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10 January, 22:48

Problem 1: Energy from Flow. Before the advent of the steam-powered engine, most mechanical processes were driven by extracting power from a nearby river using a water wheel. A miller wants to construct a water wheel to grind grain into an hour. He needs a total power output of 0.5 kW to meet the demand of his mill. If a nearby waterfall will flow at a rate of 400 liters/minute onto the top of the wheel, what is the required diameter of the water wheel to achieve the desired power output?

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  1. 11 January, 01:19
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    Diameter will be 27394.76 m

    Explanation:

    Power P = 0.5 kW = 500 W

    Time t required for grinding = 1 hr = 3600 sec

    Energy required E = P x t

    E = 500 x 3600 = 1800000 J

    Flow rate of water Q = 400 ltr/min

    We convert to m3/sec

    400 ltr/min = 400 / (1000 x 60) m3/ses

    Q = 0.0067 m3/sec

    Energy provided by flow will be

    E = pgQd

    Where p = density of water = 1000 kg/m3

    g = acceleration due to gravity 9.81 m/s2

    d = diameter of wheel.

    Equating both energy, we have,

    1800000 = 1000 x 9.81 x 0.0067 x d

    1800000 = 65.73d

    d = 1800000/65.73

    d = 27394.76 m
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