# Video of “Compressible vs incompressible flow and conservation of mass”

Below are GIFs of the compressible and incompressible versions of the “Compressible vs incompressible flow and conservation of mass” demonstration. The full videos are linked from the GIF headings.

Compressible flow (air)

Incompressible flow (water)

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.

# Compressible vs incompressible flow and conservation of mass

This is a really simple demonstration of how conservation of volume can be used for incompressible fluids but not for compressible fluids. The demonstration was suggested by Dr. Baburaj of IIT Madras. I teach in a civil engineering department where practically everything is incomopressible and we mostly talk about conservation of volume. The demonstration below is so simple yet so clear.

Equipment

You will need:

1. Two identical syringes,
2. A few feet of clear tubing that fits tightly over the end of each syringe,
3. Some water, and
4. Food dye (optional)

Demonstration

Compressible flow

1. Have one syringe (A) with the plunger fully pushed in and the second plunger (B) fully pulled out.
2. Connect each end of the tube to the syringes
3. Slowly press the plunger on syringe (B)

Assuming that the syringe plunger’s are a little stiff you should be able to push the plunger on (B) all the way in before the plunger on (A) is pushed all the way out. Mass is conserved because there are no leaks but volume is not conserved as the plungers move different distances on identical syringes. This works better with stiffer syringe plungers.

Incompressible flow

1. Have one syringe (A) with the plunger fully pushed in and the second plunger (B) fully pulled out and the syringe full of water.
2. Fill the tube with water (food dye can help with visualization) and connect the tubes in the same way as for the previous version. This is tricky as you want to ensure that there are no air bubbles in the lines.
3. Slowly push in the plunger on syringe (B). The plunger in syringe (A) should move out at exactly the same speed. you can show this clearly by having the syringes pointing away from each other with the plunger ends next to each other. As you push one in the other should move right next to it.

Analysis

There is no analysis for this demonstration. The gas is compressible so volume is not conserved whereas the liquid is incompressible so volume is conserved. Analysis of the change in pressure in the compressible case and resulting motion of the plungers is complex as you need to know about the friction in the syringe.

Thanks again to  Dr. Baburaj for suggesting the demonstration.

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 “Radial flow, Bernoulli, and levitating an index card”

Here are the videos of the “Radial flow, Bernoulli, and levitating an index card” demonstration. The higher resolution videos are linked from the titles.

Foam plate version

Index card version

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.

# Radial flow, Bernoulli, and levitating an index card

This experiment was suggested by Dr. John Foss from Michigan State University. He presents a more detailed write up, along with a discussion of Reynolds number effects in Experiments in Fluid Mechanics, R.A. Granger, Ed. Holt, Rienhart and Winston, (1988). The basic idea is that a radial outflow between parallel plates has a velocity that decreases with increasing radial distance. Therefore, if a high Reynolds number situation exists such that the shearing effects are small and a nominal balance exists between the pressure gradient and the acceleration, the pressure will increase with radial distance. If the outflow boundary condition is atmospheric pressure then the pressure between the parallel plates must be a vacuum pressure. This is surprisingly easy to do with very simple equipment.

Equipment:

There are a couple of methods for doing this. Two are described below. The index card version is the easiest to do in large numbers.

• Foam Plate Version
• 1 Foam plate
• 1 Straight pin
• A can of compressed air
• Tape
• Index Card Version
• 1 straw
• 1 3”x5” index card
• 1 straight pin
• Tape
• Adhesive putty (optional, may help hold the straw in the spool)

Procedure:

• Foam Plate Version
1. Place the straight pin through approximately the center of the foam plate. Tape the pin to the bottom of plate to stabilize it and to keep it perpendicular to the plate.
2. Have someone hold the plate so that the pin is horizontal
3. Hold the spool of thread to where it covers most of the pin but is not touching the plate
4. Take the can of compressed air and aim it through the spool of thread. The nozzle does not need to be placed directly in the spool. Just aim it so that the air will flow through the spool.
5. When the air is released from the can the plate should move towards the spool of thread and should stay there without support as long as the compressed air can is blowing

*CAUTION:  Do not aim the compressed air can downward. The air will become very cold and could possibly burn someone

• Index Card Version
1. Place the straight pin through approximately the center of the index card. Tape the pin to the bottom of the card to stabilize it and keep it perpendicular to the card
2. Place the index card on the table with the pin pointing straight up
3. Hold the spool of thread directly above the pin but not touching the index card
4. Insert the straw into the spool. The adhesive putty can be used to attach the straw to the spool so that you only need one hand.
5. Blow through the straw and, if the spool is close enough to the card, you should be able to lift the card off the table. The card should stay as long as there is a steady flow of air

** Trial and error may need to be used to in both experiments to determine the gap distance needed between the spool and card/plate in order to pick the object up.

Foam Plate Version                             Index Card Version

Analysis

Consider an incompressible fluid flowing horizontally and radially out from a point source between two parallel plates separated by a distance T. At any arbitrary radial distance r from the source the area of the flow is

A= 2π r T

(see diagram below). For a constant volume flow rate Q the velocity is given by

U(r)=Q/2 πr T

Writing Bernoulli’s equation from r to the outlet at a radial distance R and taking the outlet pressure to be atmospheric leads to

Pr = (Q/2 π T)2 (R-2-r-2)

Therefore, given that r<R, Pr<0 and the plate/card will be pushed toward the spool. However, for this to work the gap width needs to be small. If T is too large the pressure vacuum pressure over the card will no be enough to overcome the weight of the card.

In reality life is a little more complex and a more detailed analysis of this problem is given by Prof. Foss in Experiments in Fluid Mechanics, R.A. Granger, Ed. Holt, Rienhart and Winston, (1988).

Thanks to John Foss for suggesting the demonstration and helping with the write up. Thanks to Meredith and Alex for testing the procedure, putting together pictures, and making the videos. Videos to follow soon.

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 “Discharge coefficient calculation and data presentation” demonstration

Here are the videos from the “Discharge coefficient calculation and data presentation” demonstration. The titles link to the full videos. If you really want to watch the whole thing (12 minutes) it is here.

Initial release

Depth measurement

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.