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Two Coaxial Cylinders And Repeating Analogous Problems In Concentric Spheres

Question

Flow problems where the Reynolds number is very, very small (Re<<1) are called “creeping flow.” These problems are of special interest because, unlike many other fluid mechanics problems, they can often be solved analytically. The underlying reason for this is that the Navier-Stokes equation contains a non-linear term (the v. V v term within the substantial derivative). However, if the Reynolds number is so small that it approaches zero, this non-linear term also approaches zero and effectively disappears from the equation.

(a) The space between two coaxial cylinders is filled with an incompressible fluid at constant temperature. The radii of the inner and outer wetted surfaces are κR and R, respectively. The inner and outer cylinders are rotated with a steady angular velocity of Ωi and Ωo, respectively, where these are sufficiently slow such that creeping flow may be assumed. Find the differential equation and boundary conditions that may be solved to find the velocity distribution in the fluid. (Note: You are not being asked to solve this equation!)

(b) Repeat for the analogous problem of concentric spheres.

Summary

The question belongs to Chemistry and it discusses about finding the differential equation and boundary conditions between two coaxial cylinders and repeating the analogous problems of concentric spheres.

Total Word Count 65

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