Problem 6.2[Difficulty: 2]Given:Velocity fieldFind:Acceleration of particle and pressure gradient at (2,2)Solution:Basic equationsGiven dataA11s⋅=B31s⋅=x2m⋅=y2m⋅=ρ999kgm3⋅=For this flowuxy, ()Ax⋅By⋅+=vxy, ()Bx⋅Ay⋅−=axuxu∂∂⋅vyu∂∂⋅+=Ax⋅⋅+()x⋅⋅+∂∂⋅Bx⋅⋅−y⋅⋅+∂∂⋅+=axA2B2+x⋅=ayuxv∂∂⋅vyv∂∂⋅+=⋅⋅+x⋅⋅−∂∂⋅⋅⋅−y⋅⋅−∂∂⋅+=ayA2B2+y⋅=Hence at (2,2)ax19+1s2×m⋅=ax20ms=ay+1s2×m⋅=ay20ms=aax2ay2+=θatanayax⎛⎜⎝⎞⎠=a28.28ms=θ45 deg⋅=For the pressure gradientxp∂∂ρgx⋅ρax⋅−
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.