Hydrostatic Force on a Gate Calculator: Force, Centre of Pressure and Hinge Moment

Find the force of still water on a flat gate and where it acts, so you can size a hinge, a latch or a support.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the density of the liquid, the depth of the top of the gate below the surface, the height and width of the gate, and its angle from horizontal (90 degrees for vertical).

The calculator gives the pressure at the top and bottom, then the total force as the pressure at the centre of the gate times its area, and the centre of pressure, which is always below the centre.

It gives the moments about the top and the bottom edges and the support reactions, and the horizontal and vertical parts of the force for a tilted gate.

Formulas used

  • p = \rho g h
  • F = \rho g h_c A
  • y_{cp} = y_c + \frac{I_c}{A y_c}
  • I_c = \frac{bH^3}{12}

Worked example

With the default numbers in the calculator above:

  1. Pressure at the top and the bottom edges of the gate (gauge): 0.00 kPa at the top, 39.24 kPa at the bottom
  2. Depth of the centre of the gate below the surface: 2.00 m
  3. Total force on the gate (pressure at the centre times the area): 156.96 kN
  4. Centre of pressure: distance below the top edge, measured along the gate: 2.67 m below the top edge along the gate (66.67 percent of the way down)
  5. Vertical depth of the centre of pressure below the surface: 2.67 m
  6. Moment about the top edge (a hinge or a latch there): 418.56 kN m
  7. Moment about the bottom edge: 209.28 kN m
  8. Reactions at the two edges if the gate is simply supported there (top and bottom): 52.32 kN at the top and 104.64 kN at the bottom

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

Why is the force not at the centre of the gate?

The pressure rises with depth, so the lower part carries more load. The resultant acts below the centre, at the centre of pressure.

Where is the centre of pressure on a vertical gate with its top at the surface?

Two thirds of the way down.

Does atmospheric pressure matter?

It acts on both sides of the gate and cancels, so only the gauge pressure counts.

What about a tilted gate?

The force is still at right angles to the gate, and the depth of the centre is smaller, because the gate is not as deep for the same length.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: White, Fluid Mechanics (hydrostatic forces on plane surfaces); Munson, Fundamentals of Fluid Mechanics.

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