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The roughness Froude number is a relatively new dimensionless parameter that began appearing in the hydraulic engineering literature in the late 1970s, first for the analysis of aeration inception in smooth chutes, and then later in connection with stepped chutes. This article reviews its foundations, historical development, alternative forms, present-day applications, and physical significance, which has received little attention previously. In addition to its empirically demonstrated connection to aeration inception, this paper shows that one form of a roughness Froude number has a strong relation to the transition between nappe and skimming flow regimes of stepped chutes, while another combines the dimensionless flow friction factor and the relative submergence of roughness elements. [ABSTRACT FROM AUTHOR]

Stepped chutes effectively dissipate the energy of supercritical flow of steep channels. In general, stepped chute flows are characterized by self-aeration. For their hydraulic design, it is important to know the aerated flow depth, the aerated flow velocity, the air concentration, and the specific energy. Herein, quasi-uniform aerated skimming flow is systematically investigated over a range of chute angles from 19° to 55° for a wide range of step heights and discharges. Air concentration and aerated flow velocity profiles are presented, and the depth-averaged air concentration and the friction factor are determined. The specific energy is determined based on the aerated flow characteristics, revealing the effects of chute angle and step height on the specific energy of aerated skimming flow. This quantity was compared with the conventional specific energy of clear-water flows. [ABSTRACT FROM AUTHOR]