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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.

discharge tank Torricelli's Law Conservation of Energy fluid flow height liquid

Modeling Scenario

106

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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.

flow Torricelli's Law spigots water clock

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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.

containers Torricelli's Law shape discharge coefficient

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1-060-SalesMarketing-ModelingScenario

We lead students through a sales forecasting model based on marketing principles first espoused by F. M. Bass with definitions, assumptions, equations, and data on sales over 15 year periods against which models may be tested.

marketing Bass model sales consumer products innovators imitators

Modeling Scenario

104

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1-062-BacteriaGrowth-ModelingScenario

We offer students a simulation experience or data from a simulation and ask them to model the simulation using several approaches: exponential growth fit, difference equation, differential equation, and parameter estimation using EXCEL spreadsheet.

bacteria exponential growth

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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.

falling column of water Torricelli's Law multiple spigots spigots

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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 flow column of water Torricelli's Law water displacement submerged box

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1-065-AlgalBlooms-ModelingScenario

This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, starting in 1994.

direction fields tool:dfield algae harmful algae blooms population compartment Lake Chapala

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1-066-USCensusModeling-ModelingScenario

The United States Census, conducted every 10 years, gives data on the United States population, that can be modeled with the exponential, logistic, or Gompertz functions.

data logistic population Gompertz census goodness of fit

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1-067-ModelingWithSigmoidCurves-ModelingScenario

The assignment considers two well-known models of population growth, Verhulst-Pearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or S-shape.

logistic Gompertz sigmoid Verhulst-Pearl

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1-068-WaterBottleCooling-ModelingScenario

Students create of a differential equation describing how fluid in a water bottle will change its temperature to approach the ambient temperature in a room.

b Newton's Law of Cooling water bottle autonomous bottle

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1-071-NewtonWatson-ModelingScenario

Sherlock Holmes determines the time of death for a body found on a street in London and we need to reproduce his astute analysis

temperature death Newton's Law of Cooling time of death Sherlock Holmes

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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.

data water flow Torricelli's Law bottle

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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.

b water Torricelli's Law bottle

Modeling Scenario

103

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1-077-RLMSimSeriesCircuit-ModelingScenario

In this validation setup, the first order linear ordinary differential equation governing a small signal RL series AC circuit is solved analytically and the results are compared with the data acquired from analyzing the numerical model (using...

Measurement circuit voltage current validation SPICE RL circuit Multilsim