F.2.2.2 Outlet Control Analysis

Nomographs such as those provided in Figure F.12 and Figure F.13 may be used to determine the outlet control headwater depth at design flow for various types of culverts and inlets. Outlet control nomographs other than those provided can be found in FHWA HDS No.5 or the WSDOT Hydraulic Manual.

Figure F.12. Head for Culverts (Pipe w/n = 0.012) Flowing Full with Outlet Control.

Figure F.13. Head for Culverts (Pipe w/n = 0.024) Flowing Full with Outlet Control.

Figure F.14. Critical Depth of Flow for Circular Culverts.

The outlet control headwater depth may also be determined using the simple Backwater Analysis Method presented in F.2.1.2 Backwater Analysis Method for analyzing pipe system capacity. This procedure is summarized for culverts by Equation F.8:

Equation F.8. Outlet control headwater depth (Backwater Analysis Method)

where:

HW = headwater depth above inlet invert (ft)

H = H_f + H_e + H_ex

H_f = friction loss (ft) = (V²n²L) / (2.22R^1.33)

If (H_f + TW ‑ LS) < D, adjust H_f such that (H_f + TW ‑ LS) = D. This will keep the analysis simple and still yield reasonable results (erring on the conservative side).

H_e = entrance head loss (ft) = K_{e *} (V² / 2g)

H_ex = exit head loss (ft) = V² / 2g

TW = tailwater depth above invert of culvert outlet (ft)

If TW < (D + d_c)/2, set TW = (D + d_c)/2. This will keep the analysis simple and still yield reasonable results.

L = length of culvert (ft)

S = slope of culvert barrel (ft/ft)

D = interior height of culvert barrel (ft)

V = barrel velocity (fps)

n = Manning's roughness coefficient; see Table F.2.

R = hydraulic radius (ft)

K_e = entrance loss coefficient; see Table F.4.

g = acceleration due to gravity (32.2 ft/sec²)

d_c = critical depth (ft); see Figure F.14

The above procedure should not be used to develop stage/discharge curves for level pool routing purposes because its results are not precise for flow conditions where the hydraulic grade line falls significantly below the culvert crown (i.e., less than full flow conditions).

Table F.4. Entrance Loss Coefficients.

Type of Structure and Design Entrance	Coefficient, Ke
Pipe, Concrete, PVC, Spiral Rib, DI, and Lined CPE
Projecting from fill, socket (bell) end	0.2
Projecting from fill, square cut end	0.5
Headwall, or headwall and wingwalls
Socket end of pipe (groove-end)	0.2
Square-edge	0.5
Rounded (radius = 1/12D)	0.2
Mitered to conform to fill slope	0.7
End section conforming to fill slope*	0.5
Beveled edges, 33.7° or 45° bevels	0.2
Side- or slope-tapered inlet	0.2
Pipe, or Pipe-Arch, Corrugated Metal and Other Non-Concrete or D.I.
Projecting from fill (no headwall)	0.9
Headwall, or headwall and wingwalls (square-edge)	0.5
Mitered to conform to fill slope (paved or unpaved slope)	0.7
End section conforming to fill slope*	0.5
Beveled edges, 33.7° or 45° bevels	0.2
Side- or slope-tapered inlet	0.2
Box, Reinforced Concrete
Headwall parallel to embankment (no wingwalls)
Square-edged on 3 edges	0.5
Rounded on 3 edges to radius of 1/12 barrel dimension or beveled edges on 3 sides	0.2
Wingwalls at 30° to 75° to barrel
Square-edged at crown	0.4
Crown edge rounded to radius of 1/12 barrel dimension or beveled top edge	0.2
Wingwall at 10° to 25° to barrel
Square-edged at crown	0.5
Wingwalls parallel (extension of sides)
Square-edged at crown	0.7
Side- or slope-tapered inlet	0.2
* Note: “End section conforming to fill slope” are the sections commonly available from manufacturers. From limited hydraulic tests they are equivalent in operation to a headwall in both inlet and outlet control. Some end sections incorporating a closed taper in their design have a superior hydraulic performance.