Hydrostatic Force Calculator:
Enter the values of density of the fluid ρ(kg/m3), acceleration due to gravity, g(m/s2), depth below the surface of the fluid, h(m), atmospheric pressure po(Pa) and area of the surface, A(m) to determine the value of hydrostatic force, Hf(N).
Hydrostatic Force Formula:
Hydrostatic force is the force exerted by a fluid at rest due to the force of gravity. It acts on any surface in contact with the fluid.
Hydrostatic force, Hf(N) in Newton is calculated by subtracting the product of density of the fluid ρ(kg/m3) in kilograms per cubic metre, acceleration due to gravity, g(m/s2) in metre per second square and depth below the surface of the fluid, h(m) in meters from the atmospheric pressure po(Pa) in Pascals and multiplied with area of the surface, A(m) in metres.
Hydrostatic force, Hf(N) = (ρ(kg/m3) * g(m/s2) * h(m) – po(Pa) ) * A(m)
Hf(N) = hydrostatic force in Newton, N.
ρ(kg/m3) = density of the fluid in kilogram per cubic metre, kg/m3.
g(m/s2) = acceleration due to gravity (approximately 9.81m/s2 on the surface of the Earth)
h(m) = depth in metres, m.
po(Pa) =atmospheric pressure in Pascals, Pa.
A(m) = area of the surface in metres, m.
Hydrostatic Force Calculation:
1. Calculate the hydrostatic force on a square window 2 metres below the surface of a freshwater lake, where the window measures 1.5 metres on each side.
Given: ρ(kg/m3) = 1000kg/m3 (density of freshwater), g(m/s2) = 9.81m/s2, h(m) = 2m,
po(Pa) = 0 (assuming the atmospheric pressure is compensated by equivalent pressure outside the fluid or neglecting it for simplification), A(m) = 1.5 * 1.5m2
Hydrostatic force, Hf(N) = (ρ(kg/m3) * g(m/s2) * h(m) – po(Pa) ) * A(m)
Hf(N) = (1000 * 9.81 * 2 – 0) * (1.5 * 1.5)
Hf(N) = 44,145N.
2. Suppose you want to calculate the area of a submerged rectangular plate at a certain depth in freshwater, where the hydrostatic force experienced by the plate is known.
Given: ρ(kg/m3) = 1000kg/m3 (density of freshwater), g(m/s2) = 9.81m/s2, h(m) = 4m,
po(Pa) = 0 (assuming it’s negligible or it’s been accounted for in Hf(N)), Hf(N) = 1500N.
Hydrostatic force, Hf(N) = (ρ(kg/m3) * g(m/s2) * h(m) – po(Pa) ) * A(m)
A(m) = Hf(N) / ρ(kg/m3) * g(m/s2) * h(m) – po(Pa)
A(m) = 1500 / (1000 * 9.81 * 4 – 0)
A(m) = 0.0382m2.