System Performance

The output of a hydropower plant will be a function of the volume of water released or discharged and the vertical distance the water falls (the head). The turbine design requirements will largely be a function of the head, discharge rate, and required rotational speed of the driven device.

Turbine power (Pt) requirements are determined as:

tional area and 10 ft (3 m) height would contain 10 ft3 (0.28 m3) of water. It would impart a force of 624 (10 x 62.4) lbf (283 kg) on each ft2 (or m2) of turbine blade.

In English system units, the power potential of a water stream, in hp, is found by dividing the result of Equation 14-1 (with flow measured in ft3/sec, head measured in ft, and standard density of water at 62.4 lbm/ft3) by 550 ft-lbm/sec. For example, with a head of 100 ft (30.5 m) and a flow rate of 1,000 ft3/sec (28.3 m3/sec), an 85% mechanically efficient unit would develop (100 x 1,000 x 0.85 x 62.4 - 550) 9,650 hp. To convert to kW output, hp can be multiplied by 0.746 kW/hp. This would yield 7,195 kW developed. Alternatively, when expressed in SI units, where head is rated in m and flow rate in m3/sec, Equation 14-1 can be multiplied by 9.81 to yield kW developed. Again, this would yield (30.5 x 28.3 x 0.85 x 9.81) 7,195 kW

An important factor in initial turbine selection is a ratio of design variables, termed the power specific speed (N). In U.S. design practice, it is expressed as:



^t = Mechanical efficiency of the turbine (and generator if applicable)

c = Constant (the product of the density of water and acceleration due to gravity)

The mechanical efficiency of the turbine itself will vary. Older large capacity designs still in operation may have mechanical efficiencies below 50%. Very small capacity newer units may also have mechanical efficiencies well below 50%. On the other hand, some large capacity modern turbine designs have demonstrated mechanical efficiencies in excess of 90%. When assessing mechanical efficiency, however, one must also consider a number of other friction losses in the system, as well as mechanical losses associated with the driven device (e.g., electric generator efficiency losses). Ideal power can be converted into actual power by including all friction losses or efficiency factors in Equation 14-1.

The power produced by water depends upon the water's weight and head (height of fall). Assuming c equals 1 (at zero altitude and standard atmospheric conditions), each ft3 (0.03 m3) of water has a mass of 62.4 lbm (28.3 kg). For example, a column of water with a 1 ft2 (0.3 m2) cross-sec-


n = Rotational speed in revolutions per minute P = Power output in hp H = The head of water in ft

Turbine types can be classified by their specific speed, which applies at the point of maximum efficiency. If N ranges from 1 to 20, corresponding to high heads and low rotational speeds, impulse turbines are commonly selected. For N between 10 and 90, Francis type turbines are commonly selected, with slow-running, near-radial units selected for the lower N values and more rapidly rotating mixed-flow runners for higher N values. Deriaz turbines may be selected for N of up to 110, while for N values ranging from 70 to a maximum of 260, propeller or Kaplan turbines may be selected.

Based on Equation 14-2, a turbine designed to deliver 100,000 hp (74.6 MW) with a head of 40 ft (12.2 m) operating at 72 rpm would have a specific speed of 226. This, for example, might suggest selection of a propeller or Kaplan type turbine. Based on Equation 14-1, at a turbine mechanical efficiency of 90%, the flow rate would be about 24,500 ft3/sec (694 m3/sec) and the runner diameter would likely exceed 30 ft (10 m). This typifies the very large sizes required for high-power, low-head installations and the low rotational speed at which these turbines must operate to stay within an appropriate specific speed range.

Fig. 14-7 Aerial View of Grand Coulee Dam and Power Plant. Source: Bureau of Reclamation
Renewable Energy Eco Friendly

Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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