Intuition
If a fluid is flowing in some area, and we wish to know how much fluid flows out of a certain region within that area, then we need to add up the sources inside the region and subtract the sinks. The fluid flow is represented by a vector field, and the vector field's divergence at a given point describes the strength of the source or sink there. So, integrating the field's divergence over the interior of the region should equal the integral of the vector field over the region's boundary. The divergence theorem says that this is true.
The divergence theorem is thus a conservation law which states that the volume total of all sinks and sources, the volume integral of the divergence, is equal to the net flow across the volume's boundary.
Read more about this topic: Divergence Theorem
Famous quotes containing the word intuition:
“Reason is sight. Instinct is touch. Intuition is smell.”
—Mason Cooley (b. 1927)
“When a scientist is ahead of his times, it is often through misunderstanding of current, rather than intuition of future truth. In science there is never any error so gross that it won’t one day, from some perspective, appear prophetic.”
—Jean Rostand (1894–1977)