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21 August, 23:48

A trough is filled with a liquid of density 810 kg/m3. The ends of the trough are equilateral triangles with sides 8 m long and vertex at the bottom. Find the hydrostatic force on one end of the trough. (Use 9.8 m/s2 for the acceleration due to gravity.)

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  1. 22 August, 00:23
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    The hydrostatic force on one end of the trough is 54994.464 N

    Explanation:

    Given;

    liquid density, ρ = 810 kg/m³

    side of the equilateral triangle, L = 8m

    acceleration due to gravity, g = 9.8 m/s²

    Hydrostatic force is given as;

    H = ρgh

    where;

    h is the vertical height of the equilateral triangle

    Draw a line to bisect upper end of the trough, to the vertex at the bottom, this line is the height of the equilateral triangle.

    let the half side of the triangle = x

    x = ⁸/₂ = 4m

    The half section of the triangle forms a right angled triangle

    h² = 8² - 4²

    h² = 48

    h = √48

    h = 6.928m

    F = ρgh

    F = 810 x 9.8 x 6.928

    F = 54994.464 N

    Therefore, the hydrostatic force on one end of the trough is 54994.464 N
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