Abstract
We consider a problem of calculus of variations motivated by
the model of a tank filled with a given volume of liquid and draining
through a small orifice according to Torricelli’s law. We prove that given
any length of time, some tank exists which drains in this time. Our main
interest in this optimization (i.e., minimization and maximization) problem is that the usual Euler–Lagrange equation may not be used here, at
least directly. We consider optimization for some similar physical models where Torricelli’s law has to be modified. We also study optimization
problems on the star graphs that are inspired by our physical model.
Boris P. Belinskiy, Douglas C. White. (2019) Time Optimization of a Draining Tank and Some Similar Problems on Star Graphs, Punjab University Journal of Mathematics, Volume 51, Issue 7.
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