Prof. CappelliWinter 2007-08ME 70Problems due Wednesday April 9, 2008Molecular Scales in Fluid FlowsThe density of air above the earth varies (approximately) exponentially with height, ρ= ρoexp (-z/zo) where the characteristic length zo= 7.3 km for air, and ρo, 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 μm in a free-molecule 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 AccelerationThe velocity field of a steady fluid flow is given by:V= -Voy/(y2+ x2)1/2i + Vox/(y2+ x2)1/2j Here, Vois a constant. What is the acceleration of a fluid element in the flow? Where in the field is the speed equal to Vo? Determine the equations of the streamlines, and discuss the flow characteristics.
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