SIMIODE: Resources

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1-064-TorricelliBox-ModelingScenario

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.

groundwater flowcolumn of waterTorricelli's Lawwater displacementsubmerged box

Modeling Scenario

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1-058-WaterClocks-ModelingScenario

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.

flowTorricelli's Lawspigotswater clock

Modeling Scenario

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6-030-SaltAndTorricelli-ModelingScenario

We build on a model for the height of a falling column of water with a small hole in the container at the bottom of the column of water. We use data from one video of a falling column of water.

whole picturetankmixingflowcolumn of watersalt mixinggraduated cylinderapertureTorricelli's Law

Modeling Scenario

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1-057-FiguringFluidFlow-ModelingScenario

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.

dischargetankTorricelli's LawConservation of Energyfluid flowheightliquid

Modeling Scenario

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1-029-ConeToCubeFlow-ModelingScenario

An inverted right circular cone with a hole at the bottom is suspended above an open-topped cube which also has a hole in the center of the bottom. The cone is filled with water and we model water flow from cone to cube and out the bottom of the...

waterflowTorricelli's Lawconecube

Modeling Scenario

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1-015-Torricelli-ModelingScenario

We help students develop a model (Torricelli's Law) for the height of a falling column of water with a small hole in the container at the bottom of the column of water through which water exits the column.

dataSpanishtankcolumn of waterapertureTorricelli's LawConservation of EnergytSolverwater flowExcel Solver

Modeling Scenario

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1-059-ContainerShapeFallingWater-ModelingScenario

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.

containersTorricelli's Lawshapedischarge coefficient

Modeling Scenario

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1-051-OneTankSaltModel-ModelingScenario

A large tank initially contains 60 pounds of salt dissolved into 90 gallons of water. Salt water flows in at a rate of 4 gallons per minute, with a salt density of 2 pounds per gallon. The incoming water is mixed in with the contents of the tank...

compartmentsalttankmixingflow

Modeling Scenario

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1-140-LeakyBucket-ModelingScenario

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.

flowTorricelli's Lawleaky bucket

Modeling Scenario

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1-073-WaterExitBottle-ModelingScenario

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.

datawaterflowTorricelli's Lawbottle

Modeling Scenario

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1-074-BottleWaterFlow-ModelingScenario

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.

bwaterTorricelli's Lawbottle

Modeling Scenario

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9-030-WaterHammer-ModelingScenario

We develop and apply a numerical algorithm that solves a system of two nonlinear partial differential equations (PDEs) that describes the time evolution of the water hammer phenomenon.

Stock and Flow modelhyperbolic equationsfinite differenceswater hammerhydrodynamicscompressibilitywave celerity

Modeling Scenario

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1-014-DrainingContainers

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?

containerstankflowTorricelli's Lawdrainingfixed volume

Modeling Scenario

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1-042-KoolAid-ModelingScenario

Students run experiments involving concentrated solution of drink powder flowing from upper to lower tank, initially filled with plain water. They make qualitative observations about the intensity of the color in the tanks, record data, and build...

concentrationcompartmenttanksKoolAid

Modeling Scenario

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5-025-SaltCompartments-ModelingScenario

Model a phenomena in which salt mixtures from two tanks are mixed using several strategies.

compartmentsalttanks

Modeling Scenario

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4-060-CircuitTuner-ModelingScenario

We present essential definitions and laws for the study of simple RLC electrical circuits and build a differential equation model using these notions. We describe how such a circuit can be used to tune a radio to a certain input frequency.

resistanceciircuittuned mass tunerfrequencyKirchhoffvoltagegainfrequency responseamplitudes Voltage LawinductancecapacitorI am currently working in redesining an existing microbiology course. I would like to be part of ed

Modeling Scenario

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1-090-EmptySphericalTank-ModelingScenario

We model the emptying of water from a spherical tank. First, we pump out water at a constant rate. Second, we allow the water to exit through a small hole in the bottom of the tank. We seek to determine how fast the water level is falling in both...

VolumesphereTorricelli's Lawtimingspherical tankfluidempty

Modeling Scenario

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1-063-ThreeHoleColumnOfWater-ModelingScenario

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.

fallingcolumn of waterTorricelli's Lawmultiple spigotsspigots

Modeling Scenario

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7-040-TankInterruptMixing-ModelingScenario

We present a first order differential equation model for the interrupted mixing of a tank with salt water. We offer two solution strategies (1) two step approach and (2) Laplace Transforms.

Laplace transforminverse Laplace Transformsalttankmixinginterrupt

Modeling Scenario

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3-070-FallingInWater-ModelingScenario

We model a small canister with ballast to keep it vertical as it falls through water in a graduated cylinder filled with water. We suggest several models in terms of resistance due to the media and estimate appropriate parameters.

datawaterresistancefallingbuoyancymass

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1-064-TorricelliBox-ModelingScenario

1-058-WaterClocks-ModelingScenario

6-030-SaltAndTorricelli-ModelingScenario

1-057-FiguringFluidFlow-ModelingScenario

1-029-ConeToCubeFlow-ModelingScenario

1-015-Torricelli-ModelingScenario

1-059-ContainerShapeFallingWater-ModelingScenario

1-051-OneTankSaltModel-ModelingScenario

1-140-LeakyBucket-ModelingScenario

1-073-WaterExitBottle-ModelingScenario

1-074-BottleWaterFlow-ModelingScenario

9-030-WaterHammer-ModelingScenario

1-014-DrainingContainers

1-042-KoolAid-ModelingScenario

5-025-SaltCompartments-ModelingScenario

4-060-CircuitTuner-ModelingScenario

1-090-EmptySphericalTank-ModelingScenario

1-063-ThreeHoleColumnOfWater-ModelingScenario

7-040-TankInterruptMixing-ModelingScenario

3-070-FallingInWater-ModelingScenario

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