University
of Michigan
ME521
� Winter 2003
Final
Exam,�� Apr 15-25
4
continuous hrs, 1 book and course notes
I have neither given nor received
aid on this examination, nor have I concealed any violation of the Honor Code.
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time
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- A 2D
inviscid liquid jet exits into air from a slot of width D with a uniform
velocity U downward in the direction of gravity g. The fluid density is r and s is the
interfacial surface tension. Write the dimensionless governing equations
and boundary conditions assuming the jet is much longer than it�s
width.�� The upstream boundary
condition is u (x=0) = U and choose a downstream boundary condition at
some location L that allows each fluid particle to be in free fall for
0<x<L when surface tension is neglected. Find an ODE to solve for u
when surface tension is not neglected.
- Explain why
we often use the normal mode representation u(z)eikxeikyest in an instability problem on, for instance,
a horizontal fluid layer. Under what conditions is this form appropriate?
Can it represent all disturbances? What are the mathematical and physical
limitations of this method.
- In class we
explained that a fluid-filled layer heated from below was a simple
convection problem with the basic state being the pure conduction
solution. We could add side walls for aspect ratio A which could
then be considered adiabatic. Now turn the problem by 90 degrees and
explain the simplest basic state for the same stability problem heated
from the side wall.� What kind of
instability would you be testing for?
- Describe
and set up a Prandtl�s mixing length model for a turbulent boundary layer
on a flat plate.
- Big whirls
have lesser whirls that feed on their ________
Lesser whirls have even lesser whirls and so on to _______