Approximations to flow in slender tubes (Q1068621)

A tube of circular cross section whose radius is a function of a slow variable \(Z=(1/R)z\), where z is the co-ordinate in the axial direction and R is a large streamwise Reynolds number, may be designated a slender tube. An elementary approximation to the flow in such tubes is obtained and results compared with an approximation based on the profiles obtained by \textit{P. G. Daniels} and the first author [J. Fluid Mech. 90, 305-314 (1979; Zbl 0392.76031)] for exponential slender tubes.