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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.

density (kg/m3)

efficiency

volume flow (m3/s)

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

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Temperature

oC
oF

Length

m
km
in
ft
yards
miles
naut miles

Area

m2
km2
in2
ft2
miles2
acres

Volume

m3
liters
in3
ft3
us gal

Weight

kgf
N
lbf

Velocity

m/s
km/h
ft/min
ft/s
mph
knots

Pressure

Pa (N/m2)
bar
mm H2O
kg/cm2
psi
inches H2O

Flow

m3/s
m3/h
US gpm
cfm

3 10