An underwater viewing window is installed at an aquarium. The window is circular with radius 5 feet. The center of the window is 40 feet below the surface of the water. Find the hydrostatic force on the window.
http://banach.millersville.edu/~bob/math211/tests/summer2009/quiz2ans.pdf
To find the hydrostatic force on the window, we need to use the formula:
F = ρghA
Where:
- F is the hydrostatic force
- ρ is the density of the fluid (in this case, water)
- g is the acceleration due to gravity
- h is the depth of the window below the surface of the water
- A is the area of the window
First, let's calculate the area of the window. Since the window is circular, we can use the formula for the area of a circle:
A = πr^2
Given that the radius of the window is 5 feet, we can substitute it into the formula and calculate the area:
A = π(5)^2
A = 25π square feet
Now, let's calculate the depth of the window below the surface of the water. Given that the center of the window is 40 feet below the surface, the depth would be equal to the radius of the window, which is 5 feet.
Next, we need the density of water. The density of water is approximately 62.4 lb/ft^3.
Finally, we can substitute all the values into the formula and calculate the hydrostatic force:
F = (62.4 lb/ft^3)(32.2 ft/s^2)(5 ft)(25π square feet)
F ≈ 25,050 lb
Therefore, the hydrostatic force on the window is approximately 25,050 pounds.