# Potential Energy

## Hydropower - elevation and potential energy

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}Δh (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}=accelerationof gravity on earth(9.81 m/s^{2},32.17405 ft/s)^{2}

Δh = 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.