contest

[Dan Squire]

lefbart@afm.org posted:
>
>CONTEST
>January 2, 1996 11:50:55 AM
>To All
>Want to challenge your mathematical skills?

lefbart@afm.org:
      Here is a real problem for you.  Derive the solutions for the pressure
distributions and the net force for axisymmetric radial flow between
parallel plates separated by a small gap for various ranges of fluid flow
parameters.  Use air as the fluid.  Derive for viscosity dominated flow,
large flow rates and large gaps (small viscous forces), and using the
momentum integral approximation.

Questions for you to answer.
1.  Under which flow parameters will the pressure gradient be positive or
negative?
2.  Under which flow parameters will the total force between the discs be
either attractive or repulsive?
3.  You have been asked to design a piano moving mechanism to move concert
pianos across the stage using compressed air to keep the piano from touching
the floor.  Using the solutions you have previously derived design such a
system.  What would be the disc radius and the necessary fluid flow rate to
make this possible for a given piano?
4.  Would you use the creeping flow, inviscid flow, or momentum integral
approximation to base your solution on?  Explain why?
5.  What would be the advantages and disadvantages of using such a piano
moving system?
HAVE FUN!

Dan Squire
Houston

And our own elders (may Allah have mercy upon them) used to say, "The study
of mathematics is for the mind as soap is for clothes,  which washes away
from them dirt and cleans the spots and stains."
                                                - Ibn Khaldun