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28 January, 01:13

The maximum flow of water in a pipe is modeled by the formula Q=Av, where A is the cross-sectional area of the pipe and V is the velocity of the water. Find the diameter of a pipe that allows a maximum flow of 50ft^3/min of water flowing at a velocity of 600ft/min

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  1. 28 January, 05:02
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    For this case we have the following equation:

    Q = Av

    Where the area is given by:

    A = pi * r ^ 2

    A = pi * (d / 2) ^ 2

    A = (pi / 4) * d ^ 2

    Substituting we have:

    Q = ((pi / 4) * d ^ 2) v

    From here, we clear the diameter:

    d = root ((4 / pi) * (Q / v))

    Substituting values we have:

    d = root ((4 / pi) * (50/600))

    d = 0.36 feet

    Answer:

    The diameter of a pipe that allows a maximum flow of 50ft ^ 3 / min of water flowing at a velocity of 600ft / min is:

    d = 0.36 feet
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