A man attaches a divider to an outdoor faucet so that water flows through a single pipe of radius 9.25 mm into four pipes, each with a radiu

Question

A man attaches a divider to an outdoor faucet so that water flows through a single pipe of radius 9.25 mm into four pipes, each with a radius of 5.00 mm. If water flows through the single pipe at 1.45 m/s, calculate the speed (in m/s) of the water in the narrower pipes.

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Thái Dương 3 years 2021-07-26T12:02:58+00:00 1 Answers 39 views 0

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    2021-07-26T12:04:40+00:00

    Answer:

    1.24 m/s

    Explanation:

    Metric unit conversion:

    9.25 mm = 0.00925 m

    5 mm = 0.005 m

    The volume rate that flow through the single pipe is

    \dot{V} = vA = 1.45 * \pi * 0.00925^2 = 0.00039 m^3/s

    This volume rate should be constant and divided into the 4 narrower pipes, each of them would have a volume rate of

    \dot{V_n} = \dot{V} / 4 = 0.00039 / 4 = 9.74\times10^{-5} m^3/s

    So the flow speed of each of the narrower pipe is:

    v_n = \frac{\dot{V_n}}{A_n} = \frac{\dot{V_n}}{\pi r_n^2}

    v_n = \frac{9.74\times10^{-5}}{\pi 0.005^2} = 1.24 m/s

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