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Calculation of Pressure Forces on Submerged Rectangular Plates (continued)

Case 4: Calculation of Pressure Forces on a submerged Slanted plate

The magnitude of the pressure force equals the pressure at the centroid of the plate times the area

of the plate. Let γ be the specific weight of the fluid. Then the pressure at the centroid of the plate is

γ (d + h cos α ). Let w be the width of the plate (into the paper). So the total pressure force F_r on the plate is [ γ ( d + h cos α ) ] (2hw). Again, the location of the pressure force, F_r is at the “centroid” of the pressure prism at a depth of d + [ sbar ] cos α .

As before, an alternate approach is to break the trapezoidal pressure distribution into two parts. The

first part is a uniform pressure distribution of γd and a triangular distribution starting from zero and increasing to γ (2h) cos α. See the figure below.

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