# Hydropower

## Water - power, head and flow rate

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### Online Hydropower Calculator

The calculator below can be used to calculate available hydroelectricity.

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)

### Example - Hydropower

The theoretically power available from a flow of *1 m ^{3}/s* water falling

*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 = 1000 μ q g h (2)

where

P = power available (W)

μ = efficiency (in general ranging 0.75 to 0.95)

Equation (2) can be simplified to express practically available hydropower in *kW*

P ~ 10 μ q h (kW)

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