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Prof. Cappelli
Winter 200708
ME 70
Problems due Wednesday April 9, 2008
Molecular Scales in Fluid Flows
The density of air above the earth varies (approximately) exponentially with height,
ρ
=
ρ
o
exp (z/z
o
) where
the characteristic length z
o
= 7.3 km for air, and
ρ
o
, is the standard density of air.
At what height (in km) is
the flow around a spec of dust that has a diameter of 1
μ
m in a freemolecule flow regime?
What is the
characteristic distance between air molecules at this height?
Using MATLAB (see below) or EXCEL
(whichever you prefer), draw a graph of the mean free path,
λ
, in air, versus height above see level, for
heights to 100 km.
Fluid Element Acceleration
The velocity field of a steady fluid flow is given by:
V
= V
o
y/(y
2
+ x
2
)
1/2
i
+
V
o
x/(y
2
+ x
2
)
1/2
j
Here, V
o
is a constant.
What is the acceleration of a fluid element in the flow? Where in the field is the
speed equal to V
o
?
Determine the equations of the streamlines, and discuss the flow characteristics.
Newton’s Law of Viscosity
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 Spring '08
 Cappelli,M

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