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# Hydropower

## Power potential vs. head and flow rate.

### Online Hydro-power Calculator

The calculator below can be used to calculate available hydroelectricity power.

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)

### 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

## Related Topics

• ### Environment

Climate, meteorology, sun, wind and environmental related engineering resources.

## Related Documents

• ### Energy Accumulated in Heated Water - kWh

The amount of thermal energy stored in heated water.
• ### Energy Storage Density

Energy density - by weight and volume - for some ways to store energy
• ### Heat, Work and Energy

Heat vs. work vs. energy.
• ### Mechanical Energy Equation vs. Bernoulli Equation

The Mechanical Energy Equation compared to the Extended Bernoulli Equation.
• ### Potential Energy - Hydropower

Elevation and potential energy in hydropower.
• ### Pumping Water - Required Horsepower

Horsepower required to pump water.
• ### Pumps, Fans and Turbines - Horsepower

British Horse Power as used for pumps, fans and turbines - and how to convert to other units.
• ### Static Pressure vs. Head

Static pressure vs. pressure head in fluids.

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## Citation

• The Engineering ToolBox (2008). Hydropower. [online] Available at: https://www.engineeringtoolbox.com/hydropower-d_1359.html [Accessed Day Month Year].

Modify the access date according your visit.

12.8.9