Fall Velocity for Live-bed Contraction Scour Calculation Using HEC-18 Equation

Fall Velocity for Live-bed Contraction Scour Calculation Using HEC-18 Equation

To apply the HEC-18 Equation 6.2 (Figure 1) to calculate the live-bed contraction scour depth, the bed material particle D50 fall velocity needs to be determined to estimate the coefficient K1 (Figure 2).

Figure 1
Figure 2

HEC-18 Figure 6.8 can be used to estimate the fall velocity for D50 up to 10mm (Figure 3).

Figure 3

To automate the fall velocity calculation process and more importantly, to estimate the fall velocities for D >10mm, two equations are introduced here whose results are in good accordance with HEC-18 Figure 6.8.

Van Rijn Equation (HEC-RAS Hydraulic Reference Manual)

Based on Stokes’ law, Van Rijn proposed a set of 3 equations to estimate fall velocities for different sizes of particles (Figure 4). HEC-RAS Hydraulic Reference Manual introduced the equations, however, the manual has a typo: the diameter d’s exponent of 2 is missing in the first equation for 0.001<d=<0.1mm. Figure 4 below has added back the exponent.

Figure 4

Ferguson Church Equation

Ferguson and Church proposed another equation to calculate the fall velocity (Figure 5).

Figure 5

The two equations including the suggested constants introduced above are for fall velocities of natural sediment particles at water temperature around 20°C (68°F). The results of the two equations match well especially at D<10mm (Figure 6).

Figure 6

The equations and the suggested constants are only meant to estimate the fall velocity of D50 and HEC-18 live-bed contraction scour Equation 6.2 coefficient K1. Their application for other purposes should be carefully evaluated for suitability.

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