Regionalization of Unit Discharge and Head Loss Stream Flow Equations at Bridge Constrictions in South Dakota

The objective of this thesis is to develop South Dakota specific regionalized flow equations for unit discharge versus downstream contraction velocity and downstream contraction velocity versus head loss at bridge constrictions in South Dakota. The significance and practical purpose of this research is to develop equations for use in a bridge scour study using the rapid estimation method in South Dakota for the U.S. Geological Survey (USGS) and South Dakota Department of Transportation (SDDOT). Similar studies have been completed in Montana, North Dakota, Missouri, and a previous study (http://pubs.usgs.gov/sir/2008/5161/) was completed on a separate set of bridges in South Dakota.;The relation between downstream contraction velocity and head loss in South Dakota can be represented with a single equation of Delta h =0.02067 V22 -- 0.00952, where Deltah is head loss in feet and V2 is the contraction velocity in feet per second; the coefficient of determination (R2) value is 0.9286. This equation was developed for use on high-flow ranges, such as approximately one-half of bridge-full to as much as bridge-full conditions. South Dakota was found to have four distinct regions (classified as A-D) for the relation between unit discharge and downstream contraction velocity. Region A (Black Hills area in western South Dakota) was V2 = 1.3921 q0.4518, Region B (remainder of area west of the Missouri River) was V2 = 0.9344 q 0.4736, Region C (area east of the Missouri River excluding the Lake Dakota Plain) was V2 = 0.7068 q 0.5007, and Region D (Lake Dakota Plain) was V 2 = 0.5544 q0.4697, where q is the unit discharge in feet per second. These four equations are valid over a wide range of flows from the unit discharge of at least 1 cubic foot per second per foot to as much as bridge-full conditions.;The new equations are similar to those published by other States, such as Montana, North Dakota, and Missouri, and have higher R2 values than those equations from other States. The new equations also are similar to theoretically derived equations. The equation relating downstream contraction velocity to head loss was similar to a previously developed equation for North Dakota.