9.12 : Fluid Pressure over Curved Plate of Constant Width

When a curved plate of constant width is submerged in a liquid, the pressure acting normal to the plate varies continuously both in magnitude and direction. Calculating the magnitude and location of the resultant force at a point is often challenging for such cases. One of the methods to determine the resultant force and its location involves separately calculating the horizontal and vertical components of the resultant force. This complex calculation can be simplified by representing the distributed loading acting on the plate by the equivalent loading in two dimensions.

The first step in this method is accounting for the weight of the liquid contained within the block. The magnitude of force due to the weight of the water is given by the product of specific weight, plate thickness and the block area. This force acts through the centroid of the block. In addition, there are pressure distributions caused by the water along the vertical and horizontal sides of the block. The pressure distribution along the vertical side is trapezoidal, while the distribution along the horizontal side is rectangular.

The force acting along the vertical side of the block has a magnitude equal to the area of the trapezoid and acts through its centroid. Meanwhile, the force acting along the horizontal side of the block is constant, with the force's magnitude being equal to the area of the rectangle, which can act through the centroid or midpoint of the rectangle's horizontal side.

Once calculations for all three forces on the block are summed, it gives the net resultant force acting on the curved plate. Also, the location of the center of pressure of the liquid acting on the curved plate is determined by applying the principle of moments. While this method may seem complex, it is necessary to ensure that the force acting on the plate is calculated accurately for various engineering applications.