SolutionHW_C4 - Homework Set #4: Due date: 10/06/06, by...

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Homework Set #4: Due date: 10/06/06, by 11:00 am. Problem #1: In Example 4.2-1 in Chapter 4 of BSL, a fluid approaches a stationary sphere from below. Now in this problem, a sphere of radius R is falling in creeping flow with a terminal velocity u through a quiescent fluid of viscosity μ. The velocity distribution of the fluid given as Eqs. (4.2- 13) and (4.2-14) in BSL are valid for this case. a. What velocity components (i.e. u θ , u r , and u Ø ) are zero on the z-plane at z=0 (see Fig. 2.6- 1 in Chapter 2 of BSL). b. Also on the z-plane at z=0, the fluid velocity increases from zero at the sphere surface to u at sufficiently far from the surface. At what horizontal distance from the sphere surface does the velocity of the fluid fall to 1% of the terminal velocity of the sphere? Answer: On the z-plane at z=0, u θ is the only non-zero velocity component. For a fixed sphere and a fluid approaching the sphere at u 3 31 1 44 RR uu rr θ ⎛⎞ ⎛⎞ ⎛⎞ =− ⎜⎟ ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ ⎝⎠
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This note was uploaded on 12/14/2011 for the course PGE 312 taught by Professor Peters during the Spring '08 term at University of Texas at Austin.

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SolutionHW_C4 - Homework Set #4: Due date: 10/06/06, by...

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