Hydrostatic Force Calculator
The force on a submerged plane is the pressure at its centroid times its area: a 2 × 3 m vertical gate with its top 1 m deep carries 147.15 kN, acting 2.8 m below the surface.
90° for a vertical wall.
147.15 kN
Full answer, then cut to fewer decimals (not rounded):
- 147.15 kN
- 147.1 kN
- Area A
- 6 m²
- Depth of centroid h̄
- 2.5 m
- Depth of centre of pressure h*
- 2.8 m
- Pressure at centroid ρgh̄
- 24.525 kPa
- Pressure at the bottom edge
- 39.24 kPa
Step-by-step solution
- F = ρ g A h̄ = 1000 × 9.81 × 6 × 2.5 = 147150 N
- h* = h̄ + IG sin²θ / (A h̄) = 2.5 + 4.5 × 1 ÷ (6 × 2.5) = 2.8 m
Hydrostatic Force Formula
F = ρ g A h̄, h* = h̄ + IG sin²θ / (A h̄)
h̄ depth of the centroid, IG second moment about the centroid, θ angle to the free surface
Worked Example
A vertical 2 m wide, 3 m high gate with its top edge 1 m below water:
- F = ρ g A h̄ = 1000 × 9.81 × 6 × 2.5 = 147150 N
- h* = h̄ + IG sin²θ / (A h̄) = 2.5 + 4.5 × 1 ÷ (6 × 2.5) = 2.8 m
Depth of centroid h̄: 2.5 m · Depth of centre of pressure h*: 2.8 m · Pressure at centroid ρgh̄: 24.525 kPa · Pressure at the bottom edge: 39.24 kPa
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Frequently asked questions
Why is the centre of pressure below the centroid?
Pressure increases with depth, so the resultant acts lower; the offset IG sin²θ/(A h̄) shrinks as the surface goes deeper.
What is the pressure at a depth h?
p = ρgh above atmospheric: about 9.81 kPa per metre of water.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Hydrostatic Force Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/hydrostatic-force-calculator/
IEEE
Scientific Converters, "Hydrostatic Force Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/hydrostatic-force-calculator/