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Unformatted text preview: MAE 101A: Introductory Fluid Mechanics Winter 2009 FINAL EXAM Professor Alison Marsden Thursday 19th, 2009. Short answers: 1. (6pt) State in words the physical meaning for a) the gradient of a scalar field f , b) the divergence of a vector field v , and c) the curl of a vector field v . 2. (2pt) State in words the physical meaning of the Reynolds number. 3. (2pt) Write down the material derivative of the temperature T in cartesian coordinates. Problems: 4. (10pt) Consider the velocity field v = u i + v j in cartesian coordinates given by u = y x 2 + y 2 , v =- x x 2 + y 2 , a) Is the flow field steady or unsteady? b) Calculate the equation of the streamline passing through the point (0 , 5), and sketch a plot of the streamline. c) Are the streamlines, pathlines and streaklines the same in this particular flow field? Why? 5. (20pt) A planar jet of a liquid of density impinges on a plate at an angle as depicted in the figure. The jet has velocity V and thickness h . Neglect viscous and gravitational effects and assume the flow is steady. The ambient pressure is....
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- Winter '08