Tangential annular flow of a highly viscous liquid, show that Eq. 11.4-13 for flow in an annular region reduces to Eq. 10.4-9 for plane slit flow in the limit as ,c approaches unity. Comparisons of this kind are often useful for checking results. 

The right side of Eq. 11.4-13 is indeterminate at k = 1, but its limit as k → 1 can be obtained by expanding in powers of ε = 1 – k. To do this, set k = 1 – ε and ζ = 1 – ε [1 – (x/b)]; then the range k < ζ c < 1 in Problem 11.4-2 corresponds to the range 0 < x < b in S10.4. After making the substitutions, expand the right side of Eq. 11.4-13 in powers of e (neglecting terms beyond ε²) and show that Eq. 10.4-9 is obtained.