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Unformatted text preview: MECH 314 Introduction to Fluid Mechanics February 16, 2009 American University of Beirut, Spring 2009 Handout # 2 The Continuum Hypothesis 1 The continuum hypothesis Fluid mechanics deals with the behavior of fluids on a macroscopic scale large compared with the characteristic molecular dimensions. For a gas the characteristic molecular di- mension is the mean free path whereas for a liquid the characteristic molecular dimension is the average inter-molecular spacing. If we consider the distribution of mass on the molecular scale, we observe that the density of a small volume varies drastically as the volume increases to contain an increasing number of molecules (Figure 1). Such a behavior is expected since the mass of an atom is concentrated in the nucleus, with the latter oc- cupying a very small fraction of the total volume of the molecule. Macroscopic properties such as temperature, pressure, and velocity are defined by averaging over a large number of molecules contained in a small volume. In the continuum hypothesis it is assumed that the macroscopic behavior expressed in terms of these macroscopic properties is such that the fluid behaves as if these properties are uniformly distributed within the small volume....
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- Spring '08
- Thermodynamics, Fundamental physics concepts, Continuum hypothesis, small volume