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Thread: Liquid Pressure and Fluid Force

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    Liquid Pressure and Fluid Force

    Liquid Pressure and Fluid Force-download-4-.pngI am so lost right now, can you explain the formula and the step by step solution
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    Re: Liquid Pressure and Fluid Force



    Let the origin be at the center of the window

    $\displaystyle F = w \int_c^d h(y) \cdot L(y) \, dy$

    $w$ is the weight-density of the fluid = $64 \, lb/ft^3$

    $h(y)$ is the depth of a representative horizontal strip of window = $100-y$

    equation of the circular window is $x^2 + y^2 = 1 \implies x = \sqrt{1-y^2}$

    $L(y)$ is the length of a representative horizontal strip of window = $2x= 2\sqrt{1-y^2}$

    $\displaystyle F = 64 \int_{-1}^1 (100-y) \cdot 2\sqrt{1-y^2} \, dy$
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