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Downloads
Views
Date
Relevance
Modeling Scenario
227
views
134
downloads
0
comments
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
Modeling Scenario
192
views
172
downloads
0
comments
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
Modeling Scenario
376
views
861
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
139
views
46
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
Modeling Scenario
139
views
57
downloads
0
comments
1-036-NeutralBuoyancy-ModelingScenario
An object may hang suspended at, say, ten foot depth in a column of water if at ten feet underwater the density of the object equals the density of water. We study this phenomenon
Density
buoyancy
Archimedes’ Principle
float
neutral buoyance
Modeling Scenario
236
views
154
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
Modeling Scenario
218
views
146
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
227
views
237
downloads
0
comments
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...
Volume
sphere
Torricelli's Law
timing
spherical tank
fluid
empty
Modeling Scenario
356
views
229
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
Potential Scenario
133
views
48
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
265
views
173
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
Potential Scenario
105
views
35
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
121
views
41
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
173
views
60
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
Modeling Scenario
247
views
196
downloads
0
comments
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.
data
water
resistance
falling
buoyancy
mass
Potential Scenario
94
views
30
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
252
views
243
downloads
0
comments
1-110-TidePoolSnails-ModelingScenario
Students use linear differential equations to model temperature change, in a sand tide pool and inside the shell of a snail in the tide pool. We offer data on temperature in a tide pool as the sun heats the water. Students model the tide pool's...
data
snails
temperature
Newton's Law of Cooling
cooling
Newton
warming
tital pool
tide pool
Modeling Scenario
319
views
202
downloads
0
comments
1-142-WaterBottles-ModelingScenario
This project involves the application of Newton's law of cooling to the study of insulated water bottles. Students have the option to conduct experiments with their own bottles outside of class or use data included in the student version.
data collection
experiment
half-life
Newton's Law of Cooling
water bottle
Modeling Scenario
233
views
220
downloads
0
comments
1-052-SaltWaterTanks-ModelingScenario
We offer three mixing problems, of increasing order of difficulty, in which salt is coming into a tank of water and upon instantaneous mixing is leaving the tank.
salt
tank
mixing
Modeling Scenario
300
views
306
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
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