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1. 09 Dec 2019 | Technique Narratives

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. 15 Dec 2018 | Modeling Scenarios

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. 03 Mar 2018 | Potential Scenario Ideas

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. 26 Nov 2017 | Potential Scenario Ideas

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. 09 Oct 2017 | Potential Scenario Ideas

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. 12 Sep 2017 | Potential Scenario Ideas

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. 11 Sep 2017 | Potential Scenario Ideas

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. 11 Sep 2017 | Potential Scenario Ideas

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. 09 Sep 2017 | Potential Scenario Ideas

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. 09 Sep 2017 | Potential Scenario Ideas

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. 08 Sep 2017 | Potential Scenario Ideas

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. 08 Sep 2017 | Potential Scenario Ideas

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. 08 Sep 2017 | Potential Scenario Ideas

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. 05 Sep 2017 | Potential Scenario Ideas

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. 14 Aug 2017 | Modeling Scenarios

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.

16. 17 Apr 2017 | Modeling Scenarios

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.

17. 17 Apr 2017 | Modeling Scenarios

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.

18. 17 Mar 2017 | Modeling Scenarios

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?''

19. 26 Nov 2016 | Modeling Scenarios

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...

20. 25 Nov 2016 | Modeling Scenarios

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.