Which Tanks Empty Faster?

Leonid G. Hanin
1999 The American mathematical monthly  
Suppose that water towers like those shown in Figure 1 are initially filled with water and have the same volume, height, and cross-sectional outlet area. Which one empties first? This problem arises naturally when designing watersupplying tanks or funnels. We find a formula expressing the emptying time as a function of the volume of liquid and its initial height. We compute the emptying time for several specific tank shapes, in particular, for those shown in Figure 1 . We also address the
more » ... o address the question whether there exists a tank with a given volume and height for which the emptying time is minimal.
doi:10.1080/00029890.1999.12005143 fatcat:7dwporktcrfqvegt2ggu7qhhji