The Niagara Falls Hydroelectric Station

The Niagara River flows over steep cliffs in two cataracts we call Niagara Falls.

On the left is the "American Falls", and on the right, the "Canadian" or "Horseshoe Falls". Some information about each:

Falls        Height           Liters per second
American      54 m               600,000

Canadian      51 m             2,400,000

Starting over one hundred years ago, power companies have used water in the Niagara River to generate electricity. Strangely enough, they don't touch the water which goes over the falls. Instead, about a mile above the falls, much of the river is diverted into pipes which lead it downwards to the generating stations.

Once the water reaches the stations, it is sent into huge turbines. Below is a picture of one such turbine. Water flows from the pipe on the right side of the diagram into the circular casing at the center:

Here's a picture of the casing by itself. Note how large it is! The diameter of the tube is about 10.5 feet at the intake end.

Each turbine contains a giant waterwheel attached to a shaft; as the water rushes through, it spins the wheel, the shaft, and all the equipment attached to the shaft. The top of the shaft sits inside a cylindrical housing, shown at the top of the diagram below.

A set of twelve very large magnets fixed in a circular housing is attached to the shaft. Each magnet provides a field of around 0.1 Tesla.

The magnets spin around inside a big coil of wire, which is in turn set within giant cylindrical covers. The wire turns many times around a frame which is very roughly a square 3 meters on a side; thus, an area of about 9 square meters. The power plant contains a number of these generators.

As the caption of the picture above indicates,

each generator produces 13,000 volts (RMS). The shaft turns at 107 revolutions per minute, but has 6 North/South/North sets of magnets; thus, the magnetic flux due to the magnets will oscillate 642 times each minute. The output of each generator is about 70,000 horsepower. (Today's power stations produce about 2 GW GigaWatts for Canada and about 2.4 GW for the US).

Now, can you answer the following questions?

    Some energy questions:

  1. How much energy does a single chunk of water, of mass 1 kg, gain as it drops over the falls?
  2. If only half of that energy is captured by the generator, how many kilograms of water must flow flow through each generator's turbie each second?
  3. How does this compare to the mass of all the water actually spilling over the falls each second?
  4. There are about twenty generators combined in the US and Canadian hydropower plants. What is the total mass of water flowing through the turbines?
  5. How fast is the water going as it runs through the turbine?

    Some electricity questions:

  6. What is the frequency of the voltage created by one generator?
  7. How many turns, N, of wire must there be inside a single generator?
  8. How large is the current running through the coils of wire?
  9. How long is the wire?
  10. All that current running through the wire could heat up the wire quite a bit -- wasting lots of the energy generated. If the wire is made of pure copper, and circular in cross section, what is the minimum possible diameter it can have?
  11. What is the mass of all that copper?
  12. Is it really possible to pack the required number of turns of wire, of the required diameter, into the space around one of these generators?

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