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:
“All appeared new, and strange at first, inexpressibly rare and delightful and beautiful. I was a little stranger, which at my entrance into the world was saluted and surrounded with innumerable joys. My knowledge was divine. I knew by intuition those things which since my Apostasy, I collected again by the highest reason.”
—Thomas Traherne (1636–1674)
“Well, intuition isn’t much help in police work. Facts are what we need.”
—Crane Wilbur (1889–1973)
“Reason is sight. Instinct is touch. Intuition is smell.”
—Mason Cooley (b. 1927)