Drainage Time and Shape: Inequalities from Torricelli's Law
Eugen J. Ionascu
TL;DR
This paper develops integral inequalities related to drainage time in convex shapes based on Torricelli's Law, introduces the Torricelli number as a shape invariant, and constructs solids for asymmetrical clepsydrae.
Contribution
It presents new integral inequalities for drainage time, defines the Torricelli number as a shape invariant, and constructs specific solids for use in asymmetrical clepsydrae.
Findings
Derived integral inequalities for drainage time.
Introduced the Torricelli number as a shape invariant.
Constructed solids for asymmetrical clepsydrae.
Abstract
We derive integral inequalities governing drainage time in convex solids, inspired by Torricelli's Law, and introduce the Torricelli number as a shape invariant. We use these considerations to construct a class of solids that can be used in building asymmetrical clepsydrae.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic and Geometric Analysis · History and Theory of Mathematics