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# Potential Energy - Hydropower

## Elevation and potential energy in hydropower.

When a body of mass is elevated against the gravitational force - the increase in it's potential energy can be calculated as

Ep = F g Δh

=  m a g Δ h                                (1)

where

F g = gravitational force ( weight ) acting on the body (N, lbf )

Ep = potential energy (J, ft lb)

m = mass of body (kg, slugs )

a g = acceleration of gravity on earth (9.81 m/s2, 32.17405 ft/s2)

Δ h = change in elevation (m, ft)

### Example - Potential Energy of Elevated Body - in SI units

A body of 1000 kg is elevated 10 m . The change in potential energy can be calculated as

Ep = (1000 kg) (9.81 m/s2) (10 m)

= 98100 J

= 98 kJ

= 0.027 kWh

### Example - Potential Energy of Elevated Body - in Imperial units

A body with weight (force) 500 lbf is elevated 30 ft. The change in potential energy can be calculated as

Ep = ( 500 lbf ) (30 m)

= 15000 ft lb

A body with mass 15 slugs is elevated 30 ft. The change in potential energy can be calculated as

Ep = ( 15 slugs ) ( 32.17405 ft/s2< ) (30 m)

= 14478 ft lb

### Potential Energy in a Tank or a Reservoir - Spreadsheet Calculator

You can estimate potential elevation energy (hydropower) in a tank or a reservoir by dividing the volume in horizontal slices and calculate the elevation energy for each slice - as it is done in the spreadsheet calculator below:

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## Citation

• The Engineering ToolBox (2008). Potential Energy - Hydropower. [online] Available at: https://www.engineeringtoolbox.com/potential-energy-d_1218.html [Accessed Day Month Year].

Modify the access date according your visit.

7.8.15

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