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15 April, 15:12

Three fire hoses are connected to a fire hydrant. Each hose has a radius of 0.017 m. Water enters the hydrant through an underground pipe of radius 0.088 m. In this pipe the water has a speed of 2.7 m/s. (a) How many kilograms of water are poured onto a fire in one hour by all three hoses

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  1. 15 April, 15:31
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    2.36 x 10^5 kg

    Explanation:

    radius of hose, r = 0.017 m

    radius of underground pipe, R = 0.088 m

    number of hoses, n = 3

    velocity of water in underground pipe, V = 2.7 m/s

    Let v is the velocity of water in each hose.

    According to the equation of continuity

    A x V = n x a x v

    π R² x V = n x π x r² x v

    0.088 x 0.088 x 2.7 = 3 x 0.017 x 0.017 x v

    v = 24.12 m/s

    (a) Amount of water poured onto a fire in one hour by all the three hoses

    = n x a x v x density of water x time

    = 3 x 3.14 x 0.017 x 0.017 x 24.12 x 1000 x 3600

    = 2.36 x 10^5 kg

    Thus, the amount of water poured onto the fire in one hour is 2.36 x 10^5 kg.
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