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19 August, 06:01

A garden hose with an internal diameter of 1.6 cm is connected to a (stationary) lawn sprinkler that consists merely of a container with 25 holes, each 0.30 cm in diameter. If the water in the hose has a speed of 0.96 m/s, at what speed does it leave the sprinkler holes?

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  1. 19 August, 06:25
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    s = 1.024 m/s

    Explanation:

    The volume of water passing through the hose (Vh) must equal the volume of water leaving the sprinkler (Vs)

    Thus, using the volume of a cylinder, we have;

    Vh = 0.96 x π x (1.6/2) ²

    Vh = 0.576π

    Let s be the speed from the sprinkler. Thus;

    Vs = s x 25 x π x (0.3/2) ²

    Vs = 0.5625π (s)

    Since the condition is; Vh = Vs

    Thus,

    0.576π = 0.5625π (s)

    π will cancel out to give;

    0.576/0.5625 = s

    s = 1.024 m/s
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