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What is the hydrostatic force on one side of a square plate immersed?
A square plate with sides c is immersed vertically in the water with a peak at the surface of the water (submerged diagonally). Expressing the hydrostatic force against one side of the plate as an integral and evaluate it.
F = ∫ ∫ p (x, y) p dA (x, y) = ρgy, where y is the depth of water, the limits of the integral of X is Y – √ [2] c to x and x from 0 to ½ √ [2] The c is for the right side of the plate for total force is sufficient to multiply by 2 the integration wrt y: ½ ρgy from x ² – √ [2] c to x, yields ½ ρg [(x - √ [2] c) ² – (-x) ²) ½ ρg [2 + x ² - 2 √ [2] x – x ²) ½ ρg [2c ² - 2c √ [2]) incorporating WRT xx: ½ ρg [2c X ² - √ [2] CX ²], 0 ½ √ [2] c ½ ρg [(2c ² (½ √ [2] c) – √ [2] c (½ √ [2] c) ²) – (2c ² (0) – √ [2] C (0 )²)], ½ ρg [c ³ √ [2] – c ³] ³ ½ ρgc [√ [2] – 1] multiplied by two to obtain the total force: F = ³ ρgc [[√ 2] – 1 photo]: http://img248.imageshack.us/my.php?image=aaanm8.png
My Condor Tactical Plate Carrier Vest – Part 1
