Fluids for AP Physics 1: pressure in a static column, demonstration and/or lab

Fluid mechanics is trading places.  Since 2015, fluids has been part of the P2 curriculum, for the 25,000 or so students who take that exam.  But next year, fluids moves over to P1 and its 150,000 students.  So now's probably a good time to share some thoughts about teaching fluids.  

I do recommend coming to an AP Summer Institute, where you can see me do this and other fluids demonstrations live!  You can see my APSI schedule in the left sidebar.

Pressure in a static column

When a tank of fluid is not moving, the pressure anywhere in the fluid is given by P =P0 + ρgy. Here P0 represents the pressure at the surface* of the fluid, ρ is the fluid density, and y is the depth below the surface at the position where you're measuring pressure.  

*Yes, this is *usually* atmospheric pressure... but not always.  Consider one fluid on top of another.  The pressure in the bottom layer is the pressure at *its surface* plus ρgy.

I have one of them giant graduated cylinders filled nearly to the top with water.  My pressure sensor is connected to my ipad under the document camera; I set the Vernier Graphical Analysis app to produce a graph of pressure vs. time.

I attach a long tube to the pressure sensor.  First, I read the pressure when the tube is NOT submerged - this is P0.  The sensor generally reads in kPa; we want a reading in Pa, where 1 Pa is equal to 1 newton per square meter.

Next, I announce that I will predict the pressure sensor reading when the tube is submerged to the very bottom of the container.  The relevant equation is P =P0 + ρgy.  What additional information do we need?

We have the surface pressure - usually around 102,000 Pa, but that varies by weather and especially altitude.  We can measure the depth y with a meterstick - this is usually about 18 cm, i.e. 0.18 m.  We know the gravitational field g to be 10 N/kg.  

What about the density of water?  

AP Physics 1 does not require unit conversions!  The number of times that a student is even asked to give a numerical answer to anything is minimal.  So for this in-class problem where conversions are necessary, I do the conversions in my head and state the result; or I use google ("convert 102 kPa to Pa").  De-emphasize number crunching, and you'll un-de-emphasize concepts.  :-)

That said, thought experiments are well within the scope of AP Physics 1.  Students don't hesitate to volunteer that the density of water is "one."  One what?  The standard units of density are kilograms per cubic meter.  So one kilogram per cubic meter for water, right?

How big is a cubic meter, anyway?  That question provokes several seconds of pure puzzlement, followed by students waving their hands about a meter apart.  "It's as much as you can possibly hug," I say.  Close enough.

So, consider a tank filled with a cubic meter of water - as big a tank as you can possibly hug.  Can you lift that tank?  Oh.  No way.  Well, you can lift a kilogram without trouble - here, catch this 2 pound thing.  That huggable tank doesn't weigh 2 pounds.  No, it weighs a ton.  The density of water is a THOUSAND kilograms per cubic meter.

Back to the calculation.

The gauge pressure at the bottom of the cylinder - gauge pressure means just the ρgy bit, ignoring P0 - is (1000 kg/m^3)(10 N/kg)(0.18 m).  That's 1800 Pa, or 1.8 kPa.  

Thus, the pressure sensor reading should increase from about 102 kPa to 104 kPa.  The actual sensor has a precision in the neighborhood of +/- 0.2 kPa, so this difference will be pretty much dead on when you send the tubing to the bottom.

Follow-up questions include "what's the gauge pressure halfway down?   Greater than, less than, or equal to 0.9 kPa?  Answer?  Equal to: because in ρgy, y is in the numerator and neither squared nor square-rooted, halving y halves the gauge pressure, too.  Sure enough, submerging the tube halfway verifies this prediction.

Physics works.

Make this a laboratory investigation!

Put pressure on the vertical axis, depth on the horizontal.  The slope of the graph should be ρg, and the y-intercept should be atmospheric pressure.  You can use the slope to determine the density of water.  Or, use a different fluid like vegetable oil, and you'll determine the density of the mystery fluid!

Edna meets Mr. Chubbs at the Conceptual Physics Tournament

Will Keay, who teaches in Fairfax, Virginia, came to judge the Woodberry Forest Conceptual Physics Tournament last weekend.  His class pet, Mr. Chubbs, met my pet hippopotamus Edna.  They seemed to like each other.  

We've been doing the tournament as our 9th grade final exam for seven years now.  Feedback from students is universally positive.  They like that they don't sit for yet another two-hour written exam, of course - even though, to a person, they recognize that they work harder to prepare for the tournament than they do for any written exam.  

This year they particularly articulated how much they like the collaborative nature of their preparation.  They get to give presentations and argue about physics with their classmates during their nightly study period.  The process feels social!  It doesn't feel like studying!  Yet, everyone recognizes how much their understanding of their particular physics fight problems - and of physics in general - improves through this social process.

I pointed out that there's nothing stopping these 9th graders from doing similar practice for their history exam as if they were going to have "history fights".  This point met with very confused and skeptical faces.  

The other interesting piece of feedback this year was about the difficulty of the AP-style problems that we posed.  More students than ever said that, once they had dug into the problems for a day or two, they felt easy.  Really!  A couple of students even suggested tougher problems for the following year.  While this peaceful, easy feeling was engineered by design - familiarity over the three-week preparation period breeds comfort - the fact that college-level problems seemed straightforward to general-level 9th graders means the tournament is accomplishing its goal.  We want students to leave physics with a good experience, feeling challenged, but good about meeting the challenge of a difficult subject.  

And, of course, the end-of-year positivity is helped significantly by the invited tournament jurors.  The conceptual physics teachers help students prepare for the tournament, but we don't judge the tournament.  When we give feedback, that feedback is authentic.  "No, you don't *have* to redo your graph, of course not.  But the jurors are more likely to say 'the data points on the graph don't take up anywhere near half a page' than 'oh, I'll bet you spent ten minutes on that graph, you shouldn't have to spend ANOTHER ten minutes making the scale more reasonable.'"  It's always been true that I am the publisher, not the author, of my students' grades.  The large jury, from a pool external to our school, makes my role even more clear.

New online APSI Physics 1 offering - June 24-27, through PWISTA

By popular request, my June 24-27 APSI through PWISTA will now be online.  You can sign up through this link.

Online means you can attend from anywhere, and even bug out for a moment to feed/clean up after the dog/kid.  :-)  Demand was not there for a New York session in person, but we've had a number of requests for another online session!

The PWISTA online session runs synchronously through Zoom from 9am to 3pm each day.  I'm also available for "office hours" from 8:30 each morning, and until 4pm each day.  And I'm happy to arrange for further conversations outside of these times.  As with all institutes, online or in person, you'll get access both to the official College Board materials, AND to my personal files with problem sets, lab activities, quizzes, and tests.  

The AP Physics 1 exam is changing for 2024-25, adding fluid mechanics and a few other minor topics.  And, the exam format will change significantly.  I'll discuss all the changes, but I'll also do all the labs, demonstrations, teaching/culture building tips, etc. that are the hallmark of a Jacobs Physics institute.

Join us in June - you won't be disappointed!  Please feel free to contact me via email with questions.

GCJ

Upperclass AP Physics students in the spring

In the spring, our headmaster reminds us how this is a tremendously emotional time for seniors as they approach a significant ending of one life chapter / beginning of another.  I overheard some parents (from another school) the other day rightly noting how much difficulty their kids are having holding themselves together.  These kids are making a good faith effort to complete so, so many year-end capstone requirements from their classes and their school, on top of life events that matter like proms and sports and social events.  Even seniors who try to be good citizens are being pushed to their mental limits in May.  

What's my reaction to this (unfortunate, I think) feature of 2020s schooling as an AP physics teacher?  I try to make my class one of the most fun parts of the students' day, full of camaraderie.  I'm trying to cash in the culture building I've done for four years with these seniors at our school.  For students who do want to leave the school on a positive note, those who want to work in good faith in each class, they are incredibly happy to be in a comfortable place where they can learn together.  My P2 students are having fond memories of freshman year, when they prepared for AP physics 1 in a similar atmosphere; but their confidence is through the roof now in physics 2, and they know their classmates as true brothers* who've bonded over four years in classes with one another.  

*I'm at a boys' school. You're likely gonna want to use the word "siblings".  :-)

I know, teaching upperclasspeople is not all Care Bears and Smurfs.  Teenagers trying to manage social and parental pressure plus their own boiling crock of hormones can behave in frustrating and nasty ways.  I have to remind myself not to let my seething anger at a few students color my relationships with their classmates who haven't been nasty.  

This year more than ever before, I'm getting the sense that most of my seniors are appreciative of their teachers, their classmates, our school.  This is the class who entered my boarding school in the fall of 2020... right after they had been locked down for months.  They were being denied the social contact that is so critical to all of us, but especially to young teenagers who are developing their sense of themselves and the world.  This senior class seems more grateful than any class I've been around... because, perhaps, they've seen that teachers who care about them are in fact a force for good, not merely a set of jailers.

So in AP Physics 2, we do the "quizzes" that I've been posting each day, but not for grades.  We do experiments where I join in as a regular lab partner.  We sometimes just talk about things other than physics.  This group has learned physics well; they are intrinsically motivated to be as ready as they can be for the exam.  I, and they, can relax and enjoy our time together.