Transition between sub- and supercritical flows in open channel occurs at the so-called critical point, for which critical flow conditions appear. This particular flow state has been originally introduced for flows with parallel streamlines. However, as streamlines are considerably sloped and inclined in the vicinity of the critical point, these effects have to be accounted for. The present investigation explores in detail these effects. In particular, present investigations include i) first order analysis expressing discharge in terms of upstream head and channel geometry (calibration of discharge measurement structures) and ii) determination of surface profiles for transitional flow states by accounting for the effective pressure and velocity distributions. Analysis is based on a first order model with restriction to typical channel bottom and sidewall geometry. Results are compared with observations, and a fair agreement between the two is noted.