In bridge hydraulics the features of scour at piers and abutments are a major issue. This paper summarizes research conducted at ETH Zurich as a collaboration with University of Basilicata, Italy. A previously established scour equation for the temporal progress of scour under well controlled laboratory conditions is discussed first, and the significant effect of the densimetric particle Froude number is particularly mentioned. The limitations of the new scour equation are also detailed. Then, the progress of scour depth is compared between the transitional and the fully turbulent regimes. It is found that the transition regime, occurring for most of the laboratory observations, is dominated by a significant scale effect due to fluid viscosity. The implications of this finding, that may explain present deviations with field observations, are finally highlighted.