Energy Balance at Inlet

The outlet control headwater, HW
oc
, is computed by balancing the energy equation, depicted as Equation 8-15. The hydraulic grade at the inside face of the culvert at the entrance will need to be known. See
Energy Losses through Conduit
. The velocity at the entrance (v
i
) is used to compute the velocity head at the entrance (h
vi
).
EquationObject247272
Equation 8-15.
where:
  • HW
    oc
    = headwater depth due to outlet control (ft. or m)
  • h
    va
    = velocity head of flow approaching the culvert entrance (ft. or m)
  • h
    vi
    = velocity head in the entrance (ft. or m) as calculated using Equation 8-9
  • h
    e
    = entrance head loss (ft. or m) as calculated using Equation 8-16
  • H
    i
    = depth of hydraulic grade line just inside the culvert at inlet (ft. or m).
    Generally, when using Equation 8-15, the velocity approaching the entrance may be assumed to be negligible so that the headwater and energy grade line are coincident just upstream of the upstream face of the culvert. This is conservative for most department needs. The approach velocity may need to be considered when performing the following tasks:
  • determining the impact of a culvert on FEMA designated floodplains
  • designing or analyzing a culvert used as a flood attenuation device where the storage volumes are very sensitive to small changes in headwater.
The entrance loss, h
e
, depends on the velocity of flow at the inlet, v
i
, and the entrance configuration, which is accommodated using an entrance loss coefficient, C
e
.
EquationObject248273
Equation 8-16.
where:
  • C
    e
    = entrance loss coefficient
  • V
    i
    = flow velocity inside culvert inlet(fps or m/s).
NOTE: The pipes of pipe runner SETs have been proven to be within the tolerance of the entrance loss equations. Therefore, the entrance should be evaluated solely for its shape and the effect of the pipes should be ignored.
Values of C
e
 are shown on the following table (Entrance Loss Coefficients) based on culvert shape and entrance condition. (AASHTO Highway Drainage Manual Guidelines, 4th Ed, Table 4-1)
Table 8-5: Entrance Loss Coefficients (Ce)
Concrete Pipe
C
e
Projecting from fill, socket end (groove 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 1/12 D)
0.2
Mitered to conform to fill slope
0.7
End section conforming to fill slope
0.5
Beveled edges, 33.7º or 45º bevels
0.2
Side- or slope-tapered inlet
0.2
Corrugated Metal Pipe or Pipe Arch
-
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, 33.7º or 45º bevels
0.2
Side- or slope-tapered inlet
0.2
Reinforced Concrete Box
-
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 30º to 75º 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 10º to 25º 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