By Sir James H. Jeans, Physics
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Extra resources for An elementary treatise on theoretical mechanics
04 FIG. 3-4. 4 This point is discussed in more detail in Chapter 4. T he way in which friction alTects the Mach number may be shown as follows. First the conservation equations are transformed (by ihtroducing the perfect gas law and the definition of Mach number) to read: Frictionless flow of a perfect gas in a constant-area duct with stagna tion It may be seen from Fig. 3-4 that inc reasing the stagnat ion tempera ture drives the Mach number toward un ity whether the flow is supersonic o r subsonic.
This suggested the major simplification o~ the ~avier-Stokes e~uati~ns which is the basis of boundary layer theory. For fairly hIgh-speed flow, In WhICh the boundary layer is so thin that the pressure gradient normal to the wall is negligible, Prandtl and others showed how to treat the boundary lay~r mathematically for special cases, many of which have been solved in the past SIX~y y~ars. Given that a boundary layer exists on a body, it is easy to see qualitatively why the case of vanishing viscosity is fundamentally different from the case of zero viscosity .
Boundary layer velocity distribution. Thus Prandtl showed that the flow field may be broken into two parts; a thin viscous zone near the waIl, and an outer zone where the nonviscous theory is adequate. This suggested the major simplification o~ the ~avier-Stokes e~uati~ns which is the basis of boundary layer theory. For fairly hIgh-speed flow, In WhICh the boundary layer is so thin that the pressure gradient normal to the wall is negligible, Prandtl and others showed how to treat the boundary lay~r mathematically for special cases, many of which have been solved in the past SIX~y y~ars.
An elementary treatise on theoretical mechanics by Sir James H. Jeans, Physics