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17 November, 04:51

A cowboy at a dude ranch fills a horse trough that is 1.5 m long, 60 cm wide, and 40 cm deep. He uses a 2.0-cm-diameter hose fromwhich water emerges at 1.5 m/s How long does it take him to fillthe trough?

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  1. 17 November, 07:42
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    It will take him 763.68 s to fill the trough

    Explanation:

    Flow rate,

    V = Qt ... Equation 1

    Where Q = flow rate, V = volume, t = time

    making t the subject of equation 1

    t = V/Q ... Equation 2

    But,

    Q = Av ... Equation 3

    Where A = area, v = velocity.

    Given: v = 1.5 m/s, and

    A = πd²/4 where d = 2.0 cm = 0.02 m, π = 3.143

    A = 3.143 (0.02) ²/4

    A = 0.0003143 m³

    Substituting these values into equation 3,

    Q = 1.5*0.0003143 = 0.0004714 m³/s

    Also, V = lbw ... Equation 4

    Where l = length, b = width, w = width.

    given: l = 1.5 m, b = 40 cm = 0.4 m, w = 60 cm = 0.6 m.

    Substituting these values into 4,

    V = 1.5*0.4*0.6

    V = 0.36 m³.

    using Equation 2,

    t = V/Q

    Where V = 0.36 cm³, Q = 0.0004714 m³/s

    therefore,

    t = 0.36/0.0004714

    t = 763.68 s

    Therefore it will take him 763.68 s to fill the trough
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