For flow between concentric cylinders, with the outer

Chapter 6, Problem 6.110

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For flow between concentric cylinders, with the outer cylinder rotating at an angular velocity \(\omega\) and the inner cylinder fixed, it is commonly assumed that the tangential velocity \(v_\theta\) distribution in the gap between the cylinders is linear. Based on the exact solution to this problem (see Problem 6.109) the velocity distribution in the gap is not linear. For an outer cylinder with radius \(r_o=2.00\) in. and an inner cylinder with radius \(r_i=1.80\) in., show, with the aid of a plot, how the dimensionless velocity distribution, \(v_\theta / r_o \omega\),varies with the dimensionless radial position, \(r/r_o\), for the exact and approximate solutions.