![]() ![]() 2.17) is dF = gh dA and is perpendicular to the surface. At any given depth, h, the force acting on dA (the differential area of Fig. We wish to determine the direction, location, and magnitude of the resultant force acting on one side of this area due to the liquid in contact with the area. ![]() The area can have an arbitrary shape as shown. The x-y coordinate system is defined so that 0 is the origin and y is directed along the surface as shown. The resultant force of a static fluid on a plane surface is due to the hydrostatic pressure distribution on the surface. ■ FIGURE 2.16 Pressure and resultant hydrostatic force developed on the bottom of an open tank. Let the plane in which the surface lies intersect the free surface at 0 and make an angle U with For the present we will assume that the fluid surface is open to the atmosphere. 2.17, the determination of the resultant force acting on the surface is more involved. ![]() 2.16.įor the more general case in which a submerged plane surface is inclined, as is illustrated in Fig. Since the pressure is constant and uniformly distributed over the bottom, the resultant force acts through the centroid of the area as shown in Fig. Note that if atmospheric pressure acts on both sides of the bottom, as is illustrated, the resultant force on the bottom is simply due to the liquid in the tank. ![]() 2.16), the magnitude of the resultant force is simply Fr = pA, where p is the uniform pressure on the bottom and A is the area of the bottom. For a horizontal surface, such as the bottom of a liquid-filled tank (Fig. We also know that the pressure will vary linearly with depth if the fluid is incompressible. For fluids at rest we know that the force must be perpendicular to the surface since there are no shearing stresses present. The determination of these forces is important in the design of storage tanks, ships, dams, and other hydraulic structures. When a surface is submerged in a fluid, forces develop on the surface due to the fluid. When determining the resultant force on an area, the effect of atmospheric pressure often cancels. ![]()
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