Optimal Shape of Water Towers
SIAM Undergraduate Research Online
Water tanks can be seen in communities all across the country, but how well arethey designed? In this work, we study the optimal shape of water tanks to find the fastest emptyingtime. In particular, we compare emptying the efficiency for different shaped water towers with thesame volume, height, and cross-sectional outlet area. We first review a formula for the emptying timeas a function of the volume and the tank’s height and then compute the emptying time for severalspecific tank shapes. The question of whether there exists a tank with a minimal emptying time isalso considered in the context of prior work. Finally, our added contribution is to fix the volume of atypical water tank and compute the area and the emptying time for different tank shapes, includingcomposites, in order to develop an understanding for how an optimal tank might be designed.
Sulak, Anthony and Ryan, Shawn D., "Optimal Shape of Water Towers" (2017). Mathematics Faculty Publications. 293.