Due Date: Friday, 09-23-05 This homework set # 5 is for the lecture on time-dependent and 2D-velocity velocity profile. Note that, there is a homework set #6 for the turbulent flow posted soon on the blackboard. The due date for HW set #6 is also on Friday, 09-23-05. Problem #1: A sphere of radius R is falling in creeping flow with a terminal velocity u∞through a quiescent fluid of viscosity μ. At what horizontal distance from the sphere does the velocity of the fluid fall to 1% of the terminal velocity of the sphere? Problem #2: Recall the example of flow around a solid sphere (see textbook, Example 4.2.1) When a liquid flows around a gas bubble, circulation takes place within the bubble. Thus circulation lowers the interface shear stress, and, to a first approximation, we may assume
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terminal velocity, following velocity components, dr ⎝ r, terminal velocity u∞