Ms. Howe, On Rayleigh's computation of the 'end correction', with application to thecompression wave generated by a train entering a tunnel, J FLUID MEC, 385, 1999, pp. 63-78
Rayleigh's (1926, Appendix A) method for the approximate calculation of pot
ential flow from the open end of a semi-infinite flanged cylinder is applie
d to obtain analytical representations of Green's function describing the g
eneration of sound waves within a hanged cylinder by sources located in the
neighbourhood of the open end. Detailed results are given for the circular
cylinder considered by Rayleigh and extension made to a hanged cylinder of
rectangular cross-section. The validity of various approximations is asses
sed by comparison with the exact solution available (by the method of confo
rmal transformation) for potential flow from a two-dimensional, hanged duct
. The results are used to compare the profiles and the pressure gradients o
f compression waves generated when a high-speed train enters tunnels of cir
cular and rectangular cross-sections.