# Momentum – air jets and paper plates

So many momentum examples in fluids text books revolve around air or water jets striking various plates, vanes, and cups. The calculations are quite easy and a good reminder that momentum is a vector so sign and direction mater. Here is an easy to build demonstration that allows you to illustrate this point.

Equipment

1. Long thin (somewhat flexible) wooden rod
2. Duct tape
3. Plastic or paper cup
4. Plastic or paper plate
5. Compressed air can (like those used for cleaning keyboards)
6. Student volunteer

Cut out the flat section of the paper plate and cut the base of the cup out so that it is about 5-7 cm deep. Tape the cup base and plate to either end of the rod.

Demonstration

1. Hold the rod in the middle with the flat plate up.
2. Spray the compressed air jet at the center of the plate, normal to the surface, from a distance of 5-7 cm. The plate should deflect back (it will also likely twist which is unfortunate)
3. Flip the rod so that the cup is at the top.
4. Spray the compressed air again and observe the (hopefully greater) deflection.

Analysis

The analysis can be done quantitatively though the result can only be qualitatively compared. We treat the air jet as a momentum conserving flow until impingement. For the flat plate the jet is deflected radially in all directions and, other than a small component due to the plate twisting, there is no outflow momentum component parallel to the initial air jet direction. See the control volume diagram below.

The control volume version of the momentum equation is written as

ΣFx=Rplate=ρQ(0-(-Uj))

where the positive x direction is to the right. For the cup, some of the jet momentum is deflected in the opposite direction to the incoming air jet and the control volume diagram looks like this

The resulting control volume momentum equation is written as

ΣFx=Rcup=ρQ(Uout cos θ -(-Uj))

As such

Rcup> Rplate.

Therefor, the rod should deflect further when the air jet impinges on the cup compared to when it impinges on the plate.

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.