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.
- 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.
- Bend the straw so that there is a 90o bend in it.
- 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.
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.
We can then write the momentum equation in the x direction as
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
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 (firstname.lastname@example.org). I also welcome comments (through the comments section or via email) on improving the demonstrations.