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Calculation of Pressure Forces on Submerged Plates (continued)

Case 5: Calculation of Pressure Forces on a submerged Quarter cylinder

The strategy is to replace the pressure distribution on the curved surfaces with a collection of

pressure distributions on flat surfaces. Then apply the same strategy as previously discussed.

I.E., the magnitude of the total pressure force is the “average” pressure on the plate times

the area of the plate for each flat surface. The location of the pressure force is at the “centroid”

of the pressure prism for each flat surface.

A quarter of a cylinder of radius 2h and width w (into the paper) is submerged at a depth, d,

below the surface of the liquid. The weight of the quarter cylinder is W_cyl. The weight of

the liquid between the quarter cylinder and the flat surfaces encompassing it needs to be

calculated. Call it W_liq.

Let γ₁ be the specific weight of the cylinder and γ be the specific weight of the liquid.

The magnitudes of the forces are: F₁ = γ d (2wh), F₂ = γ h (2wh), F₃ = γ ( d + 2h)(2wh)

The weights are: W_cyl = γ₁ (π (2h)² / 4) (2hw) and W_liq = γ (2h)²w - γ [ π(2h)² / 4 ] w

Note: F₁, F₂, and F₃ act at the centroids of their pressure prisms respectively.

Also note that the locations of W_cyl and of W_liq are at their centroids.