Calculation
F = ρ · g · b · H · (h₀ + H/2)
Pressure increases with depth. The total force equals pressure at the gate centre times gate area when the entire gate is below the free surface.
Hydrostatische Flächenlast · F = ρgbH(h₀+H/2)
Calculate Hydrostatic Force on a Vertical Gate
Pressure increases with depth. The total force equals pressure at the gate centre times gate area when the entire gate is below the free surface.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Hydrostatic force F — Total horizontal force on one face of the gate; hinge or anchor design also needs its point of action and safety checks.
- Liquid density ρ — Mass per volume of the liquid at operating conditions. Water is roughly 1000 kg/m³ at ordinary temperatures; use a datasheet for other liquids.
- Gravitational acceleration g — Local gravitational acceleration, about 9.81 m/s² on Earth.
- Gate width b — Horizontal width of the rectangular face wetted on one side; obtain it from a drawing or measurement.
- Gate height H — Vertical height of the fully wetted gate, not its thickness; measure from the drawing.
- Depth of top edge h₀ — Vertical distance from the free water surface to the gate top. Zero means the top edge is at the surface.
Example
A 2 m wide, 1 m high gate starts at the water surface. With ρ = 1000 kg/m³ and g = 9.80665 m/s², F = 1000·9.80665·2·1·0.5 = 9810 N = 9.81 kN.
Assumptions and limits
Stationary liquid of constant density, vertical flat rectangular face and complete wetting. The force is gauge pressure relative to the free surface; extra surface pressure or pressure on the reverse face is excluded.
Understand Hydrostatic force on a vertical rectangular gate
A gate at the edge of a tank is pushed harder at the bottom than at the top. This calculator combines that distributed pressure into one horizontal force.
What does this quantity describe?
In a still liquid, gauge pressure rises with depth h: p = ρgh. Here ρ is liquid density and g gravitational acceleration. For a vertical gate of width b and height H whose top is at depth h₀, the average depth is h₀ + H/2. Pressure there times area bH gives F = ρgbH(h₀+H/2), the resultant force on one gate face.
Formula and variables
F = ρ · g · b · H · (h₀ + H/2)
Pressure at depth h: p = ρghArea: A = bHCentroid depth: hS = h₀+H/2Resultant force: F = ρgAhS
| Symbol / input | Meaning |
|---|---|
| Hydrostatic force F | Total horizontal force on one face of the gate; hinge or anchor design also needs its point of action and safety checks. |
| Liquid density ρ | Mass per volume of the liquid at operating conditions. Water is roughly 1000 kg/m³ at ordinary temperatures; use a datasheet for other liquids. |
| Gravitational acceleration g | Local gravitational acceleration, about 9.81 m/s² on Earth. |
| Gate width b | Horizontal width of the rectangular face wetted on one side; obtain it from a drawing or measurement. |
| Gate height H | Vertical height of the fully wetted gate, not its thickness; measure from the drawing. |
| Depth of top edge h₀ | Vertical distance from the free water surface to the gate top. Zero means the top edge is at the surface. |
Choose the inputs correctly
Take ρ from fluid property data; 1000 kg/m³ is a rough value for water. On Earth g is about 9.81 m/s². b and H are width and vertical height of the wetted rectangle. h₀ is the vertical depth of its top below the free surface and cannot be negative. Obtain dimensions from a drawing or measurement.
How to use the calculator
Enter density, width, height and top-edge depth. Set h₀ = 0 if the top just touches the surface. The result is force from hydrostatic gauge pressure on one face; gate hinges also need the centre of pressure and any counterpressure.
Worked example
A 2 m wide, 1 m tall gate starts at the surface. Its area is 2 m² and its centre depth is 0.5 m. For water with ρ = 1000 kg/m³ and g = 9.80665 m/s², F = 1000·9.80665·2·0.5 = 9810 N or 9.81 kN.
Understand the result and units
Doubling width doubles F. Lowering the entire gate increases force linearly with its centre depth. Force alone does not locate its action: the centre of pressure is below the gate centre.
The calculation uses kg/m³, m/s², metres and newtons internally. One kN is one thousand newtons. Offered length and force units use the shared conversion register.
Typical applications
Early load estimates for sluice gates, tank panels, lock gates and inspection covers with a vertical rectangular wetted face.
Assumptions, limits and common mistakes
Still liquid of constant density and a fully wetted vertical rectangle only. Additional surface pressure, a second fluid, counterpressure, flow, waves and gate deformation are excluded. Component design also requires reactions and strength checks.
Common mistake: h₀ is the top-edge depth, not the depth below the bottom of the gate. Applying the bottom-edge pressure over the whole area overestimates the force. Inclined or partly dry faces need another geometry.
Frequently asked questions
What is “Hydrostatic force on a vertical rectangular gate” used for?
Early load estimates for sluice gates, tank panels, lock gates and inspection covers with a vertical rectangular wetted face.
Where do the input values come from?
Take ρ from fluid property data; 1000 kg/m³ is a rough value for water. On Earth g is about 9.81 m/s². b and H are width and vertical height of the wetted rectangle. h₀ is the vertical depth of its top below the free surface and cannot be negative. Obtain dimensions from a drawing or measurement.
What does the result not cover?
Still liquid of constant density and a fully wetted vertical rectangle only. Additional surface pressure, a second fluid, counterpressure, flow, waves and gate deformation are excluded. Component design also requires reactions and strength checks.