Consider a viscous film of liquid draining uniformly down the side of a vertical rod of radius a, as in Fig. P4.84. At some distance down the rod the film will approach a terminal or fully developed draining flow of constant outer radius b, with υz = υz(r), υθ = υr = 0. Assume that the atmosphere offers no shear resistance to the film motion. Derive a differential equation for υ z, state the proper boundary conditions, and solve for the film velocity distribution. How does the film radius b relate to the total film volume flow rate Q?

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0 Pa Fully developed region Film U,