Polishing operations involve rubbing two plates past one another with an intervening fluid. The fluid holds abrasive for the polishing and keeps the surfaces cool. One theory asserts that the degree of polishing is proportional to the shear stress at the surface of the object to be polished. Consider two such oscillating plates moving past one another. The bottom plate is stationary while the top plate moves with a velocity given by:

\[v=v_{o} \sin (\omega t+\phi)\]

For the system shown in Figure P6.30, determine the velocity profile in the fluid as a function of time and the shear stress exerted on the lower plate.

Transcribed Image Text:

FIGURE P6.30 3. v=0