Understanding Fluid Pressure & Hydrostatic Force
Learn about hydrostatic pressure, Pascal's principle, and force calculations on submerged surfaces
Hydrostatic Pressure (p = ρgh)
In a static fluid, pressure increases linearly with depth. The gauge pressure at depth h equals the fluid density (ρ) times gravitational acceleration (g) times depth (h).
p_gauge = ρ × g × h
p_absolute = p_atm + p_gauge
- • Fresh water: 1000 kg/m³
- • Sea water: 1025 kg/m³
- • Every 10 m of water ≈ 1 atm
Pascal's Principle
Pressure applied to a confined fluid is transmitted equally in all directions. This principle explains why pressure depends only on depth, not container shape.
At any point in a fluid at rest, pressure acts equally in all directions and depends only on vertical depth.
This is why a narrow tube and wide tank have the same pressure at equal depths—the "hydrostatic paradox" that isn't really a paradox once you understand how pressure transmission works.
Force on Submerged Surfaces
The total hydrostatic force on a plane surface equals the pressure at the centroid times the area. For horizontal surfaces, pressure is uniform. For vertical surfaces, pressure varies linearly.
Horizontal: F = p × A = ρgh × A
Vertical: F = ρg × h_c × A
Where h_c is the depth to the centroid (geometric center) of the surface.
Center of Pressure
The center of pressure is where the resultant force acts on a surface. For vertical surfaces, it's always below the centroid because pressure increases with depth.
h_cp = h_c + I_G / (h_c × A)
For rectangle: I_G = b × H³ / 12
Knowing the center of pressure is critical for designing gates, dams, and calculating moments for structural analysis.
Pressure Unit Reference
| Unit | Symbol | Equivalent to 1 atm |
|---|---|---|
| Pascal | Pa | 101,325 Pa |
| Kilopascal | kPa | 101.325 kPa |
| Bar | bar | 1.01325 bar |
| Pounds per square inch | psi | 14.696 psi |
| Meters of water | m H₂O | ≈ 10.33 m |
Frequently Asked Questions
Common questions about fluid pressure, hydrostatic force, and center of pressure calculations
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