Fall 2017 Seminar






November 17

Douglas White, Physics and Math

Time Optimization of a Draining Tank and Similar Optimization Problems on Graphs


Time: 3:15PM-4:05PM

Date:  Friday, November 17th

Place: EMCS 422



Douglas White, Physics and MathWe consider a tank containing a given volume of liquid and suppose that the liquid drains under the influence of gravity through a small hole at the bottom. The liquid's viscosity and friction at the hole are assumed to be negligible. The velocity of the exiting liquid is given by Torricelli's law, which states that the height of the liquid affects the velocity of the exiting liquid. Given the volume, we vary the shape of the tank to optimize the time taken for a tank to drain. After exploring the results of a few tank shapes, we prove the existence of a certain class of tanks for which the draining time can be made to hold any positive draining time. We also consider the dual problem and find that a tank with a given draining time can be begin with any positive volume of liquid. We then look at similar optimization problems for physical models in which Torricelli's law has to be modified as well as related optimization problems from graph theory.