Answer :
The hydrostatic force on the fully submerged vertical rectangular tank wall is 244,408 lb, and the center of force is located 4 ft from the bottom.
The hydrostatic force exerted on a submerged surface is calculated using the formula F = ρghA, where ρ is the fluid density, g is the acceleration due to gravity, h is the depth of submersion, and A is the area of the submerged surface. In this case, the fluid is water with a specific gravity (SG) of 0.68.
The area of the tank wall in contact with the water is the product of its height and width: A = height × width = 12 ft × 40 ft = 480 sq ft. The depth of submersion is the full height of the wall, which is 12 ft.
Using the density of water (ρ ≈ 62.4 lb/ft³) and the acceleration due to gravity (g ≈ 32.2 ft/s²), we can calculate the hydrostatic force: F = 0.68 × 62.4 lb/ft³ × 32.2 ft/s² × 480 sq ft × 12 ft ≈ 244,408 lb.
The center of force on a vertically submerged surface is located at one-third of the distance from the bottom of the surface. For this tank wall, the center of force is at 4 ft from the bottom (12 ft × 1/3 = 4 ft).
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Final answer:
The hydrostatic force on the fully submerged vertical rectangular tank wall is approximately 191,923 lb.
Explanation:
To determine the hydrostatic force on a fully submerged vertical rectangular tank wall, we can use the formula:
F = ρghA
Where:
- F is the hydrostatic force
- ρ is the density of the fluid
- g is the acceleration due to gravity
- h is the height of the fluid column above the wall
- A is the area of the wall
In this case, the fluid is water with a specific gravity (SG) of 0.68. The height of the wall is given as 12ft and the width as 40ft.
First, we need to calculate the pressure at the bottom of the wall. The pressure at a certain depth in a fluid is given by the formula:
P = ρgh
Where:
- P is the pressure
- ρ is the density of the fluid
- g is the acceleration due to gravity
- h is the depth of the fluid
Since the water surface is located at the top of the tank wall, the depth of the fluid is equal to the height of the wall, which is 12ft.
Substituting the given values into the formula, we have:
P = (0.68)(62.4 lb/ft³)(32.2 ft/s²)(12 ft)
Calculating this, we find that the pressure at the bottom of the wall is approximately 2,090.496 lb/ft².
Next, we need to calculate the area of the wall. The area of a rectangular wall is given by the formula:
A = length × width
Substituting the given values into the formula, we have:
A = 12 ft × 40 ft
Calculating this, we find that the area of the wall is 480 ft².
Finally, we can calculate the hydrostatic force using the formula:
F = ρghA
Substituting the values we calculated earlier, we have:
F = (0.68)(62.4 lb/ft³)(32.2 ft/s²)(12 ft)(480 ft²)
Calculating this, we find that the hydrostatic force on the fully submerged vertical rectangular tank wall is approximately 191,923 lb.
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