Abstract
Approximate solutions of the N-S equations can be obtained in many cases of practical interest, provided that suitable simplifications can be made. Simplifications stem from the evaluation of the order of magnitude of the different terms appearing in the N-S equations. To assess the order of magnitude of each term, it is useful to write the equations in dimensionless form so that the terms of similar magnitude can be identified and the dimensionless groups that determine the structure of the flow field can be determined.
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Notes
- 1.
The solution of equation (5.75) has the following form:
$$\begin{aligned} f = \text{ constant } \cdot \left[ \cot \theta + \frac{\sin \theta }{r} \ln \left( \frac{1 + \cos \theta }{1 - \cos \theta } \right) \right] ~~~. \end{aligned}$$ - 2.
Tipically, \(\overline{h} / a \simeq 1 / 1000\).
- 3.
In a plane channel with infinite width, the equivalent diameter is equal to twice the distance between the walls
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Soldati, A., Marchioli, C. (2024). Approximate Solutions for Low Reynolds Number Flows. In: Fluid Mechanics for Mechanical Engineers. Springer, Cham. https://doi.org/10.1007/978-3-031-53950-3_5
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DOI: https://doi.org/10.1007/978-3-031-53950-3_5
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