
2020Winkel, 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/scudemaccordion.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...

2005TextSLinearizeItAll
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...

1063SThreeHoleColumn
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.

2000deOlivera, 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): 110119.See http://seniorphysics.com/physics/pinhole_water_flow.pdf .From the opening of the...

2012Urbano, 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/thedrainingofajugintegratingaphysicsexperimentintocalculus/ . Accessed 9 October 2017.Abstract: I...

2001Knisley, 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): 111123.See https://www.tandfonline.com/doi/abs/10.1080/10511970108965983 .Abstract: Although data is often used to estimate parameters for models in...

2015Unpropoganda  More on Filling a Spherical Tank, and Gravitational Drainage of a Spherical Tank.
11 Sep 2017   Contributor(s):: Brian Winkel
2015UnpropogandaMore 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...

2017Pennel, 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...

1999Hanin, 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): 943947. 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...

1999KowalczykHausknechtUsing 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 RealWorld Data. Proceedings of the Tenth Annual International Conference on Technology in Collegiate Mathematics. Reading MA: AddisonWesley Publishing Co. pp. 246250Opening of article,...

1992Sommerfeld, 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: 3033.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...

1057SFiguringFluidFlow
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.

1064STorricelliBox
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.

1074SBottleWaterFlow
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.

1073SWaterExitBottle
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.

1014SDrainingContainers
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?''

1058SWaterClocks
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...

1140SLeakyBucket
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.

1059SContainerShapeFallingWater
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.

1090SEmptySphericalTank
12 Nov 2016   Contributor(s):: Brian Winkel