Stage-fall-discharge relations for steady flow in prismatic channels

Abstract

In a prismatic channel, the shape of the surface remains fixed as long as the discharge, the slope, and the boundary conditions remain fixed. This Principle of rigidity of the profile was previously applied to the observation, under laboratory conditions, of 41 M-l type profiles for steady flow in prismatic channels. The same Principle of rigidity of the profile is now applied to the derivation, from these same profiles, of extensive data on relations among stage, fall, and discharge. These data are used to test the applicability of various methods of determining discharge under variable fall, under the particular conditions of boundary and slope which existed in the laboratory. Diagrams are presented to show that, using the uniform-flow ratings as a basis of comparisons, all the known curves of relation between stage, fall, and discharge become three-dimensional diagrams, rather than single curves. A new method of preparing such three-dimensional diagrams is proposed. Other diagrams are presented to show that by introduction of an optimum amount of backwater and substitution of the resulting fixed-backwater rating in place of the uniformflow rating as a basis of comparisons, the correlation between discharge ratios and fall ratios is so improved that a single curve of relation will, under all conditions that were tested, lead to a close approximation of the true discharge. Throughout the report emphasis is placed upon the fact that the findings and conclusions are solely with respect to the particular conditions of boundary and slope which were used in the laboratory. The applicability of these conclusions to field conditions has not been extensively explored. The final section of the report presents suggestions for use in connection with field problems. In the early part of the report, and incidental to the main theme, there is presented the theory of flow in prismatic channels. Data are presented to show the extent to which the laboratory observations are in agreement with this theory. 2 STAGE-FAIL-DISCHARGE RELATIONS