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Scales involved in bridge pier scour include the Reynolds number, the Froude number, and the ratio of the pier to the sediment diameter, among others. Consequently, it is not possible to achieve perfect similitude, and thus scale effects between model and prototype arise. In fact, these scale effects distort the scour estimations typically used in hydraulic design of bridges, as scour formulas are based mainly on results from scour experiments at the laboratory scale. In this paper, proper scales of the flow, sediment, and scour are derived theoretically. The suitability of these scales to achieve perfect similitude of scour is tested through carefully designed laboratory experiments conducted in three different flumes having different sizes and piers of different diameters, with five bed materials of different sizes and densities. Results show that the dimensionless effective flow work, W* is a suitable criteria for scaling the effects of river flows on the local scour process around a pier in a bed composed by grains represented by the dimensionless grain diameter D*. In this context, scale effects of the ratio of the pier to the sediment diameter is quantified and shown to be negligible.