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Additional resources for Basics of fluid mechanics and introduction to computational fluid dynamics
1 Incompressible Continua A continuum system is said to be incompressible if the volume (measure) of the support of any subsystem of it remains constant as the continuum moves. , on any pathline), but the value of this constant could be different from trajectory to trajectory. , is constant with respect to the spatial variables, then it is incompressible if and only if is constant vs. the time too. We note that if a continuum is homogeneous at the moment it could become nonhomogeneous later on.
More 9 For sake of simplicity we consider only the case of the heat added to P and corresponding “– n” will represent the unit inward normal drawn to S and this is the right unit normal vector we deal with in our case. The heat flux principle could be got by applying the above form of the first law of thermodynamics to a tetrahedron of Cauchy type (that is a similar tetrahedron with that used in the proof of the Cauchy theorem) 10 The transformation of the left side could be done by using the derivative of a product and the equation of continuity.
Allows us to write that or The last equality is known as the Crocco–Vazsonyi equation and it shows that H is constant in the whole domain of the flow provided that and In other words, for the isentropic steady potential fluid flows H is constant together with K. In the absence of the external forces where is the enthalpy at the zero velocity (stagnation) points. In this case the Crocco – Vazsonyi equation can be written in the simplified form as Generally, the values of the constants taken by K and H along a certain streamline, in the steady case, are different.