hw_8_solu

hw_8_solu - Solution Set 8 ME 141A Intro to Nanotechnology...

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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 Navier-Stokes 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 Navier-Stokes 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 non-dimensional 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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hw_8_solu - Solution Set 8 ME 141A Intro to Nanotechnology...

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