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6 May, 11:53

Water flowing through a pipe suddenly comes to a section of pipe where the pipe diameter decreases to 86% of its previous value. if the speed of the water in the larger section of the pipe was 66 m/s, what is its speed in this smaller section?

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  1. 6 May, 12:56
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    In all the sections of the pipe, volumetric flow rate is the same. Therefore,

    Q1 = Q2

    Q = VA, V = velocity, A = Cross-sectional area.

    Then,

    V1A1 = V2A2

    But,

    A = πD^2/4

    Then,

    V1·πD1^2/4 = V2·πD2^2/4

    V1·D1^2 = V2·D2^2

    But

    D2/D1 = 86% = 0.86, or D1/D2 = 1/0.86

    Therefore,

    V2 = (V1D1^2) / D2^2 = V1· (D1/D2) ^2 = 66 * (1/0.86) ^2 = 89.24 m/s

    The speed in the smaller section is 89.24 m/s.
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