How to use this calculator
Enter the gate’s width and its length along the slope, its angle from the horizontal (90° for vertical), and how deep its top edge is. Pick where the hinge is to get the moment and the force needed to hold the gate shut.
Formulas
ForceFR = ρg hcA
Center of pressure (along the plate from the surface line)ycp = yc + IxcycA, with Ixc = bL3/12
Worked example
2 m wide, 3 m long gate at 60°, top edge 1.5 m deep, water (the default)
- hc = 1.5 + 1.5 sin 60° = 2.799 m; A = 6 m².
- FR = 1000 × 9.81 × 2.799 × 6 = 164.8 kN.
- yc = 2.799/sin 60° = 3.232 m; ycp = 3.232 + 4.5/(3.232 × 6) = 3.464 m, which is 1.732 m down the gate from its top edge.
Frequently asked questions
Why is the center of pressure below the centroid?
Pressure grows with depth, so the lower part of the gate pushes harder and pulls the resultant down.
What about a curved gate?
Split the force into a horizontal part (the force on the vertical projection) and a vertical part (the weight of fluid above the surface).