Next: Example
Up: Continuity
Previous: FCV conversion
We want to convert the integral mass conservation equation for
a fixed control volume,

or

into a PDE that is pointwise valid. To do so, we need to get rid of
the surface integral.
The divergence theorem takes surface integrals to volume
integrals and vice-versa.
- Scalar variable:

- Vector variable:

Apply this to mass conservation:

Conservation form of the continuity equation:
|  |
(3) |
(Pure derivatives, simply put the integrals back in to go to the
conservation equations.)
Index notation (with Einstein summation convention):
|  |
(4) |
Nonconservative form:
|  |
(5) |

Material fluxion of density:
|  |
(6) |
For incompressible fluids:
|  |
(7) |
The density does not have to be constant from one fluid element to the
next (eg, oil and water, varying salinity, ...)
Next: Example
Up: Continuity
Previous: FCV conversion
01/21/00 0:35:54
01/24/00 0:04:27
01/24/00 0:21:18
01/26/00 0:02:16
01/31/00 0:32:02