ME 141A
Intro to Nanotechnology
Due: 3/9/2009
1
Solution Set 8
Problem 9.2 in book
Air is flowing through a 40 nm radius carbon nanotube. Can we use the NavierStokes
equation to analyze this flow? What about if it were in a 4 m radius pipe?
ANSWER
Since the mean free path of gases are on the order of 1000 nm, the NavierStokes
equations CANNOT be used to analyze the flow in a 40 nm nanotube, since the
continuum assumption cannot be made. However, a 4 m radius pipe is much larger
than 1000 nm, and therefore, the
continuum assumption holds and the Navier
Stokes equations CAN be used.
Problem 9.7 in book
Reynolds number is the ratio of inertial forces to viscous forces.
Can you think of
another nondimensional grouping that may be able to tell us the ratio between
gravitational forces and viscous forces?
ANSWER
Ratio of gravitational and viscous forces:
where Fr is the Froude number
Problem 9.8 in book
Compute the Reynolds number for each case:
(a) A baseball hit by Barry Bonds in Giants Stadium
(b) A 10
μ
m diameter protozoan flowing at 100
μ
m/s in water
(c) A blade of grass floating in a pond at 1 mm/s
ANSWER
Reynolds number –
, and we can use the following values for density and
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 Winter '09
 PENNATHUR
 Fluid Dynamics

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