Unstable Turbulent Flow in Open Channels

Controversy on the determination of the friction factor, f, for turbulent flow in open channels of rectangular cross section has existed among previous investigators. A number of them found that the Froude number affects the value of the friction factor, while others did not find such a dependence. In this study, the theoretical expression for the critical Froude number is first derived. Given a value of the Reynolds number, the flow becomes unstable above the critical Froude number. This critical Froude number, which appears to be strongly dependent upon the channel width, is then introduced in an equation by Rouse to calculate the values of the friction factor under unstable flow conditions. The influence of the Froude number on the friction factor appears to be important, but the channel width is a determinating factor as well.