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Downloads
Views
Date
Relevance
Modeling Scenario
216
views
137
downloads
0
comments
6-035-Shampoo-ModelingScenario
We ask students to model the amount of shampoo in a bottle if when we shower we do not cover the opening at the top of the bottle while in the shower.
shampoo
diluation
shower
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
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
Modeling Scenario
245
views
157
downloads
0
comments
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
Modeling Scenario
371
views
292
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
262
views
162
downloads
0
comments
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
Modeling Scenario
278
views
201
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
Modeling Scenario
247
views
183
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
Potential Scenario
121
views
70
downloads
0
comments
2015-Goodnow-EtAl-Mathematical Models of Water Clocks
This is a historical tour of water clocks, known as clepsydra a Greek word meaning water thief. These devices were for telling time.
Torricelli's Law
water clock
Bernoulli's Law
clepsydra
Modeling Scenario
246
views
140
downloads
0
comments
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 picture
tank
mixing
flow
column of water
salt mixing
graduated cylinder
aperture
Torricelli's Law
Modeling Scenario
250
views
267
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
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
278
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
432
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
152
views
46
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
Modeling Scenario
298
views
209
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
Modeling Scenario
220
views
227
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
Article or Presentation
200
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
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