Divergentie en krul

The divergence of a vector field at a point is the net outward flux per unit volume, as the volume at that point shrinks to zero.

Mathematically, divergence is the dot product of the del operator with the vector field.

Consider a vector field of water flowing through a pipe. If the water flows with constant velocity, it does not diverge.

On passing through a hole, the velocity of water diverges, resulting in a positive divergence.

On connecting the pipe to a multi-holed connector, the water velocity decreases, leading to negative divergence.

The curl of a vector field is the circulation of the vector per unit area, as this area shrinks to zero. It is directed normal to the area where the circulation is maximum. Mathematically, it is the cross product of del operator with the vector field.

Consider a non-uniform velocity vector of a river. A stick tossed into the river floats smoothly where the velocity vector has zero curl, and rotates where the velocity vector has non-zero curl.