Modelling tank drainage using a simple apparatus

A straightforward experimental set-up, requiring a two-liter bottle, a ruler and a stopwatch, is used to provide data appropriate for modelling with Torricelli's Law in the simplest case, and a more sophisticated differential equation when losses are taken into account and a pipe extension is considered. With only an exit hole included in the model, the governing equation can be integrated analytically to find the liquid height in the tank as a function of time. In the more complicated instance, the governing equation requires numerical integration. In both cases, a discharge coefficient can be employed as a fitting parameter. Excellent agreement between the experimental data and the theoretical modelling results has been obtained. An analytical solution with comparable accuracy to the numerical version is also possible for a pipe extension under the operating conditions considered here. Student reception of the experiment was generally positive, although some nuances were not fully grasped.