Hydropower (from Ancient Greek ὑδρο-, "water"), also known as water power or water energy, is the use of falling or fast-running water to produce electricity or to power machines. This is achieved by converting the gravitational potential or kinetic energy of a water source to produce power. Hydropower is a method of sustainable energy production. Hydropower is now used principally for hydroelectric power generation, and is also applied as one half of an energy storage system known as pumped-storage hydroelectricity. Hydropower is an attractive alternative to fossil fuels as it does not directly produce carbon dioxide or other atmospheric pollutants and it provides a relatively consistent source of power. Nonetheless, it has economic, sociological, and environmental downsides and requires a sufficiently energetic source of water, such as a river or elevated lake. International institutions such as the World Bank view hydropower as a low-carbon means for economic development. Since ancient times, hydropower from watermills has been used as a renewable energy source for irrigation and the operation of mechanical devices, such as gristmills, sawmills, textile mills, trip hammers, dock cranes, domestic lifts, and ore mills. A trompe, which produces compressed air from falling water, is sometimes used to power other machinery at a distance.
Calculating the amount of available power A hydropower resource can be evaluated by its available power. Power is a function of the hydraulic head and volumetric flow rate. The head is the energy per unit weight (or unit mass) of water. The static head is proportional to the difference in height through which the water falls. The dynamic head is related to the velocity of moving water. Each unit of water can do an amount of work equal to its weight times the head.
The power available from falling water can be calculated from the flow rate and density of water, the height of fall, and the local acceleration due to gravity:
W ˙ out = − η m ˙ g Δ h = − η ρ V ˙ g Δ h {\displaystyle {\dot {W}}_{\text{out}}=-\eta \ {\dot {m}}g\ \Delta h=-\eta \ \rho {\dot {V}}\ g\ \Delta h}
where
W ˙ out {\displaystyle {\dot {W}}_{\text{out}}} (work flow rate out) is the useful power output (SI unit: watts)
η {\displaystyle \eta } ("eta") is the efficiency of the turbine (dimensionless)
m ˙ {\displaystyle {\dot {m}}} is the mass flow rate (SI unit: kilograms per second)
ρ {\displaystyle \rho } ("rho") is the density of water (SI unit: kilograms per cubic metre)
V ˙ {\displaystyle {\dot {V}}} is the volumetric flow rate (SI unit: cubic metres per second)
g {\displaystyle g} is the gravitational acceleration (SI unit: meters per second per second)
Δ h {\displaystyle \Delta h} ("Delta h") is the difference in height between the outlet and inlet (SI unit: metres) To illustrate, the power output of a turbine that is 85% efficient, with a flow rate of 80 cubic metres per second (2800 cubic feet per second) and a head of 145 metres (476 feet), is about 97 megawatts:
W ˙ out = 0.85 × 1000 ( kg / m 3 ) × 80 ( m 3 / s ) × 9.81 ( m / s 2 ) × 145 m ≈ 97 × 10 6 ( kg m 2 / s 3 ) = 97 MW {\displaystyle {\dot {W}}_{\text{out}}=0.85\times 1000\ ({\text{kg}}/{\text{m}}^{3})\times 80\ ({\text{m}}^{3}/{\text{s}})\times 9.81\ ({\text{m}}/{\text{s}}^{2})\times 145\ {\text{m}}\approx 97\times 10^{6}\ ({\text{kg}}\ {\text{m}}^{2}/{\text{s}}^{3})=97\ {\text{MW}}}
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