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Transport in Thermofluids
ME220B
Homework #8
Problem 1
A normal shock moves
down an openended tube with a
velocity
400m/s
s
υ
=
. In advance of the
normal shock, the static air in the tube is
at the ambient conditions:
101kPa
a
P
=
and
25C
a
T
=°
.
When the shock
reaches the open end, an expansion
wave is reflected back. Determine the
velocity of the leading and trailing edges of the expansion wave that moves back through
the tube.
Use the gas properties
287J/kg/K
R
=
and
1.40
γ
=
for air. Sketch the position,
as a function of time, of a material fluid element initially at a distance
1
x
from the open
end of the tube.
Problem 2:
Consider the flow, described in Problem 1.
Derive a set of governing
differential equations that describe the transient flow in terms of
(,)
xt
ρ
,
and
T xt
.
Present these equations in nonconservation form. (The shockwave described in
Problem 1 is no longer in the domain of the solution.) Specify the initial and boundary
conditions required to solve the governing equations for
0
t
>
, when at
0
t
=
the shock
passes through the open end.
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 Winter '09
 Bennett
 Shockwave

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