327lec-statics2 - 530.327 - Introduction to Fluid Mechanics...

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Unformatted text preview: 530.327 - Introduction to Fluid Mechanics - Su Statics: Forces on a submerged, curved surface. 2 m 4 m y x H O , = 1 k g / m 2 r 3 p = p air, p = p ( ) x ,y F H F V B O C A D Figure 1: Hydrostatic forces on a sub- merged, curved surface. We are interested in the problem depicted in Figure 1, in- volving a submerged, curved surface. What we want to know is, what is the hydrostatic force (magnitude, direction, and point of application) acting on the arc AB ? The arc AB is circular, with radius 2 m. The fluid above the arc section is water; below AB is air at atmospheric pressure, p , which is also the pressure on the free surface. The density of water is 1000 kg/m 3 , and the value of the gravitational acceleration is g = 9 . 8 m/s 2 . We can treat the problem as two-dimensional, i.e. the geometry is constant in the coordinate direction that runs perpendicular to the page. The forces that we are interested in are thus forces per unit length in the out-of-page ( z ) direction. In particular well consider a section of the geometry that spans one meter in the z-direction. We will define the vertical component of the force as F V and the horizontal component as F H , and we will label the point through which the force acts as ( x , y ), where the origin of the x y coordinate system is shown in the figure as the point O ....
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327lec-statics2 - 530.327 - Introduction to Fluid Mechanics...

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