User:Tohline/Cylindrical 3D
From VisTrailsWiki
Contents 
Equations Cast in Cylindrical Coordinates
Spatial Operators in Cylindrical Coordinates 


= 


= 


= 


= 

Vector TimeDerivatives in Cylindrical Coordinates 


= 


= 


= 

Governing Equations
Introducing the above expressions into the principal governing equations gives,
Equation of Continuity
Euler Equation
Adiabatic Form of the
First Law of Thermodynamics
Poisson Equation
Eulerian Formulation
Each of the above simplified governing equations has been written in terms of Lagrangian time derivatives. An Eulerian formulation of each equation can be obtained by replacing each Lagrangian time derivative by its Eulerian counterpart. Specifically, for any scalar function, f,
Hence,
Equation of Continuity
Assuming that the initial (subscript i) configuration is axisymmetric and that, following perturbation, each physical parameter, Q, behaves according to the relation,
the linearized form of the continuity equation becomes:
(This has been obtained by combining the expressions highlighted with a lightblue background color from the accompanying table.) 


= 

Linearize each term of the Continuity Equation assuming ... 




































































Combining all terms: 




Component of Euler Equation
Component of Euler Equation
z Component of Euler Equation
See Also
© 2014  2020 by Joel E. Tohline 