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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- 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 _______