Naked Science Forum
On the Lighter Side => New Theories => Topic started by: Geezer on 26/09/2011 06:35:28
-
OK, so this is probably really silly, but it struck me that it might just be possible to simplify certain fluid analysis if it was done in two dimensions rather than three, or am I a bit late?
Fluids are three dimensional, but in a great many situations, two of the dimensions are exactly the same, so why go to all the trouble of lugging a third dimension around if it's really redundant?
-
I'm not quite sure what your goal is as fluids are space filling.
A partly-full container would have a shape + depth. However, the shape of the container may not be uniform at different depths.
Often reserviors only list a single dimension, depth, but one has to always keep in mind that the reservoir floor is never of a uniform shape, except in artificial structures.
Anyway, when describing a liquid, one is often concerned with location, volume, depth, what it is, boiling point, freezing point, vapor pressure, viscosity, etc.
-
Whilst you are correct Clifford - most of the difficult modelling of fluid is when then are in motion. The Navier_Stokes equations are still a thorn in the mathematical side - one of the millennium prizes was/is to find a method to show that NS equations have complete and singularity free solutions in 3 dimensions.
Geezer - I believe that 2d approximations are widely used (see above problem), but this is way out of my comfort zone. You can have a look at the millennium prize site - they normally have pretty good introductions to the problems