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# محاضرة 29

الكلية كلية الهندسة     القسم  الهندسة المدنية     المرحلة 2
أستاذ المادة كاظم نايف كاظم اليساري       6/6/2011 4:38:03 PM

of such two-phase flows [7]. Finally, there are situations where the distinction between a liquid and a gas blurs. This is the case at temperatures and pressures above the socalled critical point of a substance, where only a single phase exists, primarily resembling a gas. As pressure increases far above the critical point, the gaslike substance becomes so dense that there is some resemblance to a liquid and the usual thermodynamic approximations like the perfect-gas law become inaccurate. The critical temperature and pressure of water are Tc  647 K and pc  219 atm,2 so that typical problems involving water and steam are below the critical point. Air, being a mixture of gases, has no distinct critical point, but its principal component, nitrogen, has Tc  126 K and pc  34 atm. Thus typical problems involving air are in the range of high temperature and low pressure where air is distinctly and definitely a gas. This text will be concerned solely with clearly identifiable liquids and gases, and the borderline cases discussed above will be beyond our scope. We have already used technical terms such as fluid pressure and density without a rigorous discussion of their definition. As far as we know, fluids are aggregations of molecules, widely spaced for a gas, closely spaced for a liquid. The distance between molecules is very large compared with the molecular diameter. The molecules are not fixed in a lattice but move about freely relative to each other. Thus fluid density, or mass per unit volume, has no precise meaning because the number of molecules occupying a given volume continually changes. This effect becomes unimportant if the unit volume is large compared with, say, the cube of the molecular spacing, when the number of molecules within the volume will remain nearly constant in spite of the enormous interchange of particles across the boundaries. If, however, the chosen unit volume is too large, there could be a noticeable variation in the bulk aggregation of the particles. This situation is illustrated in Fig. 1.2, where the “density” as calculated from molecular mass m within a given volume  is plotted versus the size of the unit volume. There is a limiting volume * below which molecular variations may be important and 6 Chapter 1 Introduction Microscopic uncertainty Macroscopic uncertainty 0 1200   *  10-9 mm3 Elemental volume Region containing fluid = 1000 kg/m3 = 1100 = 1200 = 1300 (a) (b)       Fig. 1.2 The limit definition of continuum fluid density: (a) an elemental volume in a fluid region of variable continuum density; (b) calculated density versus size of the elemental volume. 2One atmosphere

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