s), H = net head (m), η = overall efficiency, CF = capacity factor. 1 L/s = 0.001 m³/s; 1 m³/h = 1/3600 m³/s.

Worked example

  • Q = 0.5 m³/s, net head 20 m: Phyd = 1000 × 9.80665 × 0.5 × 20 = 98.07 kW.
  • η = 85%: Pel = 83.36 kW; running 24 h a day: 2000.6 kWh/day, about 730 200 kWh/year.
  • Gross head 22 m with a 2 m loss gives the same 20 m net head.

Assumptions and limitations

  • Steady flow and head at the values entered. Use a reliable (for example seasonal or guaranteed) flow, not the peak flow.
  • Net head = gross head minus hydraulic losses up to the turbine. Losses must come from a pipe-friction calculation for your penstock.
  • One overall efficiency at this flow. Turbines are less efficient at part load and have a minimum flow.
  • A month is taken as 365 ÷ 12 days. An estimate only, not a design of a hydro scheme.

References

  • ASCE / IEC 60041 — hydraulic turbine performance (hydraulic power ρ g Q H).
  • ISO 80000-3 — standard acceleration of gravity g₀ = 9.80665 m/s².