Maximum practically achievable intensities are required for research with accelerated radioactive ion beams (RIBs). Time delays due to diffusion of radioactive species from solid or liquid target materials and their effusive-flow transport to the ion source can severely limit intensities of short-lived radioactive beams, and therefore, such delays must be minimized. An analytical formula has been developed that can be used to calculate characteristic effusive-flow times through tubular transport systems, independent of species, tube material, and operational temperature for ideal cases. Thus, the equation permits choice of materials of construction on a relative basis that minimize transport times of atoms or molecules moving through the system, independent of transport system geometry and size. In this report, we describe the formula and compare results derived by its use with those determined by use of Monte-Carlo techniques.