Abstract
Steady supercritical flow in circular bends of trapezoidal cross section is analyzed for the case in which the radius of curvature r 0 of the center line is much larger than the undisturbed depth of flow h 0 . Supercritical flow in bends of trapezoidal cross section has been analyzed for the case ϵ=h 0 /r 0 ≪1 and F 0 >2. It was found that an almost periodic pattern of crests exists along the outside edge that are exactly matched in magnitude and position by a pattern of depressions along the inside edge. The crests along the outside edge rise from near the undisturbed flow elevation to a maximum value near U²(2mh 0 +b)/(r 0 g) and back down again. The distance measured along the center line to the first peak is given by s=β(2mh 0 +b)F 0 in which β is between 1.0 and 1.20.
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