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6 November, 12:57

A water line with an internal radius of 5.29 x 10-3 m is connected to a shower head that has 15 holes. The speed of the water in the line is 0.651 m/s. (a) What is the volume flow rate in the line? (b) At what speed does the water leave one of the holes (effective hole radius = 4.13 x 10-4 m) in the head?

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  1. 6 November, 16:57
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    (a) 3.44 x 10^-3 m^3/s

    (b) 8.4 m/s

    Explanation:

    area of water line, A = 5.29 x 10^-3 m

    number of holes, N = 15

    Speed of water in line, V = 0.651 m/s

    (a) Volume flow rate is given by

    V = area of water line x speed of water in water line

    V = 5.29 x 10^-3 x 0.651 = 3.44 x 10^-3 m^3/s

    (b) area of one hole, a = 4.13 x 10^-4 m

    Let v be the velocity of water in each hole

    According to the equation of continuity

    A x V = a x v

    5.29 x 10^-3 x 0.651 = 4.1 x 10^-4 x v

    v = 8.4 m/s
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