The techniques previously employed by the writers for describing subcritical flow at open channel constrictions have been found valid for analyzing nonuniform flow in open channels. Combining the nonuniform flow analysis with the submerged flow ratings for various bridge geometrics has provided an analytical means for determining the backwater due to the bridge constrictions under “abnormal stage – discharge” conditions.
Skogerboe, Gaylord V.; Austin, Lloyd H.; and Chang, Kuan-Tao, "Subcritical Flow at Open Channel Structures Bridge Constructions" (1970). Reports. Paper 92.