Calculate hydrostatic force from fluid density, area and depth, or hydrostatic pressure at depth with optional surface pressure inputs.
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Hydrostatic Force Formula
The following formula is used to calculate a hydrostatic force (using gauge pressure) on a flat surface at a uniform depth.
- Where Hf is the hydrostatic force (N, newtons)
- ρ is the density of the fluid (kg/m³)
- g is the acceleration due to gravity (≈9.81 m/s²)
- h is the depth below the fluid surface (m)
- A is the area of the surface the pressure acts on (m²)
To calculate the hydrostatic force, multiply the fluid density, acceleration due to gravity, and depth to get the hydrostatic (gauge) pressure, then multiply by the area. If you need absolute pressure/force, use p = psurface + ρgh and Hf = pA.
What is Hydrostatic Force?
Definition:
Hydrostatic force is the resultant force a fluid at rest exerts on a submerged surface due to hydrostatic pressure, which increases with depth. It is not generally the same as buoyant force; buoyant force is the net upward force on a fully or partially submerged body and equals the weight of the displaced fluid (Archimedes’ principle).
How to calculate hydrostatic force?
Example:
The following example outlines the steps needed to calculate a hydrostatic force.
First, determine the density of the fluid. We are assuming freshwater for this example so the density is approximately 1000 kg/m³.
Next, determine the depth of the object. In this case, the object is at a depth of 100 meters.
Next, determine the surface area of the object. In this problem, the surface area is calculated to be 10 m².
Finally, calculate the hydrostatic force using the formula above (gauge):
Hf = ρ * g * h * A
Hf = 1000 * 9.81 * 100 * 10
Hf = 9,810,000 N
