# Integral governing equations

## 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

## Continuity Equation

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 Integral continuity equation

### Momentum

See Main Article Momentum

### Energy

See Main Article Energy

### Entropy

See Main Article Entropy

### Conservation of Mass Species

See Main Article Conservation of Mass Species