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الكلية كلية الهندسة
القسم الهندسة المدنية
المرحلة 2
أستاذ المادة كاظم نايف كاظم اليساري
6/6/2011 3:56:18 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
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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