Formula used
Resultant force: F = ∫ p(h) dA
Single uniform fluid: F = ρgAhc
Center of pressure: hp = (∫ h·p(h)dA) / F
Hinge moment: Mh = F(sp − sh)
Holding force: Fhold = |Mh| / |r sin α|
The calculator numerically integrates pressure over narrow gate strips. This method supports partial submergence, irregular widths, inclined gates, and multiple fluid layers without relying only on closed-form shape equations.
How to use this calculator
- Select the gate shape and its orientation.
- Enter gate dimensions using one consistent input length unit.
- Enter the vertical depth from the liquid surface to the gate top.
- Choose a fluid preset or enter a custom fluid property.
- Add fluid layers when density changes with depth.
- Select the hinge and holding-force locations.
- Enable weight or buoyancy when those moments matter.
- Choose output units and calculate the final results.
Worked example
A vertical rectangular gate is 2 m wide and 3 m high. Its top edge is 1 m below fresh water. The area equals 6 m², while the centroid lies 2.5 m below the surface.
Using F = ρgAhc, the hydrostatic force is about 146.9 kN for water near 998 kg/m³. The center of pressure lies below the centroid because pressure increases with depth.
A top hinge creates a substantial opening moment. A holding force applied near the bottom reduces the required actuator load through its longer lever arm.
| Input | Example value | Meaning |
|---|---|---|
| Shape | Rectangle | Constant gate width |
| Width | 2 m | Horizontal dimension |
| Height | 3 m | Dimension along gate |
| Top depth | 1 m | Vertical distance below surface |
| Density | 998.2 kg/m³ | Fresh water near room temperature |
| Hinge | Top edge | Moment reference |
Understanding hydrostatic gate loading
Hydrostatic pressure increases linearly with vertical depth in a uniform, stationary liquid. A gate therefore receives little pressure near the surface and greater pressure near its lower edge. The total force equals the integrated pressure over the wetted area.
The center of pressure is the point where the resultant force acts. It normally lies below the area centroid for a vertical or inclined submerged surface. This difference becomes important when sizing hinges, actuators, supports, and locking equipment.
Inclined gates require careful distinction between vertical depth and distance measured along the gate. Pressure depends on vertical depth, while hinge moments use distances along the gate plane. The calculator handles both coordinates during numerical integration.
Partial submergence changes the wetted geometry and may shift the center of pressure sharply. A gate extending above the liquid surface receives no liquid pressure on its dry portion. Only strips between the free surface and entered liquid depth contribute.
Layered fluids produce piecewise pressure gradients because each layer has a different density. Pressure at a deeper point includes the weight of every fluid layer above it. The calculator sums these contributions before integrating force over the gate.
Gate weight can either assist or oppose hydrostatic opening, depending on orientation and hinge placement. Buoyancy acts upward through the displaced-volume centroid. Their moments should be included when gate thickness and mass materially affect operation.
Holding force depends strongly on its lever arm and direction. A force applied farther from the hinge generally requires less magnitude. A force nearly aligned with the gate produces little moment and can become impractically large.
Calculated reactions are useful for preliminary hinge and support sizing. Final structural design must also consider impact, vibration, corrosion, fatigue, seals, friction, and load combinations. Applicable engineering standards should govern the final design.
Frequently asked questions
What is hydrostatic force on a gate?
It is the resultant force created by fluid pressure acting over the submerged gate area.
Why is the center of pressure below the centroid?
Pressure grows with depth, so lower portions contribute more force than upper portions.
Can the calculator handle a partially submerged gate?
Yes. It integrates only the gate strips located below the liquid surface and above the entered bottom depth.
Does inclination change hydrostatic pressure?
Pressure still depends on vertical depth, but inclination changes the submerged geometry and moment arms.
How are multiple fluid layers handled?
The pressure at each depth includes the hydrostatic contribution from every layer above that point.
What does surface gauge pressure do?
It adds a uniform pressure component to every submerged point on the gate.
How is required holding force calculated?
The hinge moment is divided by the effective perpendicular lever arm of the holding force.
Should gate weight and buoyancy always be included?
Include them when gate mass, thickness, orientation, or displaced volume significantly changes the hinge moment.
Can these results replace structural engineering design?
No. They support preliminary analysis and must be checked against structural, mechanical, and safety requirements.
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