A rectangular plate of height h feet and base b feet is submerged vertically in a tank of fluid that weighs w pounds per cubic foot. The center of the rectangle is k feet below the surface of the fluid, where k > h2. Show that the fluid force on the surface of the plate is F = wkhb

A rectangular plate of height h feet and base b feet is submerged vertically in a tank of fluid that weighs w pounds per cubic foot. The center of the rectangle is k feet below the surface of the fluid, where k > h2. Show that the fluid force on the surface of the plate is F = wkhb

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

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Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Question

F = wkhb

Expert Solution

Step 1

Given that

Rectangle plate of height= $h$ feet

and its base = $b$ feet

Weight $= w p o u n d s / f o o t^{3}$

The center of the rectangle is $k$ feet below the surface of the fluid, where $k > h / 2$ .

To prove that

The fluid force on the surface of the plate is

$F = w k h b$

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