![]() They will be given in the problems in this book. The centroids and second moments of various areas are presented in books on statics or strength of materials. For a horizontal surface, the pressure is uniform over the area so that the pressure force acts at the centroid of the area. ![]() This allows us to locate where the force acts. (2.18) and using the expression for F from Eq. Where I is the moment of the area about its centroidal axis. To determine where this point is, we must recognize that the sum of the moments of all the infinitesimal forces must equal the moment of the resultant force, that is, Let’s assume that the force acts at some point called the center of pressure ( c.p.), located by the point ( x, y ). But, the force does not, in general, act at the centroid. It does not depend on the angle a of inclination. Since γ h is the pressure at the centroid we see that the magnitude of the force is the area times the pressure that acts at the centroid of the area. Where h is the vertical distance to the centroid. Equation (2.16) can also be expressed asį i g u re 2.4 The force on an inclined plane area. Where y is the distance3 to the centroid of the plane area the centroid is identified as the point C. The force on the plane surface is due to the pressure p = γ h acting over the area, that is, The liquid acts on the plane area shown as a section of the wall a view from the top gives additional detail of the geometry. Examples will illustrate.Ĭonsider the general surface shown in Fig. We will develop equations for forces on plane surfaces, but forces on curved surfaces can be determined using the same equations. ![]() The liquid is most often water but it could be oil or some other liquid. When a liquid is contained by a surface, such as a dam, the side of a ship, a water tank, or a levee, it is necessary to calculate the force and its location due to the liquid.
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