Prof. Cappelli Winter 2007-08 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 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 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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