Question

KHomework Set 9 Pressure on a Dam As the reservoir behind a dam is filled with water, the pressure that the water exerts on the dam increases Eventually, the force on the dam becomes substantial and it could cause the dam to collapse. There are two significant issues to be considered: First, the base of the dam should be able to withstand the pressure pgh , where p is the density of the water behind the danm h is its depth, and g is the magnitude of the acceleration due to aravity. This means that the Figure 1 of 1 Homework Set 9 Pressure on a Dam significant issues to be considered First, the base of the dam should be able to withstand the pressure pgh where p is the density of the water behind the dam, h is its depth, and g is the magnitude of the acceleration due to gravity. This means that the material of which the dam is made needs to be strong enough so that it doesn't crack (compressive strength) Figure 1 of 1 Homework Set 9 Pressure on a Dam The second issue has to do with the strength of the foundation of the dam. The water pressure exerts a clockwise torque on the dam, shown in (Figure 1). The foundation of the dam should be strong enough so that the dam does not topple. The material has to be strong enough that the dam does not snap (shear strength) Figure 1 of 1 KHomework Set 9 Pressure on a Dam strong enough that the dam does not snap (shear strength) To study this phenomenon, consider the simple model of a dam depicted in (Figure 1). A reservoir of water (density p) behind the dam is filled to a height h Assume that the width of the dam (the dimension pointing into the screen) is L Figure

Answer 1

A)

Pressure, P = $\large \rho$ g(h - x)

dF = P dA

dF = $\large \rho$ gL(h - x) dx <<<<< Ans

B)

$\large T = \int_{0}^{h} x \rho g L (h - x) dx$

T = $\large \rho$ gL [h(h^2)/2 - h^3/3]

T = $\large \rho$ gLh^3/6

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