Design of Hydraulically Efficient Power-Law Channels with Freeboard

A power-law channel is a generalized form of the parabolic channel. The exponent of the governing equation is a variable that for certain maximum permissible side slopes can be determined by maximizing the cross-sectional area of flow (or minimizing the wetted perimeter). Using this exponent rather than the constant allows a hydraulically more efficient open channel section to be designed. In earlier work on power-law channels freeboard was neglected to simplify the analysis. However as pointed out by several authors, a channel without freeboard is of academic interest only and not practical. All open channels are in practice designed and constructed with freeboard as a factor of safety. In this paper freeboard has been introduced as an additional parameter to be taken into account when designing a power-law channel. The work from this paper is applied to an earlier example of a parabolic channel to demonstrate a practical design.