Meen 344- HW 1 Soln

Meen 344- HW 1 Soln - MEEN 344: HW Problem Set #1 Solutions...

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MEEN 344: HW Problem Set #1 Solutions
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Problem 2.6 A velocity field is specified as, j bxy i ax V ˆ ˆ 2 + = r , where a = 1 m -1 s -1 , b= -5 m -1 s -1 , and the coordinates are measured in meters. Is the flow field one-, two-, or three-dimensional? Why? Calculate the velocity components at the point (2, ½). Develop an equation for the streamline passing through this point. Plot several streamlines in the first quadrant including the one that passes through the point (2, ½). Solution The velocity field is a function of x and y. It is therefore 2D At the point (2, ½), the velocity components are 2 2 ) 2 ( 1 1 m s m x a u × = = s m u = 4 m m s m y x b v × × = = 2 1 2 1 5 s m v = 5 For streamlines x a y b x a y x b dx dy u v = = = 2 So, separating variables x dx a b y dy = Integrating ) ln( ) ln( x a b y = 5 = = x c x c y a b T h e s o l u t i o n i s c 5 x y = See the plot in the corresponding Excel workbook c = 10 12 14 16 x y y y y 0.05 32000000 38400000 44800000 51200000 0.10 1000000 1200000 1400000 1600000 0.20 31250 37500 43750 50000 0.30 4115 4938 5761 6584 0.40 977 1172 1367 1563 0.50 320.00 384.00 448.00 512.00 0.60 128.60 154.32 180.04 205.76 0.70
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This note was uploaded on 07/28/2010 for the course MEEN 344 taught by Professor Schobeiri during the Fall '08 term at Texas A&M.

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Meen 344- HW 1 Soln - MEEN 344: HW Problem Set #1 Solutions...

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