Open-Channel Flow at Small Reynolds Numbers

A summary and correlation are presented of the results of several theses studies on open-channel flow in a range of Reynolds numbers less than approximately 4 × 104.The hydraulic diameter is used as the length parameter in the Reynolds numbers. Smooth laminar flow, smooth turbulent flow, rough laminar flow, and rough turbulent flow are considered separately, as is transition from laminar flow to turbulent flow in smooth channels.

The results indicate that at these small Reynolds numbers, smooth channel flow, both laminar and turbulent, is quantitatively similar to smooth pipe flow. Rough channel flow is probably qualitatively similar to rough pipe flow and rough plate flow, but there is no adequate method available to correlate rough flows in the small Reynolds number range. Channel shape is important in laminar flow, but its en tire effect may be determined theoretically. There is only a negligibly small channel-shape effect in smooth turbulent flow and a somewhat more pronounced effect in rough turbulent flow. Transition generally occurs at slightly higher Reynolds numbers in channels than in pipes, the exact effect depending on shape.

Notation.-The letter symbols used in this paper are defined where they first appear, in the text or by illustration, and are assembled for convenience of reference in Appendix II.