The importance of the energy and momentum coefficients, α and β in hydraulic flow computations in stressed. Several methods of calculating them along with their values in some practical cases of Hydraulic Engineering are presented, α and β in reverse flows are defined and methods for their determination are presented. Some interesting aspects of the trends of their variation are discussed based on the experimental data of the authors as well as those of other investigators. Empirical formulae for the calculation of α and β in supercritical in rectangular channels are also presented pointing out their limitations.