Supercritical Flow in Bends of Trapezoidal Section

Steady supercritical flow in circular bends of trapezoidal cross section is analyzed for the case in which the radius of curvature r₀ of the center line is much larger than the undisturbed depth of flow h₀. Supercritical flow in bends of trapezoidal cross section has been analyzed for the case ϵ=h₀/r₀≪1 and F₀>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(2mh₀+b)/(r₀g) and back down again. The distance measured along the center line to the first peak is given by s=β(2mh₀+b)F₀ in which β is between 1.0 and 1.20.