Hydrostatic Force Calculation on a Submerged Window
What is the hydrostatic force acting on a submerged window?
If the semi-circle has a diameter of 50 centimeters and the bottom of the window is at a depth of 1.25 meters, find the hydrostatic force on the window.
Answer:
The hydrostatic force on the window is 9621.127 N.
The hydrostatic pressure on a submerged object is given by the equation:
P = ρgh
where:
P is the pressure,
ρ is the density of the fluid,
g is the acceleration due to gravity, and
h is the depth of the object below the surface of the fluid.
Given:
- The diameter of the window, d = 2r = 50 cm = 0.5 m
- Depth of the window, h = 1.25 m
- The density of water, ρ = 1000 kg/m³
Hydrostatic pressure, P = ρgh = 1000 x 9.8 x 1.25 = 12250 N/m²
So, the hydrostatic force on the window is calculated using the formula:
Force = Pressure x Area = P x πr²/2 = 12250 x π x 0.5²
Force = 9621.127 N
Therefore, the hydrostatic force on the window is 9621.127 N.