Basic Equations of Fluid Mechanics

Fluid mechanics considerations are applied in many fields, especially in engineering. Below a list is provided which clearly indicates the far-reaching applications of fluid-mechanics knowledge and their importance in various fields of engineering. Whereas it was usual in the past to carry out special fluid mechanics considerations for each of the areas listed below, today one strives increasingly at the development and introduction of generalized approaches that are applicable without restrictions to all of these fields. This makes it necessary to derive the basic equations of fluid mechanics so generally that they fulfill the requirements for the broadest applicability in areas of science and engineering, i.e. in those areas indicated in the list below. The objective of the derivations in this section is to formulate the conservation laws for mass, momentum, energy, chemical species, etc., in such a way that they can be applied to all the flow problems that occur in the following areas:

• Heat exchanger, cooling and drying technology

• Reaction technology and reactor layout

• Aerodynamics of vehicles and aeroplanes

• Semiconductor-crystal production, thin-film technology, vapor-phase deposition processes

• Layout and optimization of pumps, valves and nozzles

• Use of flow equipment parts such as pipes and junctions

• Development of measuring instruments and production of sensors

• Ventilation, heating and air-conditioning techniques, layout and tests, laboratory vents

• Problem solutions for roof ventilation and flows around buildings

• Production of electronic components, micro-systems analysis engineering

• Layout of stirrer systems, propellers and turbines

• Sub-domains of biomedicine and medical engineering

• Layout of baking ovens, melting furnaces and other combustion units

• Development of engines, catalyzers and exhaust systems

• Combustion and explosion processes, energy generation, environmental engineering

• Sprays, atomizing and coating technologies

Concerning the formulation of the basic equations of fluid mechanics, it is easy to formulate the conservation equations for mass, momentum, energy and chemical species for a fluid element, see Fig. 5.1, i.e. to derive the “Lagrange form” of the equations. In this way, the derivations can be represented in an easily comprehensible way and it is possible to build up the derivations upon the basic knowledge of physics. Derivations of the basic equations in the “Lagrange form” are usually followed by transformation considerations whose aim is to derive local formulations of the conservation equations and to introduce field quantities into the mathematical representations, i.e. the “Euler form” of the conservation equations is sought for solutions of fluid flow problems. This requires one to express temporal changes of substantial quantities as temporal changes of field quantities, which makes it necessary, partly, to repeat in this section the considerations in Chap. 2 but to explain them in a somewhat different and even deeper way.