The first objective of this investigation was to derive and compare scour depth equations in a long contraction using the most widely used sediment transport equations and a variety of other equations. The second objective was to determine a procedure to find an equivalent rectangular section which would convey the same water discharge and sediment load at same slope as an irregular, natural channel in order to simplify numerical computations of scour depth and to allow appropriate application of long contraction scour theory. Some of the transport equations were manipulated algebraically to develop equations for scour depth and slope in a long contraction; others were manipulated using computer programs written especially for each equation, thus deriving scour depth equations. A computer program was written to compare characteristics of a non-rectangular section with rectangular sections of different widths in order to derive a procedure to find an equivalent rectangular transport section (a triangular section was used in this investigation) but the procedure is equally valid for any irregular, natural section. This investigation indicated that depth in the contraction is greater than in the wider approach channel. How much greater depended on which sediment-transport equation was used. Most of the derived scour equations, based on the different sediment transport equations, predicted that the y₂/y₁ ratio decreases as slope, velocity, c, and τₒ'/τ(c) or √τ/ρ)/ω increase; a few do not. Most of the analysis predicted S₂ < S₁, but a few do not. Field and experimental data provided extra evidence that the depth in the contracted section is greater than in the approach reach and how much greater. The evidence that the slope is flatter is not sufficient to be completely convincing. The equivalent rectangular transport section which can carry the same water and sediment discharge at the same slope as the natural section has a depth which is a large fraction of the deepest part of the original section, and the width is considerably narrower than the top width of the original section. Results of the investigation also indicated that the slope, velocity, sediment concentration, and sediment size have little effect on the geometry of the equivalent rectangular section.