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Unformatted text preview: ME220A 1 Homework 4 / Take-home final exam (due at 12:30 pm on November 30, 2011) Problem 1. Find the pressure distribution in the slipper bearing assuming that the fluid motion is in the Stokes regime (cf. figure 1). z Solid Fluid p a p a L z=h(x) x U α Figure 1: Slipper bearing. The plate moves with the constant velocity U . The lower boundary of the bearing, located at z = h ( x ), is static and tilted at small angle α . p a is the ambient pressure. Problem 2. A liquid film of surface tension σ is stretched between two circular loops of radius a as shown. Find the equation(s) for r ( z ). For which ratio d/a is the configuration indicated in figure 2 stable? r(z) a 2d z Figure 2: Soap film stretched between two circular loops. ME220A 2 Problem 3. Consider an impact of a blunt body, e.g. a flat disk, on a flat liquid surface. Formulate the problem in 2D and simplify the equations of motion as much as you can. Justify your simplifications. Find the velocity of the disk right after the impact.can....
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- Fall '10
- Take-Home Final Exam, circular loops, inner radius r1, regime (cf., hydrodynamic destabilizing eﬀects