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.