4.6 POWER FUNCTION RELATIONSHIPS
In Section 4.5, three classic sediment transport equations were presented. Of the three, the
Meyer-Peter and Mller bedload equation is still widely used, and the Colby method provides
a graphical approach that can be used as a quick check on the reasonableness of the results
of other sand-bed sediment transport calculations. Both are simple enough in their
application to be considered "basic" approaches for hand calculation, although, as indicated
above, they can be integrated into computer solutions. To provide additional basic
approaches, power function relationships are discussed in this section. These provide a
practical method for quick sediment transport calculations and are readily adaptable to
computer solutions.
4.6.1 Introduction
Power relationships relate sediment transport rates to hydraulic conditions and sediment
characteristics. The value of power relationships is in (1) their ease of use, (2) application to
specific flow regimes, and (3) application to site-specific conditions. Most power function
relationships correlate sediment transport to velocity and flow depth. This simple relationship
can be used as a first estimate of sediment transport capacity or as a comparison with the
more rigorous equations. Power relationships can be developed by computing sediment
transport with a more rigorous approach and fitting the results to a power function form. The
Simons et al. (1981) power function was developed specifically for supercritical flow
conditions on sand and fine gravel bed channels. Power relationships are also well suited for
correlating measured sediment transport with observed hydraulic conditions. The resulting
equation is site specific, but can be used, with judgment, to estimate sediment transport rates
for hydraulic conditions outside the range of observations. HEC-20 (Chapter 6) illustrates the
application of power relationships to predicting the equilibrium slope for a channel that is
either sediment deficient or has an excessive sediment supply.
The following sections present the Simons et al. (1981) power function that was developed
for steep sand and gravel bed channels. A more general power function relationship, by
Kodoatie et al. (1999), is also presented. The Kodoatie equation can be used for silt, fine
sand, medium to coarse sand, and gravel bed rivers by selecting appropriate coefficients and
exponents. HEC-20 (Lagasse et al. 2001) includes a power function equation developed
using the Yang (1996) sand transport equation.
In summary, power relationships empirically relate sediment transport with hydraulic
conditions and sediment characteristics. They can be developed by fitting the coefficients to
computed sediment transport data from more sophisticated equations or to measured data.
Their utility is in their ease of use and, when developed from measured data, their site-
specific accuracy.
4.6.2 Basic Power Function Relationship
In 1981, Simons et al. proposed an efficient method of evaluating sediment discharge. The
method is based on the variables flow depth, velocity, and particle diameter, and gradation
coefficient. The basic power function relationship is:
qs = c s1y cs2 V cs3
(4.48)
4.27
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