Pressure forces on Surfaces

Static, simple fluids can exert only pressure forces on surfaces adjacent to them. Since pressure is the normal (perpendicular) force per unit area, the pressure forces must act normal to the surface. Moving fluids can exert not only pressure forces, but also shear forces, so that the combined force exerted by a moving fluid on a surface is not necessarily normal to the surface. However, in problems involving moving fluids it is often convenient to treat the pressure and shear forces as separate and thus calculate the pressure force exactly as we do here, but using the pressure distribution on the surface corresponding to the flow situation rather than to the static-fluid one discussed in this chapter. 

This dF is a vector quantity it has both direction (perpendicular to the surface) and magnitude. For a plane surface all the differentialj dF vectors point in the same direction, so that we can find the total force simply by integrating this equation  

The integration must take into account the curvature of surfaces. Before discussing curved surfaces, we consider the application of the last equation to several kinds of plane surface.  

If the pressure over an entire surface is constant then Eq. 2.19 becomes 

Because the pressure in gases changes- very slowly with position, this is practically true for all moderate-size surfaces exposed to gases. 

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