# Potential Energy - Hydropower

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

E_{ p }= F_{ g }Δh

= m a_{ g }Δ h (1)

where

F_{ g }= gravitational force ( weight ) acting on the body (N, lb_{ f })

E_{ p }= potential energy (J, ft lb)

m = mass of body (kg, slugs )

a_{ g }= acceleration of gravity on earth (9.81 m/s^{ 2 }, 32.17405 ft/s^{ 2 })

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

E_{ p }= (1000 kg) (9.81 m/s^{ 2 }) (10 m)

= 98100 J

= 98 kJ

= 0.027 kWh

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

A body with weight (force) * 500 lb _{ f } * is elevated

*30 ft*. The change in potential energy can be calculated as

E_{ p }= (500 lb) (30 m)_{ f }

= 15000 ft lb

A body with mass * 15 slugs * is elevated

*30 ft*. The change in potential energy can be calculated as

* E _{ p } = ( 15 slugs ) ( 32.17405 ft/s ^{ 2 } < ) (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:

You can copy the spreadsheet to your Google Drive or to your local drive if you want to use it as a template for your own calculations.

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