# hw 5 - T=10x+4y. a) Determine, using the material...

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AAE333 Fall 2009 Problem Set #5 Due: Monday 10/5/9 10% bonus if turned in on Friday 10/2/9 (more later) 1. Suppose you have a 2D steady velocity field u=3y, v=2x. a. Calculate the vorticity b. Calculate the area intergral of the vorticity over a square of side L covering the range 0<x<L, 0<y<L c. Calculate the circulation about the above square d. What does Stokes’ Theorem tell you about the results of these two calculations in b and c? 2. Repeat Prb 1. with the velocity field u=2y, v=2x 3. Find a velocity potential, if possible, for the velocity fields in 1. and 2. If it’s not possible, state why. 4. Find a stream function, if possible, for the velocity fields in 1. and 2. If it’s not possible, state why. 5. Suppose you have a 2D steady velocity field u=3y, v=2x and a temperature field
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Unformatted text preview: T=10x+4y. a) Determine, using the material derivative, the rate of change of temperature (with time) measured by a thermocouple moving with the fluid through the point x=3, y=2. b) Determine the rate of change of temperature (with time) measured by a thermocouple fixed at the point x=3, y=2 c) Sketch the streamline passing through the point x=3,y=2. If the thermocouple is at (3,2) at t=0, mark where it would be at t=0.01. How far has it moved in the x and y directions in that interval? What temperature does it read at the beginning and end of this interval? Compare the time rate of change of temperature calculated from DELTA(T)/DELTA(t) to what you got in a)....
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