
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.

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...

2000deOliveraEtAlPinholeWaterFlowFromCylindricalBottles
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): 110119.From the opening of the article, "We performed an experiment on elementary hydrodynamics. The basic...

2012UrbanoThe Draining of a Plastic Bottle
09 Oct 2017   Contributor(s):: Brian Winkel
2012Urbano, Lensyl. The Draining of a Plastic Bottle: Integrating a Physics Experiment into Calculus. Montessori Muddle. http://montessorimuddle.org/2012/05/01/thedrainingofajugintegratingaphysicsexperimentintocalculus/ . Accessed 9 October 2017.Abstract: I punched a small hole...

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...

2001KerleyKnisleyUsing 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): 111123.Abstract: Although data is often used to estimate parameters for models in calculus and differential equations, the models themselves are seldom...

2015UnpropogandaFilling and Draining Spherical Tank
11 Sep 2017   Contributor(s):: Brian Winkel
2015UnpropogandaMore on Filling a Spherical Tank, and Gravitational Drainage of a Spherical Tank. https://unpropaganda.wordpress.com/2015/06/14/moreonfillingasphericaltankandgravitationaldrainageofasphericaltank/ . Accessed 10 September 2017.One of several interesting columns...

PennelDifferential 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...

1999HaninWhichTankEmptiesFirst
09 Sep 2017   Contributor(s):: Brian Winkel
Hanin, Leonid G. 1999. Which tank empties first? The American Mathematical Monthly. 106(10): 943947. 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...

Math2300Torrielli'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...

Gustafson2250 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...

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,...

1992SommerfeldVesselDraining
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 is...

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...