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10 (shown by the solid lines) and the outside pressure is pa. 20 in the steady state becomes ρ q n dS = 0 2 25 cs Next we need to consider all the areas where fluid is crossing the control volume (namely the areas A1 and A2) in the figure. 10 Example: one-dimensional flow through a stream tube The Fluid Dynamic Equations 47 section 2: (u2,0,0). Also, the unit normal vector is defined as pointing outside of the control volume and therefore n1 = (−1,0,0) while n2 = (1,0,0), as shown in the figure.

17 shows a generic automobile, which is moving forward at a constant speed. 17 Using the kinetic theory of gases we can explain the high pressure near a concave curvature and the lower pressure near a convex curvature The air molecules are moving towards the car at an average velocity, in addition to their Brownian motion (see Fig. 17). At the base of the windshield the number of collisions will increase because the incoming molecules will hit head on and some may even bounce back again due to intermolecular collisions.

For example, if a Cartesian coordinate system is used, the components of the fluid velocity are given by u = u x, y, z, t v = v x, y, z, t 26 w = w x, y, z, t The Eulerian approach provides information about the fluid variables that is consistent with the information supplied by most experimental techniques and which is in a form that is appropriate for most practical applications. For these reasons the Eulerian description of fluid motion is the Automotive Aerodynamics 38 most widely used (and will be developed in this chapter).

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