Calculus. Mary designed a new viewing window consisting of a rectangle and a semi circle for a fresh water aquarium. The window is as follows and the top is located 10 feet below the water's surface. How much force is on the window?
To determine the force on the window, we need to calculate the hydrostatic pressure exerted by the water. The hydrostatic pressure is given by the formula:
P = ρgh
where P is the pressure, ρ is the density of the fluid (water), g is the acceleration due to gravity, and h is the height or depth of the fluid.
In this case, the top of the window is located 10 feet below the water's surface, so the height or depth of the fluid is 10 feet.
First, let's find the density of water. The density of water is approximately 62.4 pounds per cubic foot (lb/ft³).
Next, we need to determine the value of the acceleration due to gravity, g. The standard value for g is approximately 32.2 feet per second squared (ft/s²).
Now we can plug these values into the formula to calculate the hydrostatic pressure:
P = (62.4 lb/ft³) * (32.2 ft/s²) * (10 ft)
P ≈ 20,027 lb/ft²
So, the force exerted on the window is approximately 20,027 pounds per square foot (lb/ft²).