# Videos of “Surface tension Bernoulli, and soap bubbles II – bubble size”

Here are some videos from the “Surface tension Bernoulli, and soap bubbles II – bubble size” demonstration. The full videos are linked from the GIF headings

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.

# Surface tension, Bernoulli, and soap bubbles II – bubble size

The first demonstration on surface tension and soap bubbles was highly qualitative and the soap bubbles were merely a prop for talking about surface tension. There was a calculation of the gauge pressure in the bubble (Pi) which is given by

Pi= 4 σ/R

where R is the bubble radius and σ is the surface tension of the soap film, though this result was not taken any further. It is, however, possible to go a little further once you have gone over Bernoulli’s equation with your class.

Equipment

One container of soap bubble fluid and wand

Demonstration

The demonstration is similar to the previous one. You blow bubbles. Except this time you vary how hard you blow. If you blow very slowly you can get bigger bubbles whereas if you blow a little harder the bubbles get smaller. For a given wand shape there is a limit to the range of bubble sizes you can get. I have found it hard to get really small bubbles. I have also found it hard to get the really big bubbles to pinch off. They often just burst.

Analysis

When you blow into the loop in the bubble wand the air stream from your mouth stagnates on the soap film creating high pressure point there. This produces a curvature in the soap film. Therefore, there is a balance between the pressure in the cured film and the stagnation pressure. Eventually, the film pinches off and a bubble forms with the pressure in the bubble related to the stagnation pressure from your breath.

Recalling that the stagnation pressure is given by

P= ½ρV2

one can write an expression for the bubble radius as a function of the air speed (related to how hard you blow)

R=8σ/ρV2.

That is, the harder you blow (larger V) the smaller the resulting bubbles.

It would also be possible to leave this result unstated, run the demonstration and ask the students to discuss the relationship between pressure, surface tension, and radius. If the demonstration is done well you should be able to lead the class to discover that there is an inverse relationship between the pressure and radius. One could then introduce the exact relationship which they may have a greater ability to comprehend having observed it first.

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.

# Videos of the “Dimensional analysis – spring mass systems” demonstration

Here are the videos of the “Dimensional analysis – spring mass systems” demonstration. The full videos are linked from the titles. Sorry they are all sideways.

single mass

double mass

triple mass

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.

# Dimensional analysis – spring mass systems

You don’t need fluid mechanics to demonstrate the use of dimensional analysis to a fluids class. This demonstration uses a dimensional analysis to examine the relationship between frequency of oscillation of a spring and the mass supported by the spring.

Equipment

1. Spring supported from above (you can do is horizontally but friction can be a problem).
2. A series of equal masses that can be hung from the end of the spring alone or together.
3. A stopwatch.

Analysis

I tend to do the analysis first for any dimensional analysis demonstration and then test it with the physical demonstration. The goal is to find the functional relationship between the spring-mass frequency (f) and the possible controlling parameters, namely the spring constant (k), mass (m), and acceleration due to gravity (g). That is, we seek

f=f(k,m,g)

writing out each parameters dimensions we get

[f]=T-1, [k]=M.T-2, [m]=M, [g]=L.T-2

There are 4 parameters and 3 independent dimensions so we can get 1 non-dimensional group. We can, therefore, write

P=f.ka.mb.gc= T-1 Ma.T-2a Mb Lc.T-2c

Collecting powers of L, M, and T leads to a set of linear equations

(T) 0=-1-2a-2c      (M) 0=a+b             (L) 0=c

The solution to this set of equations is

a=-1/2 and b=1/2

That is

P=f(m/k)1/2

As there is only one P it must be a constant (say C) and

f=C(k/m)1/2

Therefore, increasing m will decrease the frequency f. This can be seen in the demonstration

Demonstration

1. Place one of the masses on the end of the spring, pull it down and release it. Estimate the frequency by counting how many oscillation there are in 30 seconds.
2. Add a second mass and repeat the frequency measurement.
3. Keep adding mass and measuring frequency until you are out of mass.

Taking the first mass as being 1 the second as 2, third 3, etc. (assuming all the masses added were equal) then you can use the dimensional analysis and the first measured frequency to make a prediction about the frequencies of the larger mass systems. I ran this in my office and measured the following frequencies.

1 – 2.5 Hz             2 – 1.9 Hz             3- 1.6 Hz

Using the unit mass as the standard then for a mass of n the frequency will be 2.5/n1/2. This leads to frequency predictions of 2 – 1.8 Hz, and 3 – 1.5 Hz. These are both quite close to the measured frequencies.

Thanks to Abdul Khan for lending me his spring – mass system.

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.

# Videos from “Viscous flow between parallel plates – lubrication and interfacial instabilities”

Here are the videos from the “Viscous flow between parallel plates – lubrication and interfacial instabilities” demonstration. The two GIFs as a single higher resolution video can be found here.

Lubrication demonstration

Taylor-Saffman instability

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.