By Titus Petrila; Damian Trif
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Auf der Grundlage eines allgemein verständlichen, beiden Gebieten gemeinsamen Konzepts wird eine Einführung in die Fluid- und Thermodynamik gegeben. Die Fluiddynamik umfaßt die Hydrostatik, die Hydrodynamik der idealen und viskosen Fluide sowie die laminaren und turbulenten Rohrströmungen. In der Thermodynamik werden nach Einführung der Begriffe und der Darstellung der thermischen Zustandsgleichungen idealer Gase der erste und zweite Hauptsatz behandelt, beginnend mit der für adiabate, einfache Systeme gültigen shape nach Caratheodory bis hin zur Bilanzaussage von Clausius Duhem mit Anwendungen auf wärmeleitende viskose Fluide und die kanonischen Zustandsgleichungen.
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Extra resources for Basics of fluid mechanics and introduction to computational fluid dynamics
From the jump relation across the discontinuity surface which moves with velocity we get , for any of the equations of the above system, the jump relations called the Rankine–Hugoniot jump relations. If it takes a coordinate system whose displacement with uniform velocity would be, at a moment equal with the displacement velocity of a discontinuity located at the origin of this system, then within this new frame of coordinates, the previous relations will be rewritten Introduction to Mechanics of Continua 47 where the subscripts identify the state “0” before the jump and the state “1” after the jump.
There are special subjects as, for instance, the wave theory in hydrodynamics, where the results obtained by considering the equation of state are close to reality. But, generally speaking, the shock phenomena should be treated with the system completed with the above energy equation instead of the equation of state. From the jump relation across the discontinuity surface which moves with velocity we get , for any of the equations of the above system, the jump relations called the Rankine–Hugoniot jump relations.
Precisely, we will show that the 22 BASICS OF FLUID MECHANICS AND INTRODUCTION TO CFD stress T, evaluated for the considered moment at a point r, situated on a surface element of normal can be expressed by the relation known as Cauchy’s theorem. The proof is backed by the theorem (principle) of momentum applied to a tetrahedral continuum element with its vertex at r, the lateral faces being parallel to the planes of coordinates, its base is parallel to the plane which is tangent to the surface element where the point r is located.