Initial turbine selection is usually based on the ratio of design variables known as the power specific speed. In U.S. design practice this is given bywhere n is in revolutions per minute, P is the output in horsepower, and H is the head of water in feet. Turbine types can be classified by their specific speed, N, which always applies at the point of maximum efficiency. If N ranges from one to 20, corresponding to high heads and low rotational speeds, impulse turbines are appropriate. For N between 10 and 90, Francis-type runners should be selected, with slow-running, near-radial units for the lower N values and more rapidly rotating mixed-flow runners for higher N values. For N up to 110, Deriaz turbines may be suitable. If N ranges from 70 to the maximum of 260, propeller or Kaplan turbines are called for.

Using the specific speed formula, a turbine designed to deliver 100,000 horsepower (74,600 kilowatts) with a head of 40 feet (12.2 metres) operating at 72 revolutions per minute would have a specific speed of 226, suggesting a propeller or Kaplan turbine. It can also be shown that the flow rate would have to be about 24,500 cubic feet per second (694 cubic metres per second) at a turbine efficiency of 90 percent. The runner diameter will be about 33 feet (10 metres). This illustrates the large sizes required for high-power, low-head installations and the low rotational speed at which these turbines have to operate to stay within the permissible specific speed range.

Turbine model testing

Before building large-scale installations, the design should be checked out with turbine model tests, using geometrically similar models of small and intermediate size, all operating at the same specific speed. Allowances must be made for the effects of friction, determined by the Reynolds number (density × rotational speed × runner diameter squared/viscosity) and for possible changes in scaled roughness and clearance dimensions. Friction effects are less important for large units, which tend to be more efficient than smaller ones.

Electric power generation

Water turbines are used almost exclusively for generating electric power that can be transmitted through high-voltage power lines to population centres. The United States and Canada are among the leaders in hydroelectric power production, though many other countries also have major production facilities. Until the late 1950s most single turbogenerator units had capacities of less than 150,000 kilowatts. By the late 1980s construction costs and the need for reliability pointed toward 250,000- to 300,000-kilowatt units, although some recent installations were equipped with turbines capable of up to 750,000 kilowatts.

Pumped storage

Electricity must be used as soon as it is generated; there are no economical means of storing large quantities of electric energy. Thus hydroelectric plants built for near-maximum power consumption during daytime peak hours would have to operate at low efficiency during nighttime or weekend off-hours. To avoid this, water can be pumped to a second, higher reservoir during off-hours for storage in the form of potential energy and then fed back through power-generating turbines at times of high demand. Even though this system does not generate new energy (there actually is a reduction in energy due to losses involved in pump and turbine operation as well as in the electric motor and generator), pumped hydro-storage often becomes economical when compared with the cost of constructing additional turbines for peak power demands.

More From Britannica

history of flight: Turbine-powered helicopters

Modern pumped storage units in the United States normally use reversible-pump turbines that can be run in one direction as pumps and in the other direction as turbines. These are coupled to reversible electric motor/generators. The motor drives the pump during the storage portion of the cycle, while the generator produces electricity during discharge from the upper reservoir.

Most reversible-pump turbines are of the Francis type. The complexity of the unit, however, increases significantly as compared to a turbine alone. In spite of the higher costs for both hydraulic and electrical controls and support equipment, the total installed cost will be less than for completely separate pump-motor and turbine-generator assemblies with dual water passages.

Some very economical pumped storage plants have heads exceeding 300 metres. In the past this was considered too high for single-stage pumps, and the use of separate multistage, nonreversible units was required. Satisfactory reversible single-stage pump turbines, however, have been developed that can operate at 700-metre heads, though most installations have smaller head differences between the upper and lower reservoirs.

For medium heads, Deriaz turbines have had some success because they allow ready adjustment of the runner-blade angles to match the opposite requirements of pumping and power generation. The pumping load can also be varied with Deriaz-type units, which cannot be done with a Francis runner. A further advantage of a Deriaz-type machine is that the runner blades can be closed to form a smooth cone, a feature that permits pump start-up with minimum load while the unit is submerged in water.

An early major Deriaz reversible-pump turbine system was installed at plants on both the Canadian and U.S. sides of Niagara Falls; this made it possible to provide “side storage” at night without impairing the tourist attraction of the falls by reducing the flow during the day. The Tuscarora plant on the U.S. side uses 12 pump turbines at heads between 18.3 to 29 metres.

Pumped storage has become widespread in industrialized nations. In the United States alone more than 30 pumped hydropower stations were in operation by the mid-1980s. The largest plant is located in Bath County, Va., where six pump-turbines have a total capacity of 2.1 million kilowatts. This amount of power can be generated over an 11-hour period.

Tidal plants

Although the majority of hydroelectric plants depend on the impoundment of rivers, tidal power still could play a role, albeit minor, in electric power generation during the coming years. Areas where the normal tide runs high, such as in the Bay of Fundy between the United States and Canada or along the English Channel, can allow water to flow into a dam-controlled basin during high tide and discharge it during low tide to produce intermittent power. One such plant is located in France on the estuary of the Rance River near Saint-Malo in Brittany. There, a reservoir has been created by a barrage four kilometres inland from the river mouth to make use of tides ranging from about 3.4 to 13.4 metres. The power station is equipped with 24 reversible bulb-type propeller turbines coupled to reversible motor/generators, each having a capacity of 10,000 kilowatts. Pumped storage is used if the tidal outflow through the plant falls below peak power demands. A pilot tidal plant with a 40,000-kilowatt capacity has been built in Russia on the Barents Sea. If this facility proves economical, it may lead to the construction of other tidal plants on the northern and eastern Russian coasts.

Cost of hydroelectric power

Although large hydroelectric plants can be operated economically, the cost of land acquisition and of dam and reservoir construction must be included in the total cost of power, since these outlays generally account for about half of the total initial cost. Most large plants serve multiple purposes: hydropower generation, flood control, storage of drinking water, and the impounding of water for irrigation. If the construction costs are properly prorated to the non-power-producing utility of the unit, electricity can be sold very cheaply. In the Pacific Northwest region of the United States, such accounting has given hydroelectric plants an apparent cost advantage over fossil-fueled units.