The conversion due to first- and second-order, irreversible, equimolar reactions in fully developed isothermal laminar flow in a round tube was computed exactly for perfect, finite, and negligible molecular diffusion of species and energy. The analogous computations for fully developed turbulent flow were based on an essentially exact velocity distribution but an empirical model for the eddy diffusion of species and energy. The effect of a moderate heat of reaction was computed numerically for constant density, constant viscosity, and adiabatic conditions. The identification and implementation of a new dimensionless variable led to the discovery of several near-invariances and, thereby, to very simple but reasonably accurate algebraic representations for the mixed-mean conversion and the mixed-mean temperature for moderately energetic reactions.