Tags: Torricelli's Law

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  1. 2-005-Text-S-LinearizeItAll

    09 Dec 2019 | | Contributor(s):: Don Hickethier

    Linear approximations are often used to simplify nonlinear ordinary differential equations (ODEs) for ease in analysis. The resulting linear approximation produces an ODE where closed form solutions may be obtained. A simple model using Torricelli's Law will compare the exact solution to...

  2. 1-063-S-ThreeHoleColumn

    15 Dec 2018 | | Contributor(s):: Brian Winkel

    We consider a column of water with three holes or spigots through which water can exit and ask students to model the height of the column of water over time.

  3. LeakingBucket: Differential Equations in Engineering

    03 Mar 2018 | | Contributor(s):: Unknown

    Differential Equations in Engineering: The Leaking Bucket. Laboratory Experiment. 4 pp.From the Text:7.1 Laboratory ObjectiveThe objective of this laboratory is to learn about first order differential equations and theirapplication to a leaking bucket. 7.2 Educational ObjectivesAfter...

  4. 2000-deOliveraEtAl-PinholeWaterFlowFromCylindricalBottles

    26 Nov 2017 | | Contributor(s):: Brian Winkel

    2000. deOlivera, Paulo Murilo Castro, Antonio Delfino, Eden Vieira Costa and Carlos Alberto Faria Leite.  Pinhole Water Flow From Cylindrical Bottles. Phys.Educ. 35(2): 110-119.From the opening of the article,  "We performed an experiment on elementary hydrodynamics. The basic...

  5. 2012-Urbano-The Draining of a Plastic Bottle

    09 Oct 2017 | | Contributor(s):: Brian Winkel

    2012-Urbano, Lensyl. The Draining of a Plastic Bottle: Integrating a Physics Experiment into Calculus.  Montessori Muddle. http://montessorimuddle.org/2012/05/01/the-draining-of-a-jug-integrating-a-physics-experiment-into-calculus/ . Accessed 9 October 2017.Abstract: I punched a small hole...

  6. Math Modeling with Differential Equations - Interesting Tank Problem

    12 Sep 2017 | | Contributor(s):: Brian Winkel

    Math Modeling with Differential Equations - Interesting Tank ProblemMath Modeling with Differential Equations - Interesting Tank Problem . Class Notes on five problems.,Several models are workd out including exponential decay, bullet traveling with resisitance, This material contains a solution...

  7. 2001-KerleyKnisley-Using data to motivate models in differential equations

    11 Sep 2017 | | Contributor(s):: Brian Winkel

    Knisley, Jeff and Lyndell Kerley. 2001.  Using data to motivate the models used in introductory differential equations. PRIMUS. 11(20): 111-123.Abstract: Although data is often used to estimate parameters for models in calculus and differential equations, the models themselves are seldom...

  8. 2015-Unpropoganda-Filling and Draining Spherical Tank

    11 Sep 2017 | | Contributor(s):: Brian Winkel

    2015-Unpropoganda-More on Filling a Spherical Tank, and Gravitational Drainage of a Spherical Tank. https://unpropaganda.wordpress.com/2015/06/14/more-on-filling-a-spherical-tank-and-gravitational-drainage-of-a-spherical-tank/ . Accessed 10 September 2017.One of several interesting columns...

  9. Pennel-Differential Equations First Order Applications

    09 Sep 2017 | | Contributor(s):: Brian Winkel

    Pennel, Steve. Differential Equations:  Applications of First Order Differential Equations. Notes. 44 p. Universiyt of Massachusetts, Lowel.This is a set of modeling activities with derivations, Matlab code, and mathematical details covering the following topics: Newton’s Second...

  10. 1999-Hanin-WhichTankEmptiesFirst

    09 Sep 2017 | | Contributor(s):: Brian Winkel

    Hanin, Leonid G. 1999. Which tank empties first?  The American Mathematical Monthly.  106(10): 943-947.  Preprint.From the opening of the paper, “Suppose that water towers like those shown in Figure 1 are initially filled with water and have the same volume, height, and...

  11. Math2300-Torrielli'LawExercises

    08 Sep 2017 | | Contributor(s):: Brian Winkel

    Math2300- Torricelli’s Law Exercises. University of Colarado.  https://math.colorado.edu/math2300/projects/2300Project12ToricelliSol.pdf . Accessed 7 September 2017.This is a set of completely worked out exercises which could be the basis for a Modeling Scenario based on...

  12. Gustafson-2250 EngineeringMathematicsApplications

    08 Sep 2017 | | Contributor(s):: Brian Winkel

    Gustafson, G. B. Science and Engineering ApplicationsSection 2.8.  http://www.math.utah.edu/~gustafso/2250SciEngApplications.pdf . Accessed 8 September 2017.This material is from a wealth of other material authored by Grant B. Gustafson in the Mathematics Department at the University of...

  13. 1999-KowalczykHausknecht-Using DEs To Model Real World Data

    08 Sep 2017 | | Contributor(s):: Brian Winkel

    Kowalczyk, Robert E.  and Adam O. Hausknecht. 1999. Using Differential Equations to Model Real-World Data. Proceedings of the Tenth Annual International Conference on Technology in Collegiate Mathematics.  Reading MA: Addison-Wesley Publishing Co. pp. 246-250Opening of article,...

  14. 1992-Sommerfeld-VesselDraining

    05 Sep 2017 | | Contributor(s):: Brian Winkel

    Sommerfeld, Jude. 1992. More Applied Math Problems on Vessel Draining. Chemical Engineering Education. Winter: 30-33. From a chemical engineering point of view emptying processing and storage tanks is important and this article considers many issues and shapes of containers. The main interest is...

  15. 1-057-S-FiguringFluidFlow

    15 Aug 2017 | | Contributor(s):: Brian Winkel

    We propose three differential equations models for the height of a column of falling water as the water exits a small bore hole at the bottom of the cylinder and ask students to determine which model is the best of the three.

  16. 1-064-S-TorricelliBox

    14 Aug 2017 | | Contributor(s):: Brian Winkel

    The time it takes a column of water to empty and the time it takes the same volume of column of water with a box (various sizes) submerged in the column of water are compared through modeling with Torricelli's Law.

  17. 1-074-S-BottleWaterFlow

    17 Apr 2017 | | Contributor(s):: Brian Winkel

    We offer an experiment in which data is collected to ascertain a parameter in the differential equation formulation of Torricelli's Law for water flow from a container.

  18. 1-073-S-WaterExitBottle

    17 Apr 2017 | | Contributor(s):: Brian Winkel

    We offer an experiment in which data is collected to ascertain a parameter in the differential equation formulation of Torricelli's Law for water flow out of a cylindrical container.

  19. 1-014-S-DrainingContainers

    17 Mar 2017 | | Contributor(s):: Brian Winkel

    We examine the question, ``Given two rectangular circular cylinders of water with the same volume, but different radii, with a small bore hole of same radius on the center of the bottom through which water exits the cylinder, which empties faster?''

  20. 1-058-S-WaterClocks

    26 Nov 2016 | | Contributor(s):: Sania Qureshi, Brian Winkel

    We apply Torricelli's Law to the task of building a water clock in which the height of the water in a container falls at a constant rate when the container has a hole in the bottom to let the water flow out. First, we review the principles and derivation of the applicable physics in...

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