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Ar and As variables The Ar and As variables are shown graphically in
Figure 2.2. An equation for Ar is
Ar = - 27.058 log10 (F + 9) + 34.289
Equation 2-13
where F is the Froude number. Data ranges from 0.2 < F < 8.0.
Using an equation of the same form, the relationship for As is
As = - 24.739 log10 (F + 10) + 29.349
Equation 2-14
Equations 2-6, 2-10, 2-12, 2-13 and 2-14 are used in SAM.hyd to calculate the
roughness coefficient when the Keulegan equations are specified.
Strickler Equation
The Strickler function is compared to measured data in Figure 2.3. (Chow,
1959) This figure shows that for a wide range in relative roughness, R/ks, the
variability of the Strickler function φ R/ks is small. Strickler assumed this to be a
constant, 0.0342 when ks and R were expressed in feet. The effective surface
roughness height, ks, is the d50 of the bed sediment in this figure. However, ks
can be correlated with other measures of the surface roughness, depending on
what is representative of the surface roughness height of the boundary materials.
For example, riprap research at WES (Maynord 1991, 1992) has shown that the
Strickler equation will give satisfactory n-values when ks is taken to be the d90 of
the stone.
Figure 2.3. The Strickler Function (Chow, 1959), used with permission from McGraw-
Hill Book Company, Inc.
Chapter 2
Theoretical Basis for SAM.hyd Calculations

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