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18 December, 15:49

Water flows through a horizontal pipe (from a wider area to narrow area section) and then out into the atmosphere at a speed v1 15 m/s. The diameters of the wide and narrow sections of the pipe are 5.0 cm and 3.0 cm.

What volume of water flows into the atmosphere during a 10 min period?

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  1. 18 December, 19:03
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    V = 6.36 m³

    Explanation:

    For this exercise we will use fluid mechanics relations, starting with the continuity equation.

    Let's write the flow equation

    Q = v₁ A₁

    The area of a circle is

    A = π r²

    Radius is half the diameter

    A = π/4 d²

    Q = v₁ π/4 d₁²

    Q = π / 4 15 0.03 2

    Q = 0.0106 m3 / s

    The volume of water in t = 10 min = 10 60 = 600 s

    Q = V / t

    V = Q t

    V = 0.0106 600

    V = 6.36 m³
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