EGM6812_F10_HW6Q - EGM 6812 Fluid Mechanics 1 Fall 2010 6th...

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EGM 6812 Fluid Mechanics 1 - Fall 2010 10/4/10, 6 th Homework 1/2 1. Consider the flow in an annulus generated by a solid cylinder of radius b rotating at a speed in a larger cylindrical tube of inner radius a . The space between the cylinders is filled with a viscous incompressible fluid. Find the resulting velocity distribution in the fluid. Plot the velocity profile for different ratios ba and discuss the analytical limit of small gaps (Hint: perform a series expansion, truncate appropriately and examine the limits). 2. For the same geometry as problem 1, find the velocity profile if the rod is pulled in the axial direction at a constant speed 0 z vV , neglecting gravity and assuming constant pressure. Plot the velocity profile for different ratios and discuss the analytical limit of small gaps. 3. For the same geometry as problem 1, find the velocity profile if a constant pressure gradient p z is applied in the axial direction and discuss the analytical limit of small gaps.
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EGM6812_F10_HW6Q - EGM 6812 Fluid Mechanics 1 Fall 2010 6th...

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