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Calculation of Pressure Forces on Submerged Rectangular Plates (continued)

Case 3: Calculation of Pressure Forces on a Vertical submerged 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. In this case the pressure at the centroid of the plate is

γ ( d + h ) . 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 ) ] (2hw).

The location of the pressure force is at the “centroid” of the pressure prism, which in this case is a trapezoid.

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). See the

figure below.

F₁ = γ d ( 2hw ) and F₂ = γ h ( 2hw ) The location of each individual pressure force acts at the “centroid” of

its pressure prism. So F₁ acts at the centroid of the rectangle. F₂ acts at the centroid of the triangle.

Notice, the strategy in each case to calculate the resultant pressure force on a plate submerged in a fluid is the same. The same strategy applies to a “slanted” plate submerged in a fluid.

Click here to continue with other cases.

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