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1
Midterm 2, AAE 334, Fall 2011
Name:_SOLUTION____________________
Exam ends at 10:20am regardless of starting time.
All questions are for steady flows of air acting as a calorically perfect gas.
Two original handwritten doublesided 8.5x11 inch formulas sheets are permitted.
A calculator is permitted.
Isentropic Flow Table (IFT) and Normal Shock Table (NST) are supplied.
Phones, Ipods, Ipads, tablets, notebook computers, web access of any kind, etc., turned off.
Do your own work.
1.
(10 points)
Consider the ratio of kinetic energy per mass of the continuum motion to kinetic
energy per mass of the random molecular motion.
Set up the ratio, simplify, and substitute as
appropriate for air acting as a calorically perfect gas.
Kinetic energy of continuum per volume is dynamic pressure,
2
2
1
V
q
so per mass is
2
2
V
.
Kinetic energy per mass of the random molecular motion is internal energy,
e
.
The ratio is
T
c
V
e
V
v
2
2
2
2
and temperature appearing under velocity squared is a hint to look for Mach number.
Since the speed of sound squared is
RT
a
2
or
T
R
a
2
then substitute this into the above equation,
2
2
2
2
2
2
2
2
2
2
2
2
M
c
R
a
V
c
R
a
V
c
R
a
c
RV
e
V
v
v
v
v
Now work on the constant.
Use
v
p
c
c
R
to get
2
2
2
2
M
c
c
c
e
V
v
v
p
and because
v
p
c
c
,
2
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 Fall '09
 COLLICOTT

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