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In this chapter we will consider an important class of problems in which the fluid is either at rest or moving in such a manner that there is no relative motion between adjacent particles. In both instances there will be no shearing stresses in the fluid, and the only forces that develop on the surfaces of the particles will be due to the pressure. Thus, our principal concern is to investigate pressure and its variation throughout a fluid and the effect of pressure on submerged surfaces. The absence of shearing stresses greatly simplifies the analysis and, as we will see,. | An image of hurricane Allen viewed via satellite Although there is considerable motion and structure to a hurricane the pressure variation in the vertical direction is approximated by the pressure-depth relationship for a static fluid. Visible and infrared image pair from a NOAA satellite using a technique developed at NASA GSPC. Photograph courtesy of A. F. Hasler Ref. 7 . 2 Fluid Statics In this chapter we will consider an important class of problems in which the fluid is either at rest or moving in such a manner that there is no relative motion between adjacent particles. In both instances there will be no shearing stresses in the fluid and the only forces that develop on the surfaces of the particles will be due to the pressure. Thus our principal concern is to investigate pressure and its variation throughout a fluid and the effect of pressure on submerged surfaces. The absence of shearing stresses greatly simplifies the analysis and as we will see allows us to obtain relatively simple solutions to many important practical problems. 2.1 Pressure at a Point There are no shearing stresses present in a fluid at rest. As we briefly discussed in Chapter 1 the term pressure is used to indicate the normal force per unit area at a given point acting on a given plane within the fluid mass of interest. A question that immediately arises is how the pressure at a point varies with the orientation of the plane passing through the point. To answer this question consider the free-body diagram illustrated in Fig. 2.1 that was obtained by removing a small triangular wedge of fluid from some arbitrary location within a fluid mass. Since we are considering the situation in which there are no shearing stresses the only external forces acting on the wedge are due to the pressure and the weight. For simplicity the forces in the x direction are not shown and the z axis is taken as the vertical axis so the weight acts in the negative z direction. Although we are primarily interested