Detailed Study of Binary Law for Open Channels

This paper presents a generalized version of the binary velocity distribution law, which combines the logarithmic law of the inner region with the parabolic law of the outer region. This combination is extended for cases of flow where the maximum velocity occurs at some distance below the free surface in a vertical. The study uses the data collected at the Indian Institute of Science over a long period for all of the four regimes of turbulent open channel flow, namely, subcritical smooth, supercritical smooth, subcritical rough, and supercritical rough. The various conditions and limitations at the junction point of the inner and outer region are derived and discussed in this paper. It is shown that the velocity distribution for the flows of narrow open channels can be described by the logarithmic law for the inner region and the parabolic law for the outer region, but the conditions at the junction point will not always be the same.