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Downloads
Views
Date
Relevance
Modeling Scenario
298
views
208
downloads
0
comments
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
Article or Presentation
187
views
83
downloads
0
comments
1979-Brian_Winkel-Elementary_My_Dear_Watson_Differential_Equation
Sherlock Homes explains to Doctor Watson how he solves a murdermystery using Newton's Law of Cooling.
Newton's Law of Cooling
Sherlock Holmes
time of detah
Modeling Scenario
309
views
175
downloads
0
comments
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
Potential Scenario
154
views
59
downloads
0
comments
2006-G_Ashline-J_Ellis-Monaghan-How high-fast-long-Modeling water rocket flight with calculus
We describe an easy and fun project using water rockets to demonstrate applications of single variable calculus concepts.
calculus
Flight
projectile
water rocket
Modeling Scenario
404
views
277
downloads
0
comments
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...
water
flow
Torricelli's Law
cone
cube
Modeling Scenario
251
views
185
downloads
0
comments
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
431
views
1060
downloads
0
comments
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.
data
Spanish
tank
column of water
aperture
Torricelli's Law
Conservation of Energyt
Solver
water flow
Excel Solver
Potential Scenario
149
views
45
downloads
0
comments
1999-Leonid_Hanin-Which tank empties first
Suppose that water towers like those shown in the opening are initially filled with water and have the same volume, height, and cross-sectional outlet area. Which one empties first?
tank
Torricelli's Law
spherical tank
empty
frustrum of cone
cylinder
Article or Presentation
199
views
582
downloads
1
comments
2020-TeachingModule-ModelingFallingColumnOfWater
We discuss how to model a falling column of water empirically and analytically from first principles in physics laws.
module
column of water
Torricelli's Law
Torricelli
Teaching Module
Modeling Scenario
278
views
198
downloads
0
comments
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
Potential Scenario
156
views
72
downloads
0
comments
2012-Lensyl-Urbano-The Draining of a Plastic Bottle-Integrating a Physics Experiment into Calculus
I punched a small hole (about 1mm radius) in a one gallon plastic bottle and had my students measure the rate at which water drained.
in-class activity
experiment
Torricelli's Law
cylinder of water
expderiment
Potential Scenario
163
views
69
downloads
0
comments
2009-G_Recktenwald-Tank Draining Exercise
This paper describe deep mathematics, including differential equations concerned with modeling the draining of tank and the shape of the water coming out the bore hole at the bottom of the tank of water.
laboratory
tank
LabView
Bermoulli equation
empty draining
column of liquid
pressure
Potential Scenario
208
views
99
downloads
0
comments
2018-Chris McCarthy-Newtons Law of Cooling
You have hot water (initial temperature ) in a container, say a cup or glass. The temperature in the room is cooler, say a constant degrees Celsius. Come up with a differential equation that models the water's temperature.
data
water
Newton's Law of Cooling
cooling
Potential Scenario
128
views
69
downloads
0
comments
2000-deOlivera-Delfino-Costa-Leite-Pinhole Water Flow From Cylindrical Bottles
The water flowing from the first bottle feeds the second one located below it. The same concepts of mass and energy conservation now lead to a non-trivial differential equation for the lowest bottle dynamics.
Torricelli's Law
Conservation of Energyt
Conservation of Mass
Bernoulli’s Theorem
Potential Scenario
112
views
37
downloads
0
comments
2004-Hill-Lozowski-Sampson-Experiments on ice spikes and a simple growth model
We observed ice-spike growth using time-lapse digital photography, using two water types in two different containers.
ice
ice spike
bulk heat transfer
mass conservation
Modeling Scenario
343
views
414
downloads
0
comments
3-006-Buoyancy-ModelingScenario
We offer data from a physical experiment in which the depth of a container in water is measured and ask students to build a model of buoyancy based on Newton's Second Law of Motion and a Free Body Diagram. We ask students to estimate the parameters.
data collection
experiment
buoyancy
Newton's Second Law of Motion
Modeling Scenario
376
views
301
downloads
0
comments
1-026-Evaporation-ModelingScenario
We provide data on evaporation of 91% isopropyl alcohol in six different Petri dishes and one conical funnel and on evaporation of water in one Petri dish. We ask students to develop a mathematical model for the rate of change in the respective...
evaporation
cone
alcohol
Petri dish
Modeling Scenario
255
views
283
downloads
0
comments
1-055-WaterFallingInCone-ModelingScenario
We offer an opportunity to model the height of a falling body of water in a right circular cone (funnel) and to estimate an appropriate parameter based on data collected from a video of the experiment found on YouTube.
Torricelli's Law
discharge coefficient
cone
contraction coefficient
Modeling Scenario
230
views
151
downloads
0
comments
6-028-SaltCompartments-ModelingScenario
Model a phenomena in which salt mixtures from two tanks are mixed with changing volumes of water.
concentration
comparment
salt
tank
mixing
Modeling Scenario
277
views
200
downloads
0
comments
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
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