FORMULATION OF THE ENERGY EQUATION IN FLUID DYNAMICS
Dubbelday, Pieter S.
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Formulations for the energy equation exist in variety in fundamental and applied texts and monographs on fluid dynamics. It is often difficult to establish the set of conditions leading to a given formulation. More deleterious is the fact that in some cases an energy equation as point of departure does not have the generality implied by the accompanying text. In two instances (Chandrasekhar, 1961; Newman and Pierson, 1966) the term ( a T/kt ) v«v in formula (7) is replaced by pv«v (for the symbols used see the list at the end of this note). For an incompressible fluid this term is zero, admittedly, while for an ideal gas one has aT//cT = p, and the difference disappears. It would appear, though, to be a didactic drawback to start from an inexact formula, even though the final approximation is unaffected. Moreover, it is quite possible to imagine situations where neither the incompressible fluid nor the ideal gas would be a satisfactory approximation to reality. In this note a hierarchy of formulations is presented for reference, from the general to some restricted cases. A few directions are given to guide in the derivations. The point of departure is the energy equation for the flow of a simple fluid system.