online_contraction_scour_live_bed:  Contraction scour under live bed conditions using modified Laursen 1960 equation Modified Laursen formula ys / y1 = ( Q2 / Q1 ) 0.86 (W1 / [W2) k1  -  ( yo / y1 ) [ yo, y1, Q and W in any consistent set of units ] [ S1 in m/m or ft/ft ] [ T in °C or °F ] [ D50 in mm or ft ] Reference: Evaluating Scour at Bridges, FHWA Hydraulic Engineering Circular No. 18, Fifth Edition, 2012. DESCRIPTION:      [Sample Input]     [Main Page] To determine contraction scour depth under live bed conditions ys, the calculator requires the following information: Mean flow depth below the bridge, before scour yo, in m (or ft). Mean flow depth upstream of the bridge y1, in m (or ft). Discharge upstream of the bridge (only in the main channel) Q1 in m3/s, or (or cfs). Discharge in the contracted section Q2 in m3/s, or (or cfs). Bottom width in the section upstream of the bridge W1, in m (or ft). Bottom width in the contracted section, excluding piers W2, in m (or ft). Energy slope in the main channel upstream S1, in m/m (or ft/ft). Median diameter of the bed material D50, in mm (or ft). Water temperature θ , in oC (or oF). 1. To determine K1, first calculate the shear velocity in the upstream section V*, and the fall velocity of bed material ω. 1.1. The shear velocity V* is calculated using the formula V* = (gy1S1)1/2 1.2. The fall velocity ω is determined using the graph in Figure 1. Figure 1.  Fall velocity of bed material. 1.3. Finally, with V* and ω, K1 can be defined using Table 1. Table 1.  Exponent K1 V* / ω Mode of bed material transport K1 < 0.5 Mostly contact bed material discharge 0.59 0.5 - 2.0 Some suspended bed material discharge 0.64 > 2.0 Mostly suspended bed material discharge 0.69 2. The contraction scour depth ys can then be calculated using the following equation:   ys           Q2              W1             yo _____  =  (____) 0.86   (____) k1  -  ____   y1           Q1              W2             y1 yo = Given y1 = Given Q1 = Given Q2 = Given W1 = Given W2 = Given k1 = Calculated in step 1.