**Ar and As variables **The *Ar *and *A*s variables are shown graphically in

Figure 2.2. An equation for *A*r is

*Ar = - 27.058 *log*10 (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 *A*s is

*As = - 24.739 *log*10 (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.

14

Chapter 2

Theoretical Basis for SAM.hyd Calculations