Editing Hydropower (section)

== Calculating the amount of available power ==
A hydropower resource can be evaluated by its available [[Power (physics)|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.<ref>{{cite web |url=https://energyeducation.ca/encyclopedia/Hydraulic_head |title=Hydraulic head |author=<!--Not stated--> |date=27 September 2021 |website=Energy Education |access-date=8 Nov 2021 |quote=Overall, hydraulic head is a way to represent the energy of stored a fluid - in this case water - per unit weight.}}</ref> The static head is proportional to the difference in height through which the water falls. 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:

::<math>\dot{W}_\text{out} =-\eta \ \dot{m} g \ \Delta h =-\eta \ \rho \dot{V} \ g \ \Delta h</math>

:where
::* <math>\dot{W}_\text{out}</math> ([[Work (physics)|work]] flow rate out) is the useful power output (SI unit: [[watt]]s)
::* <math>\eta</math> ("[[Eta (Greek letter)|eta]]") is the efficiency of the turbine ([[dimensionless]])
::* <math>\dot{m}</math> is the [[mass flow rate]] (SI unit: [[kilogram]]s per second)
::* <math>\rho</math> ("[[Rho (Greek letter)|rho]]") is the [[density]] of water (SI unit: kilograms per [[cubic metre]])
::* <math>\dot{V}</math> is the [[volumetric flow rate]] (SI unit: cubic metres per second)
::* <math>g</math> is the [[standard gravity|acceleration due to gravity]] (SI unit: [[Meter (unit)|metres]] per second per second)
::* <math>\Delta h</math> ("[[Delta (Greek letter)|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 {{convert|145|m|ft|abbr=off}}, is 97 megawatts:{{Refn|group="note"|Taking the density of water to be 1000 kilograms per cubic metre (62.5 pounds per cubic foot) and the acceleration due to gravity to be 9.81 metres per second per second.}}
:<math>\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} = 97 \times 10^6 \ (\text{kg}\ \text{m}^2/\text{s}^3) = 97 \ \text{MW}</math>

Operators of hydroelectric stations compare the total electrical energy produced with the theoretical potential energy of the water passing through the turbine to calculate efficiency. Procedures and definitions for calculation of efficiency are given in test codes such as [[ASME]] PTC 18 and [[International Electrotechnical Commission|IEC]] 60041. Field testing of turbines is used to validate the manufacturer's efficiency guarantee. Detailed calculation of the efficiency of a hydropower turbine accounts for the head lost due to flow friction in the power canal or penstock, rise in tailwater level due to flow, the location of the station and effect of varying gravity, the air temperature and barometric pressure, the density of the water at ambient temperature, and the relative altitudes of the forebay and tailbay. For precise calculations, errors due to rounding and the number of [[significant digit]]s of constants must be considered.<ref>{{Cite web |last1=DeHaan |first1=James |last2=Hulse |first2=David |date=10 February 2023 |title=Generator Power Measurements for Turbine Performance Testing at Bureau of Reclamation Powerplants |url=http://www.ighem.org/Paper2008/08.pdf}}</ref>

Some hydropower systems such as [[water wheel]]s can draw power from the flow of a body of water without necessarily changing its height. In this case, the available power is the [[kinetic energy]] of the flowing water. Over-shot water wheels can efficiently capture both types of energy.<ref>{{cite book|last1=Sahdev|first1=S. K.|title=Basic Electrical Engineering|publisher=Pearson Education India|isbn=978-93-325-7679-7|page=418}}</ref> The flow in a stream can vary widely from season to season. The development of a hydropower site requires analysis of [[streamflow|flow records]], sometimes spanning decades, to assess the reliable annual energy supply. Dams and reservoirs provide a more dependable source of power by smoothing seasonal changes in water flow. However, reservoirs have a significant [[Environmental impact of reservoirs|environmental impact]], as does alteration of naturally occurring streamflow. Dam design must account for the worst-case, "probable maximum flood" that can be expected at the site; a [[spillway]] is often included to route flood flows around the dam. A computer [[Hydrological model|model of the hydraulic basin]] and rainfall and snowfall records are used to predict the maximum flood.{{citation needed|date=July 2014}}