On the other hand, the function has zero divergence at

P; it is not spreading out at all.

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P

So, for example, if the divergence is positive at a point, it

means that, overall, that the tendency is for fluid to move away

from that point (expansion); if the divergence is negative, then

the fluid is tending to move towards that point (compression).

Fundamental theorem of divergence

The fundamental theorem for divergences states

that:

41

surfacevolume

daFdF

This theorem has at least three special names:

Gausss theorem, Greens theorem, or, simply, thedivergence theorem.

is function at the boundary element of volume (in

Cartesian coordinates, = dx, dy, dz), and The

volume integration is really a triple integral.

d

d

d

da represents an infinitesimal element of

area; it is a vector , whose magnitude is

the area of the element and whose

direction is perpendicular ( normal ) to the

surfaces, pointing outward.

42

On the front face of the

cube, a surface element

is idzdyda 1