This analysis is an expansion of research done by Rollin Hotchkiss during his Ph.D work. The research uses fluid flow, sediment transport, and perturbation theory to predict where scour will occur in a variable-width channel. The resulting equations also determine equilibrium scour depth based upon the stream bed elevation derived from a dimensionless bed slope equation. Hotchkiss perturbed the width of the channel using a second order Taylor Series perturbation but neglected second order terms. The present work follows the same procedures as Hotchkiss but maintains the second order terms. The primary purpose is to examine how the additional terms impact the final equilibrium scour depth and location results. The results of this research show a slight variation from the previous work. With respect to a hypothetical case, there was not a significant amount of change, thereby verifying that scour migrates downstream with an increase in discharge. Interestingly, the comparison shows a slight increase in sediment discharge through the test reach analyzed. Supplementary to previous research, values of scour depth and location in terms of distance from the start of channel-width perturbation are provided; at the lowest discharge maximum scour occurs 4% of a wavelength upstream of the narrowest portion, and at the highest discharge maximum scour occurs at the narrowest point. Additionally, a one-dimensional HEC-RAS sediment transport model and a two- dimensional SRH flow model were compared to the analytical results. Results show that the model output of the HEC-RAS model and the SRH model adequately approximate the analytical model studied. Specifically, the results verify that maximum scour depth transitions downstream as discharge increases.