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A person with a remote mountain cabin plans to install her own hydroelectric plant. A nearby stream is 3.00 m wide and 0.500 m deep. Water flows at 1.35 m/s over the brink of a waterfall 4.20 m high. The manufacturer promises only 25.0% efficiency in converting the potential energy of the water-Earth system into electric energy. Find the power she can generate. (Large-scale hydroelectric plants, with a much larger drop, can be more efficient.)

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DayyanKhan

Answer:

The power she can generate is 185.22 KW.

Explanation:

DATA

3.00m wide and 0.500m deep.

Cross sectional area = 1.500m^2

Velocity = 1.35m/s

Volumetric flow rate = Av = 18.00m^3/s

Mass flow rate = 18,000kg/s

Height = 4.20m

25.0% efficiency

FORMULA:

P = dE / dt * eff

SOLUTION:

18,000kg/s (9.8m/s^2) (4.20m) (25%) = 185,220 watts

= 185 kw

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