Optimal Shape of Water Towers

Abstract

Water tanks can be seen in communities all across the country, but how well are they designed? In this work, we study the optimal shape of water tanks to find the fastest emptying time. In particular, we compare emptying the efficiency for different shaped water towers with the same volume, height, and cross-sectional outlet area. We first review a formula for the emptying time as a function of the volume and the tank's height and then compute the emptying time for several specific tank shapes. The question of whether there exists a tank with a minimal emptying time is also considered in the context of prior work. Finally, our added contribution is to fix the volume of a typical water tank and compute the area and the emptying time for different tank shapes, including composites, in order to develop an understanding for how an optimal tank might be designed.