We address the differences observed due to heat release between reacting and non-reacting versions of otherwise identical shear flows under conditions for which buoyancy effects are negligible. The differences considered here result from density changes produced by exothermic reaction, and are shown to be similar to those produced by free-stream density differences in non-reacting flows. The piecewise linear variations of temperature with mole fraction allow the density changes due to exothermic reaction to be related to an equivalent non-reacting flow, in which the temperature of one of the fluids is raised to an effective value determined by the peak temperature and overall stoichiometry. This leads to a general equivalence principle by which the scaling laws for non-reacting flows can be extended to predict effects of heat release by exothermic reaction. This equivalence principle is then applied to axisymmetric turbulent jets, where it leads to a generalized momentum diameter d+ in which the scaling laws for burning and non-burning jets become identical – it effectively extends the classical momentum diameter d* of Thring & Newby (1953) and Ricou & Spalding (1961) to exothermic reacting flows. The resulting predicted effects of heat release, in both the near and far fields, show good agreement with experimental data from momentum-dominated turbulent jet diffusion flames. The equivalence principle is then applied to planar turbulent jets, for which it also accurately predicts the observed effects of combustion heat release.