A round pipe of varying diameter carries petroleum from a wellhead to a refinery. At the wellhead, the pipe’s diameter is 57.3 cm ( 0.573 m)

Question

A round pipe of varying diameter carries petroleum from a wellhead to a refinery. At the wellhead, the pipe’s diameter is 57.3 cm ( 0.573 m) and the flow speed of the petroleum is 13.5 m/s. At the refinery, the petroleum flows at 5.83 m/s. What is the volume flow rate of the petroleum along the pipe and what is the pipe’s diameter at the refinery?

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Trúc Chi 5 years 2021-07-24T05:38:53+00:00 1 Answers 127 views 0

Answers ( )

  1. Dau
    0
    2021-07-24T05:39:54+00:00
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    Answer with Explanation:

    We are given that

    Diameter of pipe,d_1=0.573 m

    v_1=13.5 m/s

    v_2=5.83 m/s

    Volume flow rate of the petroleum along the pipe=Q_{refinery}=A_1v_1=v_(\frac{\pi d^2_1}{4})

    Q_{refinery}=13.5\times (\pi\times \frac{0.573)^2}{4})=3.48 m^3/s

    By equation of continuity

    A_1v_1=A_2v_2

    \frac{\pi d^2_1}{4}v_1=\frac{\pi d^2_2}{4}v_2

    d^2_2=\frac{v_1}{v_2}d^2_1

    d_2=\sqrt{\frac{v_1}{v_2}}d_1

    d_2=0.573\sqrt{\frac{13.5}{5.83}}

    d_2=0.87 m

    d_2=0.87\time 100=87 cm

    1 m=100 cm

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