流体力学英文版1

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Significance of continuum concept
As a consequence of the continuum assumption, each fluid property is assumed to have a definite value at every point in space. Therefore fluid properties such as density, temperature, velocity, and so on, are considered to be continuous functions of position and time, and this lead to a field* description of fluid flow. In particular the velocity field is given by
Instead, molecular theory may be used for above cases
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How to represent flow property at a point in a continuum
For example, the density at point C
C
When δ V is shrank (收缩) to a very small size, it then will
δ V*～10−9 mm3
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In a continuum, volume of a fluid particle or element satisfy (连续介质中的流体质点、流体微团满足下 列条件):
Large enough in microscope（微观足够大), Small enough in macroscope（宏观足够小）, i.e. 10−9 mm3 of air at standard conditions contains approximately 3× 107 molecules.
ML−1T −2
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z The Principle of Dimensional Homogeneity 量纲一致性原则
In engineering and science, all equations must be dimensionally homogeneous, that is, each additive term in an equation must have the same dimensions.
如果对空间区域的每个点， 都对应某个物理量的一个确 定的值，则称在上确定了该量的一个场。物理量是数量
r r 还是向量决定其为数量或者向量场。 V=V(x,y,z,t)
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NOTE: 连续介质概念对下列场合适用吗？
1. 稀薄气体 2. 微小空间(尺度)的流动
“Continuum concept” breaks down whenever the mean free path of the molecules （分子自由行程） approximately becomes the same magnitude order (相 同数量级) as the smallest significant characteristic dimension (特征长度) of the problem.
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Problem: Fluids under a shear stress must be in a kind of motion
-------- deformation. How to keep the fluid at rest ? (FW p4)
ANS: Fluid takes shape of container!
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1.2 Continuum concept
连续介质概念
All fluids are composed of molecules in constant motion. However in most engineering applications we are interested in the average or macroscopic effects that we ordinarily perceive and measure. We thus treat a fluid as an infinitely divisible substance, a continuum, thus from macro point of view, we do not need to concern with the behavior of individual molecules. This is the so-called continuum concept in classical fluid mechanics.
若连续介质不适用，应如何处理呢？ 13
1.3 Dimension and Units 单位与量纲
Dimensions are properties that can be measured, e.g. length, velocity, area, volume, acceleration etc. 可以测量的性质叫量纲。
It breaks down whenever the mean free path of the molecules （平 均分子自由行程,10−7 ）approximately becomes the same magnitude order as the smallest significant characteristic dimension (特征长度) of the problem.
represent a fluid particle/element, and this volume is termed
elemental volume.
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ρ
=
δm
lim
δV →δV
*
δ
V
For all liquids and for all gases at atmospheric pressure, the value of lower limiting volume is about
or secondary units
导出单位
They are derived units from combination of the above primary ones (units, dimensions or quantities)
For instance, a force has a dimension and SI unit
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Figure 1.1 Behavior of (a) solid and (b) fluid, under the action of a constant shear
solid
fluid
与时间无关
与时间有关
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Main differences between the behavior of solids and
– Basic flow analysis Techniques, control volume and system, Eulerian and Lagrangian Descriptions
– Thermodynamic properties of a Fluid
– Viscosity and other secondary properties (Newtonian/nonNewtonian; no-slip condition, turbulence; surface tension )
在经典流体力学中，只考虑分子平均或宏观 作用，不考虑单独分子的性能 。
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Validity of continuum concept
The concept of a continuum is the basis of classical fluid mechanics. The continuum assumption is valid in treating the behavior of fluids under normal conditions.
Chapter 1 Introduction
概论
Main Subjects
In this chapter, we focus on the following concepts and
definitions:
– Definition of a fluid;
– Continuum concept;
– Units and Dime源自sions;fluids under an applied force
(1) Time-dependency – For a solid, the strain（应变）/deformation is a function of the applied stress and independent of the time over which the force is applied, providing that the elastic limit is not exceeded; – For a fluid, the strain is dependent on time.
(2) Recovery – For a solid, if the elastic limit is not exceeded, the deformation disappears when the force is removed; – A fluid continues to flow as long as the force is applied and will not recover its original form when the force is removed.