# Fluid Mechanics-Isn't the volume flux for an incompressible fluid always zero?

• Dec 31st 2012, 04:19 PM
uthpi
Fluid Mechanics-Isn't the volume flux for an incompressible fluid always zero?
In fluid mechanics, when we need to find the volum flux we use ʃsq.nds.
By Gauss Divergence thm ʃsq.nds = ʃvdivqdv
For incompressible fluids divq=0
Then shoudn't the volum flux for an incompressible fluid be zero always??

Looking forward for an explanation
• Dec 31st 2012, 05:02 PM
ILikeSerena
Re: Fluid Mechanics-Isn't the volume flux for an incompressible fluid always zero?
Hi uthpi! :)

What makes you think volume flux for an incompressible fluid isn't zero?
Because it is.

Actually, I'd like to think of it the other way around.

Suppose we take a small volume at a fixed point.
And suppose we can say that at any moment in time the amount fluid that goes in is equal to the amount that goes out.
Then that means 2 things:
1. The fluid is incompressible, or rather it is never compressed or decompressed.
2. The divergence is zero (as a result of the definition of divergence).

As for the definition of divergence, in words it is (abbreviated from wikipedia):
"the divergence represents the outward flux from an infinitesimal volume"

Or more formally (also from wikipedia):
"the divergence of a vector field F at a point p is defined as the limit of the net flow of F across the smooth boundary of a three dimensional region V divided by the volume of V as V shrinks to p."