This paper complements earlier papers by Van Dyke (1970) and by Wilson (1971) which have appeared under the same title. Second-order boundary-layer theory is used to examine the region near the entrance to a single channel placed in a uniform stream. It is found that there are additional effects to those present in the three models treated by Van Dyke and Wilson. In particular, the cascade model misses the leading term in the separation force while the irrotational-entry model misses that in the skin friction.
There are also two new effects far downstream: logarithmic terms appear (apparently for the first time in second-order theory); and a resonance with the first eigensolution occurs.