We’ve previously looked at how to derive divergence for cylindrical coordinates . If you’re like me though, knowing the rather lengthy derivation won’t help you understand or memorize the resulting formula. So, let’s take a look at why the result makes sense. The formula for the gradient of a function in cylindrical coordinates is: Why is the factor of 1/r in the phi term? Remember what question the divergence is asking. We want to find out the amount the function changes vs. a small change in distance along each coordinate’s direction. For coordinates that actually correspond to distances, like x, y, and z of Cartesian coordinates, or r and z of cylindrical coordinates, this is straightforward. The change in the coordinate corresponds to the change in distance along the coordinate. For coordinates that correspond to angles in the cylindrical coordinate system, there’s an extra twist. The direction of phi always points tangent to a circle centered on the z axis. The small chang...