Tags: Torricelli

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  1. 2020-Winkel, Brian - Remote Teaching Module - Modeling a Falling Column of Water

    07 Jun 2020 | | Contributor(s):: Brian Winkel

    {xhub:include type="stylesheet" filename="pages/resource.css"}{xhub:include type="stylesheet" filename="pages/scudem-accordion.css"}We place here and in the Supporting Docs all the materials in support of the SIMIODE Remote Teaching Module - Modeling the Falling Column of Water.This module...

  2. 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...

  3. 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.

  4. 2000-deOlivera, Paulo Murilo Castro, Antonio Delfino, Eden Vieira Costa and Carlos Alberto Faria Leite - Pinhole Water Flow From Cylindrical Bottles.

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

    deOlivera, Paulo Murilo Castro, Antonio Delfino, Eden Vieira Costa and Carlos Alberto Faria Leite.  2000. Pinhole Water Flow From Cylindrical Bottles. Phys.Educ. 35(2): 110-119.See http://seniorphysics.com/physics/pinhole_water_flow.pdf .From the opening of the...

  5. 2012-Urbano, Lensyl - The Draining of a Plastic Bottle: Integrating a Physics Experiment into Calculus.

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

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

  6. 2001-Knisley, Jeff and Lyndell Kerley - Using data to motivate the models used in introductory 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(2): 111-123.See https://www.tandfonline.com/doi/abs/10.1080/10511970108965983 .Abstract: Although data is often used to estimate parameters for models in...

  7. 2015-Unpropoganda - More on Filling a Spherical Tank, and Gravitational Drainage of a Spherical Tank.

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

    2015-Unpropoganda-More on Filling a Spherical Tank, and Gravitational Drainage of a Spherical Tank.One of several interesting columns written by an anonymous author on applications of differential equations.Consider the previous post which is referred to in this mentioned post, A Friendly...

  8. 2017-Pennel, Steve - Differential Equations First Order Applications - Notes

    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...

  9. 1999-Hanin, Leonid G. - Which tank empties first? Preprint.

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

    Hanin, Leonid G. 1999. Which tank empties first?  The American Mathematical Monthly.  106(10): 943-947.  Preprint.See https://www.tandfonline.com/doi/abs/10.1080/00029890.1999.12005143 .From the opening of the paper, “Suppose that water towers like those shown in...

  10. 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,...

  11. 1992-Sommerfeld, Jude - More Applied Math Problems on Vessel Draining

    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...

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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?''

  17. 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...

  18. 1-140-S-LeakyBucket

    25 Nov 2016 | | Contributor(s):: Brian Winkel

    We seek to model the height of water in a cylindrical tank (bucket) in which water flows out the bottom of the tank through a small bore hole while we are pouring water into the tank at the top of the tank at a constant (or varying) rate.

  19. 1-059-S-ContainerShapeFallingWater

    22 Nov 2016 | | Contributor(s):: Brian Winkel

    We examine many different physical situations to determine the time it takes a fixed volume of water to flow out of different shape containers through the same size exit hole at the bottom of the container.

  20. 1-090-S-EmptySphericalTank

    12 Nov 2016 | | Contributor(s):: Brian Winkel