# 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/m ^{3})*

*efficiency*

*volume flow (m ^{3}/s) *

*head (m)*

The theoretically power available from falling water can be expressed as

P_{th}= ρ q g h (1)

where

P_{th}= power theoretically available (W)

ρ = density (kg/m^{3}) (~ 1000 kg/m^{3}for water)

q = water flow (m^{3}/s)

g = acceleration of gravity (9.81 m/s^{2})

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 m ^{3}/s* water with a fall of

*100 m*can be calculated as

*P = (1000 kg/m ^{3}) (1 m^{3}/s) (9.81 m/s^{2}) (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

P_{a}= μρ q g h(2)

where

P_{a}= 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 (m ^{3})*

#### Example - Energy in Elevated Water Volume

*10 m ^{3} *volume of water is elevated

*10 m*above the turbine. The potential energy in the water volume can be calculated as

*W = (1000 kg/m ^{3}) (10 m^{3}) (9.81 m/s^{2}) (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.