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Final - Winter 2005

# Final - Winter 2005 - ME 320 Winter 2007 Sample Exam 2...

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ME 320 Winter 2007 Sample Exam 2 Problem 1 : A viscous-shear pump is made from a stationary housing with a close-fitting rotating drum inside, as shown in the figure. The clearance is small compared to the drum diameter so flow in the annular space may be treated as flow between parallel plates. Fluid dragged around the annulus by viscous forces and ejected through the outlet (a seal between the inlet and outlet prevents leakage). Evaluate the performance characteristics of the shear pump (pressure differential, input power, and efficiency) as functions of volume flow rate Q . Assume that the depth normal to the diagram is b . Problem 2 : A simple slider bearing has a uniform taper from the inlet, where the gap is b 1 , to the exit, where the gap is b 2 . The bottom surface moves at a steady speed V as shown. The local channel height is h . Assuming v = w = 0, answer the following questions. (a) From the Navier-Stokes Equation, show that the flow rate per unit depth normal to the figure can be written as dx dP h Vh q μ 12 2

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