Hydropower
Power potential vs. head and flow rate.
Online Hydro-power Calculator
The calculator below can be used to calculate available hydroelectricity power.
density (kg/m3)
efficiency
volume flow (m3/s)
head (m)
The theoretically power available from falling water can be expressed as
Pth = ρ q g h (1)
where
Pth = power theoretically available (W)
ρ = density (kg/m3) (~ 1000 kg/m3 for water)
q = water flow (m3/s)
g = acceleration of gravity (9.81 m/s2)
h = falling height, head (m)
Download and print Hydro Power vs. Volume Flow and Head chart
Example - Hydro-power
The theoretically power available from a flow of 1 m3/s water with a fall of 100 m can be calculated as
P = (1000 kg/m3) (1 m3/s) (9.81 m/s2) (100 m)
= 981 000 W
= 981 kW
Efficiency
Due to energy loss the practically available power will be less than the theoretically power. Practically available power can be expressed as
Pa = μ ρ q g h (2)
where
Pa = power available (W)
μ = efficiency (in general in the range 0.75 to 0.95)
Energy from Hydro-power
The potential theoretical energy in a volume of elevated water can be calculated
W = m g h
= ρ V g h (3)
where
W = energy (J)
m = mass of water (kg)
V = volume of water (m3)
Example - Energy in Elevated Water Volume
10 m3 volume of water is elevated 10 m above the turbine. The potential energy in the water volume can be calculated as
W = (1000 kg/m3) (10 m3) (9.81 m/s2) (10 m)
= 981000 J (Ws)
= 981 kJ (kWs)
= 0.27 kWh
Potential Energy in a Tank or Reservoir
You can estimate the total energy in a tank or a reservoir where the surface area varies with elevation - as typical in a natural reservoir - by integrating the potential energies for horizontal segments as done in the template
Copy the document to your Google Drive or download it as a spreadsheet to make your own calculations.