Calculation
hM = hS + H²/(12hS), hS = h₀ + H/2
Hydrostatic force acts below the gate's geometric centre because pressure increases downward. Width and density cancel out of the position calculation.
Druckmittelpunkt der senkrechten Rechteckfläche · hM = hS + H²/(12hS)
Calculate the Centre of Pressure of a Vertical Gate
Hydrostatic force acts below the gate's geometric centre because pressure increases downward. Width and density cancel out of the position calculation.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Depth of centre of pressure hM — Vertical distance from the free water surface to the resultant force's point of action. Use its distance to the hinge axis for moment calculation; it lies below the face centre.
- Gate height H — Vertical height of the fully wetted rectangular face from a drawing or measurement; for example 0.5 to 3 m.
- Depth of top edge h₀ — Vertical distance of the gate top below the free surface; zero when it touches the surface.
Example
For H = 1 m and h₀ = 0 the face centre is 0.5 m below the surface. The centre of pressure is 0.5 + 1²/(12·0.5) = 0.667 m, or two thirds down the gate.
Assumptions and limits
Stationary constant-density liquid, fully wetted vertical rectangle, and hydrostatic gauge pressure relative to the surface only. Extra surface pressure or counterpressure shifts the point of action.
Understand Centre of pressure of a vertical rectangular gate
A hinge needs to know not only how hard water pushes, but where the combined force acts. That location is the centre of pressure.
What does this quantity describe?
Hydrostatic gauge pressure rises with depth: p = ρgh. The lower half of a gate therefore carries more load than the upper half. Let h₀ be its top-edge depth, H its vertical height and hS = h₀ + H/2 its geometric centre depth. The moment of the distributed pressure gives hM = hS + H²/(12hS). Here hM is the centre-of-pressure depth below the free surface. Width, density and gravity cancel from this position-only calculation.
Formula and variables
hM = hS + H²/(12hS), hS = h₀ + H/2
Area centre: hS = h₀ + H/2Centre of pressure: hM = hS + H²/(12hS)Top at water surface: hM = 2H/3
| Symbol / input | Meaning |
|---|---|
| Depth of centre of pressure hM | Vertical distance from the free water surface to the resultant force's point of action. Use its distance to the hinge axis for moment calculation; it lies below the face centre. |
| Gate height H | Vertical height of the fully wetted rectangular face from a drawing or measurement; for example 0.5 to 3 m. |
| Depth of top edge h₀ | Vertical distance of the gate top below the free surface; zero when it touches the surface. |
Choose the inputs correctly
H is the fully wetted vertical height of the rectangular gate; 0.5 to 3 m gives useful gate examples. h₀ is the vertical depth of its top edge below the free surface and cannot be negative. Obtain both lengths from a section drawing or measurement.
How to use the calculator
Enter H and h₀. The result hM is measured downward from the free water surface. For a hinge moment, multiply the total hydrostatic force by the distance between hM and the hinge axis; check reverse-side pressure separately.
Worked example
A 1 m tall gate begins at the surface. Its area centre is at 0.5 m. Thus hM = 0.5 + 1²/(12·0.5) = 0.667 m, 0.167 m below the geometric centre.
Understand the result and units
At the surface, the centre of pressure is two thirds of the height below the gate top. A deeper gate's pressure centre approaches, but stays below, its geometric centre. This point is the resultant-force location, not the place of maximum pressure.
All lengths are converted to metres internally. hM, h₀ and H can use offered length units. Depth is always measured vertically from the free surface.
Typical applications
Estimating hinge and anchor actions on tank gates, sluice gates and flat covers.
Assumptions, limits and common mistakes
Still constant-density liquid, vertical flat rectangle and full wetting only. Extra surface pressure, counterpressure, tilted or partly dry faces and flow change the pressure distribution and hM.
Common mistake: Do not place the force at the geometric centre; this underestimates moment about an upper hinge. hM is measured from the water surface, not the gate top. Calculate the force magnitude separately.
Frequently asked questions
What is “Centre of pressure of a vertical rectangular gate” used for?
Estimating hinge and anchor actions on tank gates, sluice gates and flat covers.
Where do the input values come from?
H is the fully wetted vertical height of the rectangular gate; 0.5 to 3 m gives useful gate examples. h₀ is the vertical depth of its top edge below the free surface and cannot be negative. Obtain both lengths from a section drawing or measurement.
What does the result not cover?
Still constant-density liquid, vertical flat rectangle and full wetting only. Extra surface pressure, counterpressure, tilted or partly dry faces and flow change the pressure distribution and hM.