When the flow from an open channel is discharged freely into the air, the depth at the brink can be often closely correlated with the flow rate. Free-vortex velocity distribution and curvature are used to simulate the flow at the brink of smooth horizontal channels of various cross sections. A summary of the analysis is given herein for exponential channels of rectangular, triangular, and parabolic cross sections. The final theoretical values are also given for trapezoidal and circular cross sections. The final relationships for the case of jetted shooting flow just upstream of the end section of a rectangular channel are also given.