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To calculate the fluid force on one side of the plate, we need to apply the formula for fluid force on a submerged surface, which depends on the fluid density, depth, and the area of the submerged surface.

### Given:
- **Density of water** (\( \rho \)): \( 62.4 \, \text{lb/ft}^3 \)
- **Plate coordinates**: It appears the plate is submerged between \( x = -12 \) and \( x = 12 \), and the depth extends from the surface of the pool (at \( y = 0 \)) to a certain negative depth (marked as \( y = -3 \) at the edge).

### Approach:
The pressure at a depth \( y \) in a fluid is given by:
\[
P(y) = \rho g |y|
\]
where \( |y| \) is the depth below the fluid surface.

The differential fluid force \( dF \) on a horizontal strip at depth \( y \) is given by:
\[
dF = \rho g |y| \cdot dA
\]
where \( dA \) is the area of the differential strip.

For a plate that extends vertically along the \( y \)-axis and horizontally from \( x = -12 \) to \( x = 12 \), the total width of the plate at any depth \( y \) is the horizontal distance between \( x = -12 \) and \( x = 12 \), which is constant at 24 feet.

Thus, the differential area \( dA \) is:
\[
dA = \text{width} \cdot dy = 24 \cdot dy
\]

Now, integrate the force over the submerged depth from \( y = 0 \) to \( y = -3 \) (or deeper, depending on the full shape of the plate).

### Do you want me to proceed with the exact calculation steps based on this model?

Calculate the fluid force on one side of the plate using the coordinate system shown below. Assume the density is 62.4 lb/ft³.

This problem involves calculating the fluid force on a submerged vertical plate with a density of 62.4 lb/ft³. Learn how to apply the principles of hydrostatic pressure and use integration to find the total force on the plate, with detailed formulas and concepts from fluid mechanics.

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