For most natural channels and many designed channels, the roughness varies along the wette...

For most natural channels and many designed channels, the roughness varies along the wetted perimeter of the channel. In order to perform normal flow computations for these composite channels it is necessary to compute the composite (equivalent or effective) roughness factor. For the composite channel in Figure 5.4.2, compute the effective roughness factor (ne) at river mile 1.0 for a water surface elevation of 125 ft using the following equations:

and

where Pi and ni are, respectively, the wetted perimeter and Manning’s n for each subsection of the channel; is the wetted perimeter of the complete channel section, and N is the number of subsections of the channel.

Figure 5.4.2 Cross-section and reach length data for example 5.4.3 (from Hoggan (1997)).

EXAMPLE 5.4.3

For the compound cross-section at river mile 1.0 shown in Figure 5.4.2, determine the energy correction factor α. The discharge is Q = 11,000 cfs and the water surface elevation is 125 ft.

SOLUTION

Step 1 Compute the cross-sectional areas of flow for the left overbank (L), channel (C), and right overbank (R):

Step 2 Compute the hydraulic radius for L, C, and R:

Step 3 Compute the conveyance factor for L, C, and R:

Step 4 Compute totals At and K1:

Step 5 Compute K3/A2 and :

Step 6 Use equation (5.4.24) to compute α: