Comparison of celerity-based with velocity-based time-of-concentration of overland plane and time-of-travel in channel with upstream inflow

Traditionally, the overland time-of-concentration and the time-of-travel in channel are estimated based on the flow velocity. However, the kinematic wave theory shows that they ought to be estimated based on the wave celerity. In this paper, the comparison on the overland time-of-concentration shows that the average velocity-based time-of-concentration is longer than the maximum velocity-based time-of-concentration which is generally longer than the average celerity-based time-of-concentration for four flow regimes from laminar to turbulent. The comparison on the time-of-travel in channel shows that except for the deep rectangular channel, the average velocity-based time-of-travel is longer than the maximum velocity-based time-of-travel which is generally longer than the average celerity-based time-of-travel for six other channel shapes. Based on the above, a drainage design which uses the average velocity to estimate the time-of-concentration and the time-of-travel produces smallest design discharge (i.e. least conservative design). Despite the perception that a design which uses the maximum velocity to estimate the time-of-concentration and the time-of-travel produces a conservative design, this comparison shows that this is not the case when compared to another design which uses the average wave celerity.