General Form Of Reservoirs Equation Of Motion

Fluids are composed of molecules in constant motion and collisions. A fluid has no structure. They are not distinguished by their microscopic (molecular) structure. To take account of each molecule in a flow, may be difficult for engineering purposes. Instead we are interested in average measuring of the molecule manifestations such as density, pressure and temperature which are their macroscopic structure. The continuum concept offers a great deal of simplification in analysis.

A fluid point (particle) represent a spatial average over some small volume V. Consider some variable as a = V J a'dV, in which a' has a random characteristic(figure 2.1). The variable a can be density, p, velocity v, etc.. There must be a volume V such that a range of V value exist over which a is constant. Therefore for a big V we get different values of a for a range of V. However if we make V successfully smaller we get same value of a. We want 6 < V 3 < L, in which 6 is the largest length scale of the fluid structure (say mean free path) and L is the length scale of the domain of the problem. The restriction V 3 < L is for a to be measurable at a point while the criteria 6 < V 3 is for a to be statistically significant and deterministic (always get same answer if we start from same initial condition and boundary conditions).

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