The time-dependent bridge pier scour during flood waves is analysed. Scour experiments were conducted in a novel installation able to produce complex hydrographs with high precision. Experimental data were used to test scour formulas including a new mathematical model. Results confirm the reliability and superior performance of the proposed dimensionless, effective flow work based model under steady and unsteady hydraulic conditions. Analyses highlight the impact of different hydrographs on scour, demonstrating the strong control by the hydrograph shape of the temporal evolution of scour depth and scour rate, although final scour after a flood only depends on the total effective flow work exerted by the hydrograph on the sediment bed. Hysteresis between flow discharge and scour rate is reported and explained. Flow acceleration is shown to play a minor role in scouring. The proposed model is a promising alternative for computation of local scour under highly unsteady hydraulic conditions.