How to use this calculator
Choose where the circle’s center is (level with the top or bottom edge of the gate) and whether the liquid is above or below the gate. Enter the radius, the width into the page, the depth of the top edge and the liquid density.
Formulas
HorizontalFH = ρghcAproj, Aproj = Rw
Line of actionyp = hc + Ic/(hcA)
VerticalFV = ρgVabove
ResultantFR = √(FH² + FV²), through the circle’s center
Worked example
Quarter-circle gate, R = 2 m, 3 m wide, top edge 1 m below the surface, water above, center level with the top edge
- hc = 1 + 2/2 = 2 m, FH = 9810 × 2 × (2 × 3) = 117.7 kN.
- Water above: rectangle 1 × 2 plus a quarter circle π(2)²/4 = 3.14 m², times 3 m: V = 15.4 m³.
- FV = 9810 × 15.4 = 151.3 kN downward.
- FR = √(117.7² + 151.3²) = 191.6 kN at 52.1° below horizontal.
Frequently asked questions
What if the liquid is below the gate?
The vertical force equals the weight of the liquid that would fill the space above the gate up to the free surface (an imaginary volume), but it points up.
Why does the resultant pass through the center?
Pressure always acts normal to the surface, and every normal to a circular arc passes through its center, so their sum does too.
Does atmospheric pressure matter?
Not when it acts on both sides of the gate; it cancels. Use gage pressure, as this calculator does.