Surface tension – Parting of the pepper sea

This is another demonstration that I learned from Ben Sill . As with all his demonstrations, it can be done straight or with some slightly over the top dramatization (there are other conceptually similar versions of this demonstration posted online). The goal of the demonstration is to illustrate how surface tension can keep heavier objects afloat and how surfactants and surface tension gradients can drive a flow.

Equipment

  1. Box of ground black pepper or pepper in a pepper grinder
  2. Overhead projector
  3. Clear square flat bottomed glass bowl
  4. Water to pour into the bowl
  5. A bar of soap in your pocket
  6. A student volunteer

Equipment minus the water, OHP and student.

Photo Mar 18, 9 55 37 AM

Demonstration

  1. Set up the projector and place the bowl full of water on it
  2. Sprinkle the ground pepper on the surface
  3. Ask the student volunteer to divide the peppers in half by running their finger down the middle of the bowl. The pepper should not divide because it will be drawn into the wake behind the student’s finger
  4. [optional step for the extreme extroverts] tell the class that the student did not do it correctly because they should have said “Divide, O great pepper!” Do the next step with the class repeating this phrase.
  5. Scrape a little soap under your finger nail while it is still in your pocket. Then run your finger across the top of the water. The pepper flakes should divide. Note that you have to have the soap flake run along the surface of the water. If the soap is submerged the surfactant will not create the surface tension gradient needed to part the water.

Analysis/discussion:

When you sprinkle the pepper on the water some of it sinks and some floats. The pepper that floats is held up by curvature in the water surface just like water a strider.

The soap (surfactant) creates a region of low surface tension down the middle of the bowl. This surface tension gradient drives a flow away from the region of low surface tension and divides the pepper flakes. Surface tension driven convection (Marangoni convection) is used by some insects to propel themselves across a water surface.

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.

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Video of “Blood pressure and Bernoulli”

Here is a video of the “Blood pressure and Bernoulli” demonstration. The full video is here.

BP

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.

Blood pressure and Bernoulli

I first saw this demonstration as a grad student and it has taken me years to get around to building my own demonstration rig. The demonstration illustrates the same Bernoulli behavior as the Ping-Pong ball in a funnel demonstration but requires a lot more equipment.

Equipment

  1. A bucket full of water
  2. A sump pump
  3. A bike pump to pressurize the cylinder
  4. A sealed cylinder with:
    1. A flexible rubber hose passing down the middle of the cylinder with a connection to the sump pump at one end and an outlet return to the bucket at the other end.
    2. A valve to connect to the bike pump to pressurize the cylinder

Equipment

Photo Jan 27, 10 35 14 AM

Details on the connections, air seal, inner tube, and valve

Photo Jan 27, 10 42 55 AM

The demonstration rig fully assembled

Photo Jan 27, 10 48 44 AM

Demonstration

The demonstration is very straight forward. I often try and get a bunch of students involved, one to pressurize the cylinder with the bike pump and one to hold the drain tube. I have a student hold the drain tube because you sometimes get quite a reaction from them when it suddenly starts to pulse.

  1. Ensure that the cylinder is not pressurized
  2. Connect the sump pump to the rubber inner tube and hold the outlet so that it drains back into the bucket
  3. Turn on the sump pump. You should get a steady flow through the inner tube.
  4. Connect the bike pump to the valve and start to pressurize the cylinder.  Eventually the pressure in the cylinder will be large enough that the flow through the inner tube starts to pulse. If you have a large sump pump, the pulsing can be quite violent.
  5. Release the pressure on the cylinder and the pulsing should stop.

Analysis

The analysis is fairly qualitative. Draw a schematic diagram of the setup as shown below. When the cylinder is not pressurized then the tube has a constant cross sectional area and the flow is steady.

b1

When you pressurize the cylinder you begin to compress the rubber tube. Therefore, there is a section of tube where the cross sectional area is reduced. Conservation of volume tells you that the velocity in the contraction must be higher than in the uncompressed section of the tube. Bernoulli tells you that the pressure in the contraction must be lower than the pressure in the uncompressed section of the tube because of the increased velocity (the tube is horizontal so the z terms cancel). Therefore, if a section of tube begins to compress, it will continue to compress as the water pressure in the tube drops in the contraction.

b2

Eventually, the contracted section will completely collapse blocking the flow. At this point the pressure in the contraction is the pump shut-off head. This pressure is much higher than the cylinder pressure so the blockage is forced open again. This cycle continues as long as the pressure remains high enough in the cylinder. As such, you get a fairly dramatic pulsing flow out of the end of the tube.

b3

This is somewhat analogous (though not a direct analogy) to the measurement of blood pressure. The cuff that is placed on your arm compresses the veins. You can sometimes feel the pulsing while the cuff is pressurized.

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.

Video of “Momentum, angular momentum, and bendy straws”

Here are the videos of the “Momentum, angular momentum, and bendy straws” demonstration. The full videos are linked from the GIF titles.

Blowing, showing the straw rotation.

blow

Sucking, showing the straw not moving (very much).

suck

This part was not written up in  the main demonstration but is discussed in Alan Mironoer’s ASEE conference paper.

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.

Momentum, angular momentum, and bendy straws

I have been looking for a simple demonstration for the momentum equation and it would be hard to get simpler than this. The demonstration written up here is just the first and simplest part of a more complex demonstration written up by Alan Mironoer at an ASEE conference.

Equipment

  1. One bendy straw (or any tube with a bend in it).

You may need to reinforce the bend so that it does not straighten during the demonstration.

Photo Mar 10, 1 32 03 PM

Demonstration

  1. Bend the straw so that there is a 90o bend in it.
  2. Blow through the long end of the straw.

The straw should flex away from the outlet due to the change in direction of the flow. The extension to the demonstration in which you suck air into the straw is nicely written up here.

Analysis

The demonstration is clearly qualitative as there is no easy way to measure the flow rate at which you blow. However, the analysis can be done symbolically. Denoting the straw cross sectional area to be A, the air velocity to be U and the density of air to be ρ, we can draw a diagram with a control volume showing the inflow, outflow, dimensions, and the force (in the x direction) that the straw applies to the airflow.

momentum

We can then write the momentum equation in the x direction as

ΣF=ρAU(U-0)

where the zero is the component of the inflow velocity in the direction of the outflow. Assuming that the outlet pressure is atmospheric, then the only force remaining is the force that the straw applies to the airflow to change its direction. Therefore, there is a reaction force that the air applies to the straw in the opposite direction to the airflow at the exit. As a result, the air acts to deflect the straw away from the outlet. The same analysis can be done with angular momentum (or moment of momentum as some like to describe it). If you take your mouth as the point about which you take moments and calculate the angular momentum then the equation is

ΣM=ρAUL(U-0)

where L is the distance from your mouth to the bend in the straw. Hence there is a positive (anticlockwise) moment applied to the airflow by the straw producing a reaction clockwise moment on the straw. This clockwise moment acts to bend the straw in the clockwise direction about your mouth.

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.