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PkW = Q (H - hf) e 127.72 where P = power (kW) Q = discharge (l/sec) H = gross head between intake and draft tube (m) hf = head losses within system (H - hf = net head) e = overall system efficiency, usually about 0.80 127.72 = constant related to the weight of water The term hf, "head losses within system", represents friction, such as that created when water comes in contact with the walls of pipes, screens, and control valves within the hydroelectric equipment. The equation shows that, for a given head, power can be increased by reducing losses due to friction (i.e., the net head is increased), increasing the discharge, increasing overall system efficiency, or some combination of these actions. The most direct way to obtain more power is to increase the gross head by building a dam or increasing the height of an existing dam. Another way to obtain more power is to increase the flow by diverting more water through the hydropower system. Head losses can be reduced by optimal choices of design, equipment, and materials. The developer of a hydroelectric energy project is interested in determi n i ng how much power can be obta i ned annua lly from a given site and the related costs. Plant capacity usually is less than the maximum amount that could be obtained at a particular site because it is not economically feasible to install extra capacity just to capture energy from an exceptionally rare flood. Figure 5 shows how natural discharge variations affect power output for three different installed capacities over the course of an average year (based on 10 years of data). Table 2 illustrates the fact that the amount of power available over an annual period is well below the amount of energy that hypothetically could be obtained if the turbines ran at full capacity 100% of the time. In this example, the percentage of the installed capacity that could be productively used will decrease as the installed capacity increases. This diminishing returns relationship is typical of hydroelectric sites; the challenge of a feas- ibility analysis is to determine the installed capacity that will yield the highest return on developer investment. It should also be noted here that the amount of flow available for power production will depend upon flow releases required to service downstream users and to meet minimum flow requirements imposed to maintain aquatic/wetland resources. The problem of matching the size of the SSH plant to the site is discussed further in Chapter 6, Turbine-related Impacts. 18