Leaky Bucket - Student Expectations

The general purpose of this lab exercise is to

1. Introduce the concepts of a mathematical model of a physical system,

2. Instill in you the value of multiple working hypotheses and alternative models,

3. Force you to confront the messy attributes of real world data as they relate to quantitative predictions, and

4. Give you more practice in technical, scientific report writing.

The following specific objectives of the leaky bucket model will determine what kinds of models you build and how you go about testing them.

1. The question of interest is: ``Will the poor students correctly predict the time required for the bucket to empty, and thereby save their lives?''

2. To solve the problem, the students will create 2 models (or more, but 2 is plenty) which will allow the students to determine the emptying time. The models must be ``signficantly different'' from each other.

3. The students will have the opportunity to calibrate their models (i.e., estimate parameters) on data they collect.

4. The models, however, must be apply to different containers which were not available when the models were created and calibrated. These new containers will differ from the first by having holes of different sizes, number, and shapes. The container shapes will be similar. In other words, the models must have a minimal degree of ``generality'' in the sense that they will work on these new containers.

The tasks to complete are:

1. Define the models
2. Define the experimental protocol needed to estimate the parameters
3. Do the measurements and estimate the parameters
4. Verify that the model does ``acceptably well'' (to be defined by the modelers) on the original containers
5. Apply the models to the new containers supplied by the Evil Genius
6. Answer the questions: ``Did we survive the guillotine?'' and ``Which model did best? Why?''
7. Write it up nicely as a Mathematica Notebook