Integral governing equations

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Transformation Formula

A fixed-mass system describes an amount of matter that can move, flow and interact with the surroundings, but the control volume approach depicts a region or volume of interest in a flow field, which is not unique and depends on the user. So conservation laws for a fixed-mass system need to be transformed to apply to a control volume. The transformation Formula allows one to mathematically and physically link the conservation laws for a control volume with that of a fixed-mass system.

See Main Article Transformation formula


The law of the conservation of mass dictates that mass may be neither created nor destroyed. For a control volume that contains only one phase, the integral continuity equation is

\frac{\partial }{{\partial t}}\int_V {\rho dV + \int_A {\rho ({{\mathbf{V}}_{rel}} \cdot {\mathbf{n}})dA} }  = 0     \qquad \qquad(1)

See Main Article Continuity


See Main Article Momentum


See Main Article Energy


See Main Article Entropy

Conservation of Mass Species

See Main Article Conservation of Mass Species