# What is divergence

1. Aug 25, 2007

### ehrenfest

My book says that divergence can be understood in the context of fluid flow as the rate at which density flows out of a given region. It says that if F(x,y,z) is the velocity of a fluid, then that is the interpretation of the divergence. I fail to understand where the density comes in when we are only dealing with velocities at first and we only take a spatial derivative. It seems like the interpretation should be the rate of change of velocity i.e. acceleration.

2. Aug 25, 2007

### HallsofIvy

Staff Emeritus
"Acceleration" implies a velocity changing with time. If you have a fluid flowing toward a central drain, for example, the velocity may vary with position but not time. A single molecule of the fluid could move toward the drain with constant velocity while different particles, around the drain, move with the same speed but different velocities.

3. Aug 26, 2007

### learningphysics

Rate of fluid flow is related to volume, and not mass so the density doesn't enter...

Do you see how over a closed volume... the rate at which fluid is leaving the the volume is F.A (dot product of velocity with the area) over the volume... ie the flux of F through the area enclosing the volume...

4. Aug 26, 2007

### ehrenfest

OK and you just make that volume infinitesimal? How does making the volume infinitesimal get you the equation for the divergence? Is