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Hydro Turbines:Power & Efficiency

The Potential Energy of Reservoirs

Dams force water to back up behind them into reservoirs which store the gravitational potential energy of water.

head,h

The amount of energy stored is proportional to the head – the height of water in the reservoir above the turbine. The stored energy can be used to generate power.

Volumetric Flow RateVolume Flow Rate Through a

Pipe

Q = AVQ, volumetric flow rateA, cross-sectional area

V, average fluid velocity

In this case, the pipe we’re talking about is the penstock that channels water from the reservoir to the turbines where power is transmitted to the generators.

Example: Water flows at a rate of 1 m/s through a round pipe with a diameter of 3 cm. What is the volumetric flow rate [L/s]?

How much power does a hydro turbine produce?

Power = hrghQ

h, efficiency g, acceleration of gravity

r, density h, head

Q, volume flow rate

 Example: A hydroelectric plant employs a turbine with an overall efficiency of 85% in conditions where the flow rate is 30000 liters per second and the surface of the reservoir is 20m above the turbine. How much power is produced [kW]?

Power, Head & Flow Rate

This image shows a cross-section of surface run-off at three separate locations: (A) a small, fast-flowing, steep mountain stream; (B) a deep, quick flowing river in a narrow channel; and (C) a very wide, but shallow, slow-moving river.

As we follow the run-off from A to C, the vertical drop of the water flow decreases (h goes down), but the volumetric flow rate increases (Q goes up).

This means that, in theory, it would be possible to achieve the same power when installing a hydroelectric power plant at any of the three locations shown.

Large hSmall Q

Average hAverage Q

Small hLarge Q

Types of TurbinesImpulse

◦Pelton Wheel - large h, small QReaction

◦Kaplan - small h, large Q◦Francis - large h, large Q

Pelton Wheel Kaplan Francis

Choosing Turbines

Which type of turbine would you choose if you were designing a hydroelectric power plant for a site similar to the conditions at location C? Why?

What’s Coming Up?Impacts on Environment/Society