NEW THEORETICAL CONSIDERATIONS ON THE FLOW PARAMETERS IN THE TRANSITION AND SMOOTH REGIMES

Abstract

Transition and smooth flows are often encountered during experiments in the laboratory and even sometimes in the field. The transition domain occupies a fairly large space in Moody's diagram while the smooth flow is reduced to a curve which represents the lower envelope of the diagram. The characteristic length corresponding to these two domains, such as the width of a channel or the flow depth, is currently calculated by an iterative process such as the trial and error method. To overcome this drawback, the present study presents a direct method consisting of first calculating the characteristic length in the domain assumed to be rough. The characteristic length sought is equal to this length corrected for effects of a dimensionless correction coefficient. In the transition domain, the correction coefficient depends both on the Reynolds number and on the relative roughness corresponding to the rough domain while for the smooth regime the correction coefficient depends only on the Reynolds number in the rough zone. Expressions for Reynolds numbers in the transition and smooth domains are also presented. The governing relationships are practical and differ from those usually found in the literature. Practical numerical examples are provided to show both how the method should be applied and the evidence for its reliability.