Video of “Compressibility and incompressibility demonstrated with soda bottles and ketchup”

Here is a video of the “Compressibility and incompressibility demonstrated with soda bottles and ketchup” demonstration. The full video is here.

Video Jan 12, 4 09 29 PM 00_00_02-00_00_11

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Compressibility and incompressibility demonstrated with soda bottles and ketchup

Introduction

I teach in a civil engineering department so we pretty much only deal with incompressible flows. However, this is a really simple demonstration to illustrate the compressibility of gasses and the relative incompressibility of liquids that uses stuff you can pick up at a fast food restaurant and recycling bin. I found it in a number of different books on science experiments for kids.

Equipment

  1. 2 liter soda bottle with cap
  2. a small ketchup (or other condiment) packet that floats (test this before you wedge it in to the bottle).
  3. water

Photo Jan 12, 4 09 06 PM

Demonstration

  1. Stick the ketchup packet into the soda bottle and then fill the bottle with water until there is only a small volume of air below the top of the bottle.
  2. Tightly screw on the cap so that the bottle is sealed. The ketchup packet should be floating.
  3. Squeeze the bottle firmly with your hand and the ketchup packet should sink.
  4. release the bottle and the ketchup packet will float back up to the surface.

Discussion

This is effectively a cheap way to make a Cartesian diver. The demonstration relies on the water being effectively incompressible and the air being compressible. When you squeeze the bottle it is the air pocket at the top of the bottle that is compressed by the change in volume. This increases the pressure in the water but does not compress it so the water density stays the same. However, the ketchup packet has a small air bubble in it which also compresses. This reduces the volume of the bubble enough that the net density of the packet changes from being less than that of water to greater than that of water so it sinks. This process is reversed when you stop squeezing the bottle.

You can also get the packet to sink just by leaving the bottle out in the sun. In this case the water and air both heat up. however, given the finite volume, as the water expands slightly from heating, the air is compressed and the packet sinks.

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Buoyancy – Balancing ping-pong balls

Background

I saw this demonstration on Veritasium’s YouTube channel (see Beaker Ball Balance Problem video). It is really simple to run as long as you have a good balance. The result is not obvious and so the reason for the result requires a little analysis. Therefore, I think it would be good to write it up and provide a more detailed explanation of the demonstration complete with free body diagrams.

Equipment

  1. Balance
  2. Three identical cups
  3. Water
  4. Two ping pong balls, one filled with sand of something to weigh it down (actually any two balls with the same diameter as long as at only one of them floats)
  5. Tape
  6. String
  7. A stand

Photo Aug 12, 11 06 18 AM Photo Aug 12, 11 06 23 AMPhoto Aug 18, 4 17 13 PM

Procedure

  1. Place identical volumes of water in two cups but leave enough space for at the top of the cups so that it will not overflow when you place the balls in the cups.’
  2. lock the balance so that it is level for steps 3-7.
  3. Take the empty ping-pong ball and tape some string to it and then tape the string to the base of the empty cup. Use as little string as possible. When you pour the water in, the ball has to be fully submerged.
  4. Pour the water from one of the cups into the one with the taped ball.
  5. Place the two cups with water (one with a ball attached) on either side of the balance.
  6. Suspend the heavy ball from the stand into the second cup such that it is fully submerged.
  7. Poll your students to see which way they think the balance will tip when it is released.
  8. Unlock the balance and observe which way the balance tips (it should go up on the side with the ball taped to the bottom of the cup)

Analysis

We start by looking at the setup (see figure below). The two cups have identical volumes of water in them and both have a submerged ball with identical volumes which, therefore, displace identical volumes of water. Therefore, the depth of water in each cup is the same. For the purposes of this explanation light ball is denoted as ball (1) and the heavy suspended ball is ball (2).

balance1

We now examine the forces acting each ball (see figure below). Ball (1) has weight down (W1), buoyancy force up (FB), and the tension force in the string acting down (T1). The forces sum to zero as the system is in equilibrium. Ball (2) has the same set of forces acting on it. However, for ball (2) the tension force (T2) is acting up as the ball is denser than water such that the buoyancy force is less than the weight. Hence the ball must be suspended from above. The only important thing here is that the balls displace the same volume of water such that the water levels in each cup are identical.

balance2

We now turn our attention to the forces acting on the cups (see figure below).

balance3

For cup (1) there is the hydrostatic pressure force acting down, PA, that depends only on the cup geometry and the depth of water in the cup. There is also the weight of the cup (Wcup), the tension on the string acting up (T1) and the force due to the scale Fscale(1). Therefore,

Fscale(1) = PA+Wcup-T                                                                                                (1)

The forces acting on cup (2) are the hydrostatic pressure force acting down, PA, the weight of the cup (Wcup), and the force due to the scale Fscale(1). Therefore,

Fscale(2) = PA+Wcup                                                                                                        (2)

As the cups are identical and the water depth in is the same in each then both PA and Wcup are the same in equations (1) and (2). Therefore, subtracting (1) from (2) gives

Fscale(2) – Fscale(1)= T1

or

Fscale(2) > Fscale(1)

and the balance goes down on the side with the suspended ball.

In fact, you could run this test with any two sized balls as long as:

  1. One ball floats and is tethered to the base of a cup
  2. One ball does not float and is suspended from above
  3. The water level in the two identical cups is the same.

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Take home lab experiment – Density of oil

This is another early semester take home lab. When I give this to my students they have already been down to the lab and used a U-tube manometer to measure the specific gravity of oil (See post https://teachingfluids.wordpress.com/2014/01/13/measuring-specific-gravity-of-oil-with-a-u-tube-manometer/). This goes a step further and requires them to find 2 more ways to measure the density of common cooking oil. They have to look at the course material covered so far (typically we just finished hydrostatics when I hand this out) and work out what topics will enable them to measure the density of cooking oil. The two main goals are to (1) have them review the course to find possible measurement techniques and (2) to start doing some error quantification. They are required to give 3 different values of density based on three different measurement tecuniques and explain any possible differences. At this stage in the semester I typically only ask for estimates of their direct measurement uncertainty but not their uncertainty in their final calculated density.

In general the students are able to come up with three different methods for doing the measurement. They also, typically, measure densities that are slightly less than that of water. This puts them in the right ball park for the actual density. However, the students sometimes end up measuring some very small quantities (such as the height differences in the U-tube manometer. This in turn leads to large measurement percentage errors and even larger density percentage errors. The analysis of this error propagation is left to later take home labs though I do discuss error propagation in class around the time when I hand back the graded lab reports.

As with all the take home labs I will not publish methods for conducting the tests as I still use them in class and want my students to figure it out on their own.


Introduction

Fluid density is needed for many fluid mechanics calculations (hydrostatic pressure, forces on submerged structures, buoyancy, conservation of mass calculations). You have already measured the specific gravity of cooking oil in the lab. You are now required to measure its density.

Task

  1. Use three different methods to measure the density of cooking oil (you can repeat the approach you used in the lab if you like).
  2. Write a brief report that
    1. Is 3 pages max including photos of you running your experiments
    2. Details how you made the measurements
    3. Details how you used the measurements to calculate the cooking oil density
    4. Has clear diagrams showing your setup
    5. Compares the three different measured values of density.
    6. Quantifies potential sources of error in your measurements including a table of what you measured directly, typical values, and estimated uncertainty.

Rules

  1. You can use tubing from the fluids lab and a scale from the materials lab if you can get permission and access. Otherwise you are limited to household implements.
  2. You can take the density of water to be 1,000 kg/m3.
  3. If you need to go to a store to buy something please come and see me first. I may be able to lend you something or I will buy it and then lend it to you. You will need to explain why you need it and it should be cheap.

Due in 2 weeks


An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Take home lab – Personal specific gravity

This is a fun take home lab as the students have to measure themselves. It is also a lab in which the student should know roughly the answer before they start. Generally speaking, most people either just float or just don’t and therefore their specific gravity should be approximately S.G.=1. As with all the take home labs the students are required to use more than one method. The fundamental problem is measuring a person’s volume. There are a range of methods for doing this which often have significant uncertainty/error. There is, therefore, the possibility of having significantly different values from the two different measurements that must be reconciled through the error analysis.

When giving this as a take home lab I have generally found that the students are able to find two, and sometimes more, ways of doing the measurements. The students also sometimes borrow methods they learned about in other classes such as their materials lab. Once a team even worked out how to measure their submerged weight. It is a nice introductory take home lab as the measurements are easy to make but have significant uncertainty. Therefore, it is a good platform for discussing error analysis before they get into the more complex take home labs to follow.

As with all the take home labs I will not publish detailed methods for conducting the tests as I still use them in class and want my students to figure it out on their own.


Instructions to students

Introduction

The specific gravity of a fluid is its density divided by the density of water. But specific gravity is not unique to fluids. Your goal is to calculate the specific gravity of one of your team members using at least 2 different approaches.

Task

  1. Run a series of experiments to establish the specific gravity of either a member of your team or the team as a whole (or both if one particular method suits an individual test and the other suits a group test).
  2. Write a brief report that
    • Is 3 pages max including photos of you running your experiments.
    • Describes the experiment(s) you used to establish your result including:
      1. How the test was run.
      2. What data you collected.
      3. How you performed your calculations including diagrams, equations, and relevant theory that has been covered in in this class.
      4. A quantitative discussion of the uncertainties in your measurements and calculations including an analysis of the differences between your two sets of measurements.

Due in 2 weeks


An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.