Flow reactors, denuders, and sampling tubes are essential tools for many applications in analytical and physical chemistry and engineering. We derive a new method for determining radial diffusion effects and the penetration or transmission of gas molecules and aerosol particles through cylindrical tubes under laminar flow conditions using explicit analytical equations. In contrast to the traditional Brown method [Brown, R. L. J. Res. Natl. Bur. Stand. (U. S.) 1978, 83, 1-8] and CKD method (Cooney, D. O.; Kim, S. S.; Davis, E. J. Chem. Eng. Sci. 1974, 29, 1731-1738), the new approximation developed in this study (known as the KPS method) does not require interpolation or numerical techniques. The KPS method agrees well with the CKD method under all experimental conditions and also with the Brown method at low Sherwood numbers. At high Sherwood numbers corresponding to high uptake on the wall, flow entry effects become relevant and are considered in the KPS and CKD methods but not in the Brown method. The practical applicability of the KPS method is demonstrated by analysis of measurement data from experimental studies of rapid OH, intermediate NO3, and slow O3 uptake on various organic substrates. The KPS method also allows determination of the penetration of aerosol particles through a tube, using a single equation to cover both the limiting cases of high and low deposition described by Gormley and Kennedy (Proc. R. Ir. Acad., Sect. A. 1949, 52A, 163-169). We demonstrate that the treatment of gas and particle diffusion converges in the KPS method, thus facilitating prediction of diffusional loss and penetration of gases and particles, analysis of chemical kinetics data, and design of fluid reactors, denuders, and sampling lines.