This study is a part of a more comprehensive research and is focused on the bed scour that would occur when rivers are forced by manmade or natural contractions. To this purpose, some experiments, typically lasted for days, were carried out at University of Basilicata in a straight rectangular channel and under clear water scour regime. The bed material was uniform sand and three contraction models, with opening ratio (i.e. ratio between the widths of the contracted and uncontracted reaches) of 0.9, 0.8, and 0.7, were used. Starting from the monomial form of sediment transport formulas, a new relationship for the quasi-equilibrium scour depth is conjectured based on Froude’s similarity and by relating the scour depth to the difference betwe...