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12 April, 09:40

Water flows over a waterfall that is 20 m high at the rate of 4.0 * 104 kg/s. a. How much KE does the water gain each second when it reaches the bottom of the waterfall? b. If this water powers an electric generator with a 40% efficiency, how many watts of electric power can be supplied? C, What is the velocity of the water when it exits the turbine that drives the generator?

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  1. 12 April, 09:49
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    a)

    7.8 x 10⁶ Watt

    b)

    3.12 x 10⁶ Watt

    c)

    15.3 m/s

    Explanation:

    a)

    h = height of the waterfall = 20 m

    m = mass rate = 40000 kg/s

    K = gain in kinetic energy per second

    Using conservation of energy

    K = mgh

    K = (40000) (9.8) (20)

    K = 7.8 x 10⁶ J/s

    K = 7.8 x 10⁶ Watt

    b)

    P = Electric power supplied

    η = Efficiency = 40% = 0.40

    Electric power supplied is given as

    P = η K

    P = (0.40) (7.8 x 10⁶)

    P = 3.12 x 10⁶ Watt

    c)

    P' = Kinetic energy remaining in water after exiting the turbine

    v = velocity of water

    Kinetic energy remaining in water after exiting the turbine is given as

    P' = K - P

    P' = 7.8 x 10⁶ - 3.12 x 10⁶

    P' = 4.68 x 10⁶ Watt

    (0.5) m v² = 4.68 x 10⁶

    (0.5) (40000) v² = 4.68 x 10⁶

    v = 15.3 m/s
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