The Physics behind fluids

This week, we spent some time discussing the role of asking questions and being wrong in the scientific endeavor. I learned about the various cultures at schools regarding these … are questions and wrongness scorned? Accepted? Embraced? We hopefully came to understand that not only should "not knowing and being wrong" be accepted and embraced, but that that they are the very defining characteristic of the process of science.

We then revisited the topic of "vortices" that came up last week: I showed an example of a 2-dimensional vortex formed in a model system called the "lid-driven cavity". I hope this was an interesting example, as it is a classic problem that is still invoked in modern academic papers on the topic of computational fluid mechanics.

For the rest of our time, we set up the basic elements of the experimental system I want to take us through for the next several sessions: flow of water through a tube from a raised reservoir. From empty gallon jugs, cheap tubing from Lowes, and a hot glue gun, the students rigged up a worthy experimental apparatus for exploring this system.

Using this apparatus, we first practiced measuring our main experimental outcome, or dependent variable, the flow rate of water coming out of the tube exit when it was near the ground (left image). Then, we challenged our intuition on what would happen if we raised the tube above the level of the reservoir sitting on the table (middle image). Rather than ceasing to flow as we expected, the flow seemed unaffected, and we measured almost the same flow rate as before.

To try to understand this unexpected result, we decided to re-do the same experiments starting from an empty tube and measuring the time it takes for water front to traverse the tube length, but when the tube fell to the ground, and when part of the tube was raised above the reservoir. Here we learned the hard way that experiments never go smoothly, and we made a mess while poor Caleb had a lung exercise to clear the water from the tubes! When we finally got the experiment working, we noticed that when the tube was raised, water flowed up the tube only to the same height as the reservoir (right image). We played around with the tube until we got water over the highest point, after which it flowed completely through the tube.

Next week, we are going to formalize our understanding of this phenomenon and recalibrate our intuitions. We will then work to develop a quantitative understanding of exactly what independent variables will affect the flow rate, and execute systematic experiments to probe these effects. Once we get enough data, we will dive into the mathematics that describe the results and later the mathematics that predict the results!