# Thread: Liquid Pressure and Fluid Force

1. ## Liquid Pressure and Fluid Force

I am so lost right now, can you explain the formula and the step by step solution

2. ## 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 = $2x= 2\sqrt{1-y^2}$

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