On Rayleigh's computation of the 'end correction', with application to thecompression wave generated by a train entering a tunnel

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.