Headwater under Outlet Control

Outlet control occurs when the culvert barrel is not capable of conveying as much flow as the inlet opening will accept. Outlet control is likely only when the hydraulic grade line inside the culvert at the entrance exceeds critical depth. (See Chapter 6 for Hydraulic Grade Line Analysis.) Therefore, outlet control is most likely when the culvert is on a mild slope (d
n
 > d
c
). It is also possible to experience outlet control with a culvert on a steep slope (d
n
 < d
c
 ) with a high tailwater such that subcritical flow or full flow exists in the culvert.
The headwater of a culvert in outlet control is a function of discharge, conduit section geometry, conduit roughness characteristics, length of the conduit, profile of the conduit, entrance geometry (to a minor extent), and (possibly) tailwater level.
The headwater of a culvert under outlet control can be adjusted, for practical purposes, by modifying culvert size, shape, and roughness. Both inlet control and outlet control need to be considered to determine the headwater. The following table provides a summary conditions likely to control the culvert headwater. Refer to Figure 8‑4 and Figure 8‑5 to identify the appropriate procedures to make the determination.
Table 8-2: Conditions Likely to Control Culvert Headwater
Description
Likely Condition
Hydraulically steep slope, backwater does not submerge critical depth at inside of inlet
Inlet control
Hydraulically steep slope, backwater submerges critical depth at inside of inlet
Outlet control
Hydraulically steep slope, backwater close to critical depth at inlet
Oscillate between inlet and outlet control.
Hydraulically mild slope
Outlet control
Outlet control headwater is determined by accounting for the total energy losses that occur from the culvert outlet to the culvert inlet. Figure 8‑7 and Figure 8‑8 and associated procedures in Section 4 should be used to analyze or design a culvert.
Outlet control headwater HW
oc
 depth (measured from the flowline of the entrance) is expressed in terms of balancing energy between the culvert exit and the culvert entrance as indicated by Equation 8-8.
EquationObject240265
Equation 8-8.
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
    f
    = friction head losses (ft. or m) as calculated using
    Equation 8-11
  • S
    o
    = culvert slope (ft./ft. or m/m)
  • L
     = culvert length (ft. or m)
  • H
    o
    = depth of hydraulic grade line just inside the culvert at outlet (ft. or m) (outlet depth).
    EquationObject241266
    Equation 8-9.
    where:
  • v
     = flow velocity in culvert (ft./s or m/s).
  • g
     = the gravitational acceleration = 32.2 ft/ s
    2
     or 9.81 m/s
    2
    .
For convenience energy balance at outlet, energy losses through barrel, and energy balance at inlet should be considered when determining outlet control headwater.
When the tailwater controls the outlet flow, Equation 8-10 represents the energy balance equation at the conduit outlet. Traditional practice has been to ignore exit losses. If exit losses are ignored, the hydraulic grade line inside the conduit at the outlet,outlet depth, H
o
, should be assumed to be the same as the hydraulic grade line outside the conduit at the outlet and Equation 8-10 should not be used.
EquationObject242267
Equation 8-10.
where:
  • h
    vo
    = velocity head inside culvert at outlet (ft. or m)
  • h
    TW
    = velocity head in tailwater (ft. or m)
  • h
    o
    = exit head loss (ft. or m).
The outlet depth, H
o
, is the depth of the hydraulic grade line inside the culvert at the outlet end. The outlet depth is established based on the conditions shown below.
Table 8-3: Outlet Depth Conditions
If...
And...
Then...
Tailwater depth (TW) exceeds critical depth (d
c
) in the culvert at outlet
Slope is hydraulically mild
Set H
o
 using Equation 8-10, using the tailwater as the basis.
Tailwater depth (TW) is lower than critical depth (d
c
) in culvert at outlet
Slope is hydraulically mild
Set H
o
 as critical depth.
Uniform depth is higher than top of the barrel
Slope is hydraulically steep
Set H
o
 as the higher of the barrel depth (D) and depth using Equation 8-10.
Uniform depth is lower than top of barrel and tailwater exceeds critical depth
Slope is hydraulically steep
Set H
o
 using Equation 8-10.
Uniform depth is lower than top of barrel and tailwater is below critical depth
Slope is hydraulically steep
Ignore, as outlet control is not likely.
NOTE: For hand computations and some computer programs, H
o
 is assumed to be equal to the tailwater depth (TW). In such a case, computation of an exit head loss (h
o
) would be meaningless since the energy grade line in the culvert at the outlet would always be the sum of the tailwater depth and the velocity head inside the culvert at the outlet (h
vo
).