Based on the proposition that the limit of clear-water scour is a boundary shear equal to the critical tractive force, analytical relationships are obtained for the scour in a long contraction, at an abutment, and around a pier. The pier and abutment solutions make use of the assumption that the flow beyond the scour hole can be ignored and that the depth of scour at the pier or abutment is a multiple r of the scour in the equivalent long contraction. An expression for the active phase of scour is obtained using a simplified transport equation. Comparison of predictions with measurements from several laboratories is reasonably satisfactory.