The Hoover Dam, in Arizona, encloses Lake Mead, which...

The Hoover Dam, in Arizona, encloses Lake Mead, which contains 10 trillion gallons of water. The dam is $1200 \mathrm{ft}$ wide and the lake is $500 \mathrm{ft}$ deep. (a) Estimate the hydrostatic force on the dam, in MN. (b) Explain how you might analyze the stress in the dam due to this hydrostatic force.

The Hoover Dam, in Arizona, encloses Lake Mead, which contains 10 trillion gallons of water. The dam is $1200 \mathrm{ft}$ wide and the lake is $500 \mathrm{ft}$ deep.
(a) Estimate the hydrostatic force on the dam, in MN.
(b) Explain how you might analyze the stress in the dam due to this hydrostatic force.

Key Concepts

Structural Stress Analysis

Structural stress analysis involves evaluating how applied forces, such as hydrostatic loads, are distributed within a structure. For a dam, this includes understanding both the bending moments and shear forces caused by the water pressure. Analyzing these stresses helps ensure that the dam’s design can safely support the load without failure, by assessing material strength, load paths, and potential points of structural weakness.

Center of Pressure

The center of pressure is the point on a submerged surface where the total resultant hydrostatic force can be considered to act. It is determined by taking moments of the pressure distribution about a reference point. This concept is especially important for understanding the effective point of application of the force, which influences the resulting moment and stress distributions in structures like dams.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. It increases linearly with depth according to the relation p = ?gh, where ? is the fluid density, g is the gravitational acceleration, and h is the depth. This concept is fundamental to calculating the force exerted by a fluid on a submerged surface like a dam.

Integration of Pressure Over a Surface

When a surface is submerged in a fluid, the pressure varies with depth. To compute the total force on the surface, one needs to integrate the differential force (pressure times differential area) over the entire area of the surface. This integral accounts for the changing pressure with depth and is a central method in fluid mechanics for determining hydrostatic force.

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