Abstract
This chapter offers a very concise review of the main concepts of fluid mechanics, with a particular focus on aerodynamics, the mastery of which is essential for understanding the rest of the text. Although many students may be familiar with this subject, they should revisit it to refresh concepts and units.
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Notes
- 1.
Also known as Boyle-Mariotte’s law.
- 2.
Avogadro’s law (1811): “Equal volumes of different gaseous substances, measured under the same conditions of pressure and temperature, contain the same number of molecules.”
- 3.
Note that, although surface (S) denotes the topological object and area (A) its measurement, we do not make any distinctions in this text for simplicity reasons.
- 4.
A fluid is incompressible (isochoric) if the effects of pressure on its density are negligible at a certain speed. Normally it is valid to consider air as incompressible for ventilation calculations, given its moderate circulation speed and the reduced compression ratio provided by fans. This simplification cannot be done, for example, in the case of mine compressed air networks.
- 5.
This transition regime occurs, for example, in dense media mineral separation and in certain froth flotation cases.
- 6.
Dimensionless numbers have proven very useful in scaling-up operations. That is to say, in quantifying the expected results on a real scale from those derived from tests on a smaller scale.
- 7.
The hydraulic diameter is the quotient between the cross-sectional area and its perimeter. This parameter can be used to characterize an irregular surface using a single parameter. For this reason, its use is extensible to other fields that have nothing to do with fluid mechanics, such as, for example, in dimensioning the pillars in room and pillars mining when the pillar cross section has to be characterized.
- 8.
As a consequence of the continuity equation, if the cross section in a duct is the same, so is the velocity. Thus, any pressure loss is total pressure loss if the duct has a constant cross section. Therefore, as in this case there is no variation in the dynamic pressure, the total pressure loss coincides with the static pressure loss.
- 9.
The “f” used in this text corresponds to the friction factor of Darcy’s law sometimes denoted as fD. Although this is the most widespread, it is possible to find sources that use Fanning’s friction factor (fF). The relationship between the two is fD = 4fF.
- 10.
An equation that establishes a relationship between two or more variables but cannot be written as y = f(x).
- 11.
Also termed local losses, dynamic losses or minor losses.
- 12.
A loss of energy in a pipeline is always a loss of total pressure. What happens is that, in points that have the same speed (as in the case of 1 and 3 that have the same cross section), the losses of static and total pressure coincide. Actually, the equation should look like:
\(P_{\text{shock}} = \left( {P_{1} + \frac{{v_{1}^{2} }}{2}\rho } \right) - \left( {P_{3} + \frac{{v_{3}^{2} }}{2}\rho } \right)\)
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Sierra, C. (2020). Fundamental Concepts of Fluid Mechanics for Mine Ventilation. In: Mine Ventilation. Springer, Cham. https://doi.org/10.1007/978-3-030-49803-0_1
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