What Is the Hydrostatic Force & Center of Pressure Calculator?
The center of pressure is the specific point on a submerged surface where the resultant hydrostatic force acts.
It is determined by integrating the first and second moments of pressure across the wetted area.
How Does the Hydrostatic Force & Center of Pressure Calculator Work?
Total force equals pressure at the centroid multiplied by total area: F = ρ·g·hc·A.
The center of pressure is displaced below the centroid by eccentricity Δy = Ixx / (A·yc).
Hydrostatic Force & Center of Pressure Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
F = \rho g h_c A, \quad y_{cp} = y_c + \frac{I_{xx}}{A y_c}, \quad h_{cp} = y_{cp} \sin\theta
Hydrostatic resultant thrust and parallel axis center of pressure formula.
How to Use the Hydrostatic Force & Center of Pressure Calculator
- Input gate dimensions, vertical centroid depth, inclination angle, and fluid density.
- Review total hydrostatic force, center of pressure depth, and eccentricity.
Step-by-Step Example Calculation
Vertical Sluice Gate
Input Values:
widthOrDiameterMeters:2
heightMeters:3
centroidDepthMeters:3.5
inclinationAngleDeg:90
fluidDensityKgPerM3:1000
Worked Steps: Calculates total force ~206 kN acting 0.21m below the gate centroid.
Understanding Your Result
Locating the center of pressure is critical for sizing pivot hinges, hoist cables, and structural stiffeners on dam gates.
Factors That Affect the Result
- As depth increases, the relative eccentricity diminishes and the center of pressure approaches the centroid asymptotically.
When Should You Use This Calculator?
- Sluice gate design, retaining dam walls, submarine hatch sizing, and lock chamber engineering.
Assumptions & Limitations
- Assumes an incompressible fluid at rest under uniform atmospheric pressure.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Exact analytical solution of fluid statics.