# Integral governing equations

(Difference between revisions)
 Revision as of 03:32, 27 June 2010 (view source) (→Continuity)← Older edit Revision as of 03:34, 27 June 2010 (view source) (→Continuity)Newer edit → Line 4: Line 4: ''See Main Article'' [[Transformation formula]] ''See Main Article'' [[Transformation formula]] - ==Continuity== + ==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 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
$\frac{\partial }{{\partial t}}\int_V {\rho dV + \int_A {\rho ({{\mathbf{V}}_{rel}} \cdot {\mathbf{n}})dA} } = 0 \qquad \qquad(1)$
$\frac{\partial }{{\partial t}}\int_V {\rho dV + \int_A {\rho ({{\mathbf{V}}_{rel}} \cdot {\mathbf{n}})dA} } = 0 \qquad \qquad(1)$
- ''See Main Article'' [[Integral continuity equation|Continuity]] + ''See Main Article'' [[Integral continuity equation]] ===Momentum=== ===Momentum===

## 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