A simple and inexpensive way of channel discharge measurement is to introduce an axial obstruction in the flow cross- section, thereby creating the critical flow conditions. Such flow measuring devices are referred to as baffle flumes. Literature showed that the critical flow conditions are routinely assumed to occur at the minimum flow cross-section in the flume, however practically the critical section lies slightly on the upstream side. This paper presents an analytical approach to deduce the discharge prediction model on the basis of identification of true location of critical flow section that lies near the vicinity of the least constricted section in the baffle flume. Using the experimental data, a relationship between the ratio of energy to critical depth and the geometrical configuration of the baffle flume having conical shaped obstruction in a trapezoidal channel section, is obtained. Coupled with the expression for critical contracted width, the location of the critical flow section is established. Numerical analysis has also been carried out to ascertain the applicability of the proposed discharge prediction model. The discharge prediction model presented herein for the Conical Central Baffle Flume, is found to provide the discharge with better accuracy (maximum error 2.49%) when compared with the Kapoor et al. (2021) model available in the literature (maximum error 5.24%). An illustrative example to demonstrate use of the proposed methodology, is also appended herein for the benefit of the field hydraulic engineers dealing with flow measurements.