Hydrostatic Gate Force Calculator
Calculate gauge-pressure resultant force and center of pressure on a vertical rectangular surface submerged in a constant-density liquid.
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Result
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Calculation steps
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How to calculate
Integrate the linear gauge-pressure distribution p=ρgy over the vertical rectangle. The resultant equals pressure at the area centroid times area; the center of pressure follows from the centroidal second moment.
F=ρgA ȳ; y_cp=ȳ+I_G/(A ȳ); I_G=b h³/12
Worked example
A 1.5 m wide, 2 m high vertical rectangle whose top meets the free surface in water at standard gravity has resultant force 29,419.95 N, acting 1.333333 m below the surface.
Assumptions and input details
Constant-density static liquid, vertical plane rectangle and gauge pressure relative to the free surface. The same external pressure is assumed on the reference side. Height and width must be positive; top depth is nonnegative. Waves, acceleration, stratification, sloped/curved surfaces, leakage, structural reactions, gate weight, seals, friction, dynamic loads and safety design are excluded.
References: USACE HEC-RAS: hydrostatic pressure forces
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
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Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
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