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Hydrostatic Forces on Submerged Plates

Key Concepts: Submerged plates are subjected to hydrostatic pressure forces.

The magnitude of the hydrostatic pressure force equals the pressure at the

centroid of the plate times the area of the plate. The location of the total

hydrostatic pressure force is at the centroid of the pressure prism.

In a Nutshell: Plates submerged in liquids experience pressure forces. Pressure varies

linearly with depth and is isotropic (same in all directions at a point in the liquid). Methods

to calculate the magnitude and location of the pressure force include integration and the

principle of moments.

Consider a plate of arbitrary shaped plate submerged at an angle θ at a depth D below the free surface of a liquid as shown in the figure below. Denote the specific weight of the liquid by γ. Common units for specific weight include lb/ft³ or n/m³.

The elemental pressure force dF acting on the element of area dA is dF = PdA.

Now the pressure, P, varies linearly with depth, x. So P = γ x and the differential pressure force is dF = = γ x dA . So integration gives the total hydrostatic pressure force, F.

F = ∫ γ x dA ˗ ˗ ˗ ˗ ˗ (1)

Note from the principle of first moments A x_cg = ∫ x dA so γA x_cg = γ ∫ x dA . Also γ x_cg

is the pressure at the centroid of the area of the plate. So F = (γ x_cg ) A (total hydrostatic pressure force equals pressure at the centroid of plate times total area of the plate)

Click here to determine the location of the total hydrostatic pressure force acting on the plate.

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