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Manuscript 3 - Danielle M Henak Calculus II David Sharpe...

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Danielle M. Henak Calculus II David Sharpe November 16, 2007 Manuscript #3 In this manuscript, we will be exploring hydrostatic forces, specifically, those hydrostatic forces that are exerted by a reservoir of water on a dam. The formula for the force of pressure that the water would exert on a horizontal plate is = . ( ) F 62 4A d , where 62.4 is the density of water, A is the area of the surface in feet squared , and d is the depth of the plate measured from the surface. Because Pascal’s Principle states that the pressure at any given depth in a liquid is the same in every direction, our formula also applies to vertically oriented plates, which is what a dam would be considered. If we were to apply the formula for the horizontal plate at a uniform depth under the water to that of a vertical plate, the y-axis becomes the depth and is measured in positive numbers, where y=0 is the surface. Therefore, W(y) would be the function of the width of the dam at depth y. The force of pressure
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