SCI : Burette Races - Case Notes

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Author - Caleb Arrington/John Shepherd - Summer 1998

Background The rate of water release depends on the height of the water column, since this determines the pressure at the nozzle. The volume decreases according to an exponential decay model; the time increases exponentially as a function of the volume. The form of the graph and equation imply the nature of the process underlying the behavior of the system.

1998 Teaching Notes Each group is given their materials and the burettes are filled with water (to different heights). Reading volumes is explained. The groups are asked to determine how long it will take for 10 ml to run out the burette. When they get different answers, they are asked to explain the differences (different starting points?). They are then asked to describe the phenomenon (water running out the bottom) in such a way that they can accurately (and fairly precisely) predict it will take for a given (but unknown) volume to run out from a given (but unknown) starting point. They have 30 minutes to produce a result. At the end of the allotted time, you will set a starting point and give them a volume to release. They predict the result and then you time the actual release to see how good a prediction they made. Their grade depends on how accurate their prediction is and their are bonus points for the group with the most accurate prediction.

This is quickest if you only give the group plain graph paper and tell them to draw graph that shows the volume of water in the burette at various times after the stopcock is opened. With more sophisticated students, this can be done in a lab where the students can enter their data directly into a spreadsheet. If they know how to use a spreadsheet, they can draw a graph and fit a line to it. they will thus have both an algebraic and graphic model of the burette.

After predictions are tested, a discussion can center around the difference between this sort of descriptive model, and theory which has explanatory power. They could be asked to talk about the components of a model that explained system behavior in physical and mechanical terms.

This took 2 50-minute class periods, but could be done in one 75-minute class.  I would suggest using deionized water to avoid clogging the burettes as the day wears on.   If the exercise is done over two class periods, it is important that each group be able to identify, and reclaim, the same burette.

2004 Teaching Notes Each group is given the printed directions and burette filled with colored water. Reading volumes is explained.  Generally they try letting all the fluid run out and think it will be pretty simple to estimate the time to release x ml of water.  It takes most groups 10 to 15 minutes to realize that the time depends on the starting point: fluid runs out quickly when the burette is nearly fully and slowly when it is nearly empty.  They also realize along the way that it makes a big difference how they work the stopcock and timer.  This makes prediction much more difficult.  I've (JDS) this 10-15 times.  Most groups end up with some ad hoc calculations that estimate the time per ml in different segments of the burette.  A few groups draw a graph of height vs time and interpolate the time required.  Only once did a group fit a polynomial regression to the times.  In a 75 minute class, the winning time is usually well within a second.  Predictions that are off by 3 seconds are mediocre at best.  To by off by more than 5 seconds requires a pretty poor empirical model. 

I generally ask them to run out 20-25 ml, carefully choosing starting and ending points that are not round numbers.  For example, they might be asked to start at 17 and run it out to 43.  Each group does its own timing so they can use the same techniques they used in their model-building.  The person with the stopwatch is not allowed to look at the watch during the timing.  I usually also have an observer from another group watch them do it and read the result.

They like the competitive part of this exercise.  They also feel the pressure of making a public prediction - the embarrassment or "public humiliation" if they are way off  and the "triumph" of being right.  When the results are in, it's a good time to relate this to Watson-Crick's experience with their 3-chain model of DNA. 

Their models are not "explanatory" in the way real theories are.  They concoct ad hoc empirical models.  They realize by the end that the height of the water column determines how fast the water runs out.  With some prompting, they can see that the model a physicist might create in this situation (although perhaps not in 60 minutes) would be an equation that related time to height, nozzle diameter, fluid viscosity, etc.  Such an equation would, in fact, be an explanation as well as a predictive device.