hw9_solutions

hw9_solutions - ES330 Assignment 9 Solutions Chapter 9 Due...

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Unformatted text preview: ES330 Assignment 9 Solutions Chapter 9 Due Date: Thursday November 4, 2010 I Problem 1 Beth is studying a rotating flow in a wind tunnel. She measures the u and v components of velocity using a hot-wire anemometer att x = 1 . 5 m and y = 0 . 2 m , u = 3 . 3 m/s and v =- 5 . 6 m/s . Unfortunately, the data analysis program requires input in cylindrical coordinates ( r, ) and ( u r ,u ). Help Beth transform her data into cylindrical coordinates. Specifically, calculate r,,u r , and u at the given data point. Solution We can calculate r and using equations given in the book: r = p x 2 + y 2 = p (1 . 5 m ) 2 + (0 . 2 m ) 2 = 1 . 513 m (1) = tan- 1 y x = tan- 1 . 2 m 1 . 5 m = 7 . 595 o (2) ( r, ) = ( 1 . 513 m, 7 . 595 o (0 . 1326rad) ) Finding the velocities in cylindrical coordinates is a little more difficult. We can use the figure below to help us geometrically determine u r and u . From the figure, we can see that: u r = u cos + v sin (3) = (3 . 3 m/s )cos(7 . 595 o ) + (- 5 . 6 m/s )sin(7 . 595 o ) = 2 . 531 m/s u = v cos - u sin (4) = (- 5 . 6 m/s )cos(7 . 595 o )- (3 . 3 m/s )sin(7 . 595 o ) =- 5 . 987 m/s ( u r ,u ) = ( 2 . 531 m/s,- 5 . 987 m/s ) 1 II Problem 2 A steady, two-dimensional, incompressible velocity field has Cartesian velocity components u = Cy 2 / ( x 2 + y 2 ) and v =- Cx/ ( x 2 + y 2 ), where C is a constant. Is the flow field physically possible?...
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hw9_solutions - ES330 Assignment 9 Solutions Chapter 9 Due...

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