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9 March, 08:22

Find the amount of work done in emptying a cylindrical tank completely filled with kerosene. Assume that the radius of the cylindrical tank is 3 m, height is 6 m, and the density of kerosene is 817.15 kg/m3

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  1. 9 March, 08:23
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    The formula for the work done in emptying a tank is this:

    W = ωyV

    where

    ω is the specific weight

    y is the center of gravity

    V is the volume of the liquid

    The specific weight can be calculated using the formula

    ω = ρg

    where

    ρ is the density

    g is the acceleration due to gravity

    Solving for ω

    ω = 817.15 kg/m3 (9.81 m/s2)

    ω = 8016.24 N/m3

    The center of gravity of a completely filled cylindrical tank is just 1/2 of the height. So,

    y = 3 cm

    The volume of the kerosene is just the volume of tank. Using the formula for the volume of a cylinder

    V = πr²h

    V = π (3²) (6)

    V = 54π m³

    Therefore, the word done is

    W = 8016.24 (6) (54π)

    W = 8159538.47 J or

    W = 8.16 MJ
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