Soup-to-nuts modelling of a falling column of water

Abstract

We present a complete, soup to nuts, modeling activity of a falling column of water. Many colleagues have used this material in teaching applications of first order separable differential equations. We describe how the material can be presented with students collecting their own data from online videos. One can then either offer the differential equation for the height of a falling column of water using Torricelli's Law or render a derivation using the principle of the Conservation of Energy. Once the differential equation is obtained the effort turns to solving, parameter estimation, and model validation.We discuss a derived or analytical model compared to an empirical ‘just fit’ a curve approach. We introduce a strategy for parameter estimation with Excel's Solver command. Discussions of variations on the shape of the cylinder follow.