The problem of transmission of sound in a narrow pipe carrying a mean flow has been dealt with in recent papers by solving the convected acoustic equations simplified in the manner of the Zwikker and Kosten theory. A significant difference between these studies appertains to the form of the axial mean flow velocity profile assumed in the analysis. Results have been presented previously for uniform and parabolic profiles. This paper presents a comparative study of these for pipes having circular and rectangular cross-sections. The solution of the governing equations for these cases has been presented in previous papers, except for the case of a rectangular pipe carrying a uniform mean flow, which is presented in this paper for the first time. The results indicate that the assumption of a uniform mean profile closely predicts the results based on a parabolic profile. An area in which the theories considered in this paper find application is the acoustical modelling of the honeycomb structure of a monolithic catalytic converter. Previous acoustic models proposed for the honecomb structure assume that the honeycomb pores to be circular. In the present paper a new model is presented for honeycomb structures with rectangular pores.