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Heat Chap14-074

Heat Chap14-074 - Chapter 14 Mass Transfer Diffusion in a...

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Chapter 14 Mass Transfer Diffusion in a Moving Medium 14-74C The mass-average velocity of a medium at some location is the average velocity of the mass at that location relative to an external reference point. It is the velocity that would be measured by a velocity sensor such as a pitot tube, a turbine device, or a hot wire anemometer inserted into the flow. The diffusion velocity at a location is the average velocity of a group of molecules at that location moving under the influence of concentration gradient. A stationary medium is a medium whose mass average velocity is zero. A moving medium is a medium that involves a bulk fluid motion caused by an external force. 14-75C The diffusion velocity at a location is the average velocity of a group of molecules at that location moving under the influence of concentration gradient. The average velocity of a species in a moving medium is equal to the sum of the bulk flow velocity and the diffusion velocity. Therefore, the diffusion velocity can increase of decrease the average velocity, depending on the direction of diffusion relative to the direction of bulk flow. The velocity of a species in the moving medium relative to a fixed reference point will be zero when the diffusion velocity of the species and the bulk flow velocity are equal in magnitude and opposite in direction. 14-76 C The mass-average velocity of a medium at some location is the average velocity of the mass at that location relative to an external reference point. The molar-average velocity of a medium at some location is the average velocity of the molecules at that location, regardless of their mass, relative to an external reference point. If one of these velocities are zero, the other will not necessarily be zero. The mass- average and molar-average velocities of a binary mixture will be the same when the molar masses of the two constituents are equal to each other. The mass and mole fractions of each species in this case will be the same. 14-77C ( a ) T, ( b ) T, ( c ) F, ( d ) F 14-78C The diffusion of a vapor through a stationary gas column is called the Stefan flow . The Stefan’s law can be expressed as j N A C D L y y A A AB A L A o / ln , , 1 1 where C is the average concentration of the mixture, D AB is the diffusion coefficient of A in B , L is the height of the gas column, y A, L is the molar concentration of a species at x = L , and y A, o is the molar concentration of the species A at x = L . 14-43
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Chapter 14 Mass Transfer 14-79E The pressure in a helium pipeline is maintained constant by venting to the atmosphere through a long tube. The mass flow rates of helium and air, and the net flow velocity at the bottom of the tube are to be determined. Assumptions 1 Steady operating conditions exist. 2 Helium and atmospheric air are ideal gases. 3 No chemical reactions occur in the tube. 4 Air concentration in the pipeline and helium concentration in the atmosphere are negligible so that the mole fraction of the helium is 1 in the pipeline, and 0 in the atmosphere (we will check this assumption later).
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