FT-03 · Hydrostatics

Force on a submerged surface

Sizes the resultant hydrostatic force and its line of action on gates, walls or flat windows at any inclination.

Geometry and immersion condition

Surface shapeHeight / diameter · Bottom width b · Depth of top edge h₀ · Angle from horizontal · °Liquid density · Gravedad ·

Resultant force

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Centre of pressure ycp

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Average pressure

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Wetted area

—

Moment about the edge

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Distribution

Trapezoidal

Pressure distribution with depth

Resultant force and line of action

\[F_R=\rho gA\bar y\]

\[y_{cp}=\bar y+\frac{I_G\sin^2\theta}{A\bar y}\]

I_G is the second moment of area about the centroidal axis parallel to the free surface. The angle θ is measured from the horizontal.

Hydrostatic force calculator for gates and tanks

In a static liquid, pressure increases linearly with depth. The total force equals the pressure at the centroid times the wetted area, but it acts below the centroid because of that gradient.

Second moments of area used

Superficie	Area A	I_G
Rectangle b × L	bL	bL³/12
Circle of diameter D	πD²/4	πD⁴/64

Interpreting the centre of pressure

The centre of pressure y_cp is the vertical depth at which the resultant can be concentrated without changing the hydrostatic moment. For a horizontal plate it coincides with the centroid; for an inclined or vertical surface it lies deeper.

Preguntas frecuentes

Is atmospheric pressure included?

Acting on both sides it normally cancels, so gauge pressure is used.

What if the tank is pressurised?

The uniform force P₀A must be added and the position of the combined resultant recalculated.

Does the formula work for curved surfaces?

Not directly. On curved surfaces the horizontal and vertical components are computed separately.