__Hydrostatic Force Calculator:__

__Hydrostatic Force Calculator:__

Enter the values of density of the fluid ρ(kg/m^{3}), acceleration due to gravity, g(m/s^{2}), depth below the surface of the fluid, h_{(m)}, atmospheric pressure p_{o(Pa)} and area of the surface, A_{(m)} to determine the value of hydrostatic force, H_{f(N)}.

__Hydrostatic Force Formula:__

__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, H_{f(N) }in Newton is calculated by subtracting the product of density of the fluid ρ(kg/m^{3}) in kilograms per cubic metre, acceleration due to gravity, g(m/s^{2}) in metre per second square and depth below the surface of the fluid, h_{(m)} in meters from the atmospheric pressure p_{o(Pa)} in Pascals and multiplied with area of the surface, A_{(m)} in metres.

Hydrostatic force, H_{f(N)} = (ρ_{(kg/m3)} * g_{(m/s2)} * h_{(m)} – p_{o(Pa)} ) * A_{(m)}

H_{f(N)} = hydrostatic force in Newton, N.

ρ_{(kg/m3)} = density of the fluid in kilogram per cubic metre, kg/m^{3}.

g_{(m/s2)} = acceleration due to gravity (approximately 9.81m/s^{2} on the surface of the Earth)

h_{(m)} = depth in metres, m.

p_{o(Pa)} =atmospheric pressure in Pascals, Pa.

A_{(m)} = area of the surface in metres, m.

__Hydrostatic Force Calculation:__

__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/m^{3} (density of freshwater), g_{(m/s2)} = 9.81m/s^{2}, h_{(m)} = 2m,

p_{o(Pa)} = 0 (assuming the atmospheric pressure is compensated by equivalent pressure outside the fluid or neglecting it for simplification), A_{(m)} = 1.5 * 1.5m^{2}

Hydrostatic force, H_{f(N)} = (ρ_{(kg/m3)} * g_{(m/s2)} * h_{(m)} – p_{o(Pa)} ) * A_{(m)}

H_{f(N)} = (1000 * 9.81 * 2 – 0) * (1.5 * 1.5)

H_{f(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/m^{3} (density of freshwater), g_{(m/s2)} = 9.81m/s^{2}, h_{(m)} = 4m,

p_{o(Pa)} = 0 (assuming it’s negligible or it’s been accounted for in H_{f(N)}), H_{f(N)} = 1500N.

Hydrostatic force, H_{f(N)} = (ρ_{(kg/m3)} * g_{(m/s2)} * h_{(m)} – p_{o(Pa)} ) * A_{(m)}

A_{(m)} = H_{f(N) }/ ρ_{(kg/m3)} * g_{(m/s2)} * h_{(m)} – p_{o(Pa)}

A_{(m)} = 1500 / (1000 * 9.81 * 4 – 0)

A_{(m)} = 0.0382m^{2}.