Gradient, Divergence and Curl

Divergence is an operation on a vector field that tells us how the field behaves toward or away from a point.

Divergence of a vector field  F⇀  at a particular point  P  is a measure of the “outflowingness” of the vector field at  P . 

If  F⇀  represents the velocity of a fluid, then the divergence of  F⇀  at  P  measures the net rate of change with respect to time of the amount of fluid flowing away from  P  (the tendency of the fluid to flow “out of” P). In particular, if the amount of fluid flowing into  P  is the same as the amount flowing out, then the divergence at  P  is zero.