Citation

Modeling water flow from a clepsydra in Calculus II

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Abstract:

A clepsydra, or water clock, is a clear container from which water flows out of a hole at the bottom. Markings on the side of the container indicate intervals of time. It is well known that Torricelli's Law and calculus can be used to find the optimal shape of a radially symmetric clepsydra so that equally-spaced markings correspond to equal time intervals. We will discuss a lab that asks students to model and predict water flow for a cylindrical clepsydra, as well as other extensions. This lab expects students to develop an approach, collect data using a limited amount of water and a two-liter bottle, formulate a mathematical model, and then solve the model using integration. In the next class period, students then verify their solution. Extensions include considering a non-cylindrical clepsydra that is a solid of revolution, as well as analyzing a multi-level clepsydra with the help of direction fields. This lab provides opportunities for students to use a graphing calculator, spreadsheet, or computer algebra system.
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Association:
Name: The Mathematical Association of America MathFest
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http://www.maa.org


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URL: http://citation.allacademic.com/meta/p522067_index.html
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MLA Citation:

Hollenbeck, Brian. "Modeling water flow from a clepsydra in Calculus II" Paper presented at the annual meeting of the The Mathematical Association of America MathFest, Lexington Convention Center, Lexington, KY, Aug 04, 2011 <Not Available>. 2014-11-25 <http://citation.allacademic.com/meta/p522067_index.html>

APA Citation:

Hollenbeck, B. , 2011-08-04 "Modeling water flow from a clepsydra in Calculus II" Paper presented at the annual meeting of the The Mathematical Association of America MathFest, Lexington Convention Center, Lexington, KY <Not Available>. 2014-11-25 from http://citation.allacademic.com/meta/p522067_index.html

Publication Type: Conference Paper/Unpublished Manuscript
Review Method: Peer Reviewed
Abstract: A clepsydra, or water clock, is a clear container from which water flows out of a hole at the bottom. Markings on the side of the container indicate intervals of time. It is well known that Torricelli's Law and calculus can be used to find the optimal shape of a radially symmetric clepsydra so that equally-spaced markings correspond to equal time intervals. We will discuss a lab that asks students to model and predict water flow for a cylindrical clepsydra, as well as other extensions. This lab expects students to develop an approach, collect data using a limited amount of water and a two-liter bottle, formulate a mathematical model, and then solve the model using integration. In the next class period, students then verify their solution. Extensions include considering a non-cylindrical clepsydra that is a solid of revolution, as well as analyzing a multi-level clepsydra with the help of direction fields. This lab provides opportunities for students to use a graphing calculator, spreadsheet, or computer algebra system.


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