Dear Mohammad Hooshmandzadeh ,
For what is worth (and I do believe the original question might be exapanded with greater details), Sf relates to the friction slope , whereas Sc relates to the critical slope in a gravity open channel flow.
In case of uniform flow, since current lines are almost parrallel and pressure is uniformly distributed in a cross section, friction slope is almost equal to the channel slope, noted S0.
The ratio S0/Sc (assumed to be equal to Sf/Sc for uniform flow) will then relate to the type of flow regime which is likely to occur normally (without any singularity in the channel). if greater than 1 (S0 > Sc), channel slope is steep, hence supercritical flow. if lower than > 1 (S0 < Sc), channel slope is mild, hence subcritical flow.
Also note that some authors, when developping backwater curve equations, usually wrap the aforementionned ratio under the symbol β. An example is Bakhmeteff's (1932) varied flow equation.
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