lمقاله مکانیک 4 - جریان لزج تراکم ناپذیر

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In Chapter 3 the effects of pressure in a fluid were isolated (because the fluid was not
moving), and in Chapter 4 the inertia terms were added. The inclusion of viscosity,
its effects, and the resulting velocity distribution are discussed here. For example,
the velocity distribution for the laminar flow inside a pipe is formulated and the
average velocity is calculated. This provides the relation between the simple 1D
average velocity model (of Chapter 4) and the more complex (and realistic) 2D or
3D flows.
The solutions presented early in this chapter are often called exact solutions.
This means that, for a few limited cases, a set of logical assumptions leads to simplifi-
cation of the fluid dynamic equations, which allows their solution (for laminar flow)!
Also, the cases presented in this chapter (e.g., the flow in pipes) is often termed as
internal flows. The discussion on external flows is delayed to the following three
The second part of this chapter demonstrates the approach that evolved during
the past 200 years for solving fluid dynamic problems (because there is no closed-
form analytic solution to the complete fluid dynamic equations). According to this
approach, to develop a practical engineering solution, we must start with a simple
but exact solution that determines the major parameters and the basic trends of the
problem (e.g., the pressure drop in a circular pipe versus the Reynolds number).
Based on these parameters, an empirical database can be developed for treating
a wider range of engineering problems. As an example, the viscous laminar flow
model in circular pipes is extended into the high-Reynolds-number range and the
effects of turbulent flow are discussed.

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