By Katz, Joseph
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Extra resources for Automotive aerodynamics
Therefore, the disciplines of fluid mechanics and aerodynamics are based on simplified models using only portions of the full equations. This simplification can be accomplished by identifying the dominant terms in the formulation and neglecting terms of much lower orders of magnitude. It appears that this approach allows the engineers to appreciate both the power and the limitations of the techniques that will be presented in this text. Furthermore, the learning process will be easier, as the link between the various chapters is understood.
26 into Eq. 25 results (for an ideal gas): E = ρ RT The units for E, based on Eq. 4 Compressibility of a liquid For this example, let us consider the compressibility of sea water. 34 109 N/m2 and let us evaluate the change in volume at a depth of 1 Km. The change in pressure at 1000 m depth is dp = ρgh = 1000 9 8 1000 N m2 and dV V = dp E = 1000 9 8 1000 2 34 109 = 4 188 10 −3 0 42 which is less than half a percent. This shows that water is really incompressible. It is interesting to point out that compressibility relates to the speed of sound in a fluid.
This is proved later in Chapter 11. 7 Modulus of Elasticity, E The modulus of elasticity E is a measure of compressibility. It can be defined as E = dp dV V or dp = E dV V 1 23 And the second form indicates how much pressure is needed to compress a material having a modulus of E. Also, the change in volume is directly related to the change in density, and we can write: dρ ρ = dV V 1 24 And by substituting dV/V instead of dρ/ρ in Eq. 23 we get: E = dp dρ ρ 1 25 Most liquid are not very compressible, but gases are easily compressed and for an ideal gas we already introduced this relation (in Eq.
Automotive aerodynamics by Katz, Joseph