Calculator Inputs
Assumes a fully submerged rectangular plane gate in static liquid. Angle is measured from the horizontal. A vertical gate uses 90°.
Formula Used
Area of gate:
A = b × L
Centroid depth:
hc = htop + (L × sinθ) / 2
Hydrostatic force:
F = ρ × g × A × hc
Pressure at any depth:
p = ρ × g × h
Centroidal second moment:
IG = b × L3 / 12
Center of pressure depth:
hcp = hc + (IG × sin²θ) / (A × hc)
Distance from top edge to line of action:
s = (hcp − htop) / sinθ
Moment about top edge:
M = F × s
This page is intended for rectangular gates under static liquid loading. It is useful for quick screening, preliminary checks, and comparison studies in construction and civil work.
How to Use This Calculator
- Enter the liquid name for reference.
- Provide fluid density and gravity. For fresh water, use 1000 kg/m³ and 9.81 m/s².
- Enter the vertical depth from free surface to the top edge of the gate.
- Enter gate width and gate height measured along the gate surface.
- Enter gate angle from the horizontal. Use 90° for a vertical gate.
- Set gate count and a safety factor if you want total factored demand.
- Press Calculate to view force, pressure, center of pressure, moment, and graph.
- Use the CSV and PDF buttons to export the results for reporting.
Example Data Table
| Case | Fluid | Density (kg/m³) | Top Depth (m) | Width (m) | Height (m) | Angle (°) | Approx. Force (kN) |
|---|---|---|---|---|---|---|---|
| 1 | Fresh Water | 1000 | 1.20 | 2.50 | 3.00 | 90 | 165.54 |
| 2 | Fresh Water | 1000 | 0.80 | 2.00 | 2.50 | 60 | 82.65 |
| 3 | Seawater | 1025 | 1.50 | 3.00 | 2.20 | 75 | 161.34 |
FAQs
1) What is hydrostatic force on a gate?
Hydrostatic force is the resultant liquid load acting on a submerged gate due to pressure increasing with depth. It depends on density, gravity, wetted area, and centroid depth.
2) Which angle should I enter?
Enter the gate angle measured from the horizontal. A horizontal plate would be near 0°, while a fully vertical gate should be entered as 90°.
3) Does this calculator work for vertical gates?
Yes. For a vertical rectangular gate, simply enter 90° as the angle. The calculator then evaluates the standard vertical-plane hydrostatic loading case.
4) What depth should I use for the top edge?
Use the vertical distance from the liquid free surface down to the top edge of the gate. Do not use along-surface distance for this input.
5) Why is the center of pressure below the centroid?
Pressure rises with depth, so deeper portions carry more load. That shifts the resultant force downward, placing the center of pressure below the centroid.
6) Can I use seawater or other liquids?
Yes. Replace the density value with the correct liquid density. The rest of the equations remain the same for static liquid conditions.
7) What is the factored total force?
It is the calculated hydrostatic force multiplied by gate count and safety factor. It helps estimate a more conservative demand for design review.
8) Can I use this for curved or partially submerged gates?
Not directly. This version is for fully submerged rectangular plane gates. Curved surfaces or partial submergence require different geometry treatment and load resolution.