Personal Reflection #3

I just had a moment of creativity while doing my fluid mechanics homework (due tomorrow, so thank goodness). One of our problems involved deriving an equation for flow through a 3D object (called the continuity equation) using spherical coordinates. The problem for me is I really do not understand spherical coordinates all that well. To come up with the equation, the flow had to be broken up into 3 components, similar to splitting a 3D object into x, y, and z using Cartesian coordinates. Our instructor had given us hints for one of the sides, so I was able to figure it out. For the other sides, I noticed a pattern that was constant for all three sides. Without going into too much detail, I basically figured out that I needed to multiply the terms that I knew by the missing terms that would form change in volume and take the limit of the change in the variable I was looking at as it goes to zero. By noticing this pattern, I was able to arrive at the correct equation that is defined in our book.