The recommended clear-water contraction scour equation by the HEC No. 18 publication is an equation based on research from Laursen (1963):

1) \displaystyle y_2 = \left[ \frac{Q^2_2}{CD^{2/3}_m W^2_2} \right]^{3/7}
2) y_s = y_2 - y_0
SymbolDescriptionUnits

D_m

Diameter of the smallest non-transportable particle in the bed material (1.25 D50) in the contracted sectionfeet (meters)

D_{50}

Median diameter of the bed materialfeet (meters)

C

130 for English units (40 for metric)

Note

If the bridge opening has overbank area, then a separate contraction scour computation is made for the main channel and each of the overbanks.