Professor Cimbala was recently involved in some medical research at Hershey Medi

Question

Professor Cimbala was recently involved in some medical research at Hershey Medical Center in which the effects of shear stress on bone cells was studied. The cells are mounted on a stationary, round, flat dish of radius R. At distance h above the dish is a spinning disk, also of radius R. rotating at rpm (angular velocity omega). Sandwiched between the upper spinning disk and the lower stationary disk is a liquid with viscosity mu. Generate an expression for shear stress tau on the dish as a function of radial coordinate r and the parameters h, mu, and angular velocity omega. Hint: The gap height h between the two disks is very small compared to disk radius. Figure for Problem 1.

Explanation / Answer

According to newtons law of viscosity

shear stress = dv/dy

dv=r-0 = r (as bottom disc is static)

dy = h-0 =h

= dv/dy= * (r/h)

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