The South Holston Dam uses hydroelectric energy to produce 38,500 kilowatts of power. If the density of water is 997 kg/m^3 and the dam allows 3,290 m^3/s of water through. How high does the waterfall from to produce that much power a second

The waterfall must 1.197 meters high to produce the abovementioned power in a second.

Explanation:

Let suppose that South Holston Dam is a conservative system, that is, there is no non-conservative forces that dissipates energy. According to the Principle of Energy Conservation, final kinetic energy equals to initial gravitational potential energy, whose form per unit time is:

Where:

- Power, measured in watts.

- Instantaneous change in kinetic energy in time, measured in watts.

- Instantaneous change in gravitational potential energy in time, measured in watts.

Now, let suppose that final speed is constant, so that:

Where:

- Mass flow, measured in kilograms per second.

- Volume flow, measured in cubic meters per second.

- Gravitational constant, measured in meters per square second.

- Height change, measured in meters.

The change is finally cleared in the latter equation:

Given that , , and , the height change is:

The waterfall must 1.197 meters high to produce the abovementioned power in a second.

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