Vorticity and walking in circles

This is a really simple demonstration that requires no equipment at all, though it is slightly enhanced if you have a stool that you can place at the front of the room. The demonstration shows the difference between rotational and irrotational flow for both straight and circular streamlines.

Equipment

Ideally you would have a stool or chair to walk around for the first two parts of the demonstration. If you do not, then you just need a space on the floor to walk around. The demonstration is exactly the same with or without the stool. You just don’t have the visual reference to walk around if you don’t have a stool.

Demonstration

The demonstration has four parts covering rotational and irrotational flows for both circular and straight streamlines.

(1)    Rotational flow around a circle

Place the stool in the front of the room with space all around it. Start off facing the class with the stool in front of you. Simply walk around the stool while facing the stool the whole time. Stop after one trip around the stool and point to the back of the room. Point out to the class that your body (the model fluid particle) is facing the back of the room. Start walking around the stool again and stop half way around, you should have your back to the class. Point to the front of the room and point out to the class that you are now facing in the opposite direction and have, therefore, rotated. Hence, this is a rotational flow with circular streamlines.

(2)    Irrotational flow around a circle

Repeat the first demonstration, only this time always face the back of the room as you walk in a circle around the stool. Again, stop after one trip around the stool and point to the back of the room. Continue for another half circle and stop. The stool should be behind you and you should be facing the back of the class room. Point to the back wall and point out that, while you were walking in a circle you were not rotating (you always faced the same direction). Hence, this is an irrotational flow with circular streamlines.

(3)    Rotational flow along a straight line

Start at one side of the room with a clear path across the front of the room. Roll yourself across the front wall of the room. That is, walk across the front of the room while rotating as if you were a wheel rolling along the wall. Stop a third of the way along while you are facing the back of the room and point to the back wall telling the class which way you are pointing. Continue rolling and stop a bit further on when you are facing the front wall. Point out to the class that you are now facing the front wall and must therefore have rotated. This is a rotational flow with straight streamlines.

(4)    Irrotational flow along a straight line

This is the easiest part. Simply walk across the front of the room in a straight line while always facing in the same direction. The degree of difficulty can be raised (though only slightly) by facing the students while walking sideways. This is an irrotational flow with straight streamlines.

Discussion

For each of the components of the demonstration you can give an example of such a flow. Examples might include (1) solid body rotation, (2) the bath tub vortex, (3) laminar flow in a pipe, and (4) Wind above the atmospheric boundary layer where there is negligible shear. You can also use examples from outside of fluid mechanics. For example, (1) is analogous to how the moon rotates around the earth such that we only ever see one side of the moon. Example (3) is analogous to a car tire as it drives along a flat road.

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One thought on “Vorticity and walking in circles

  1. Pingback: Videos of Vorticity and walking in circles | Teaching Fluid Mechanics

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