Hydraulic Grade Line Procedure

Use the following procedure to determine the entrance control head:
  1. Determine an appropriate water level in the outfall channel or facility. For an open channel outfall, the appropriate water level will be a function of the stage vs. discharge relation of flow in the outfall facility and designer’s selection of design frequency for the storm drain facility. If the outfall tailwater level is lower than critical depth at the exiting conduit of the system, use the elevation associated with critical depth at that point as a beginning water surface elevation for the Hydraulic Grade Line calculation.
  2. Compute the friction loss for each segment of the conduit system, beginning with the most downstream run. The friction loss (h
    f
    ) for a segment of conduit is defined by the product of the friction slope at full flow and the length of the conduit as shown in Equation 6-23.
    EquationObject217238
    Equation 6-23.
    The friction slope, S
    f
    , is calculated by rearranging Manning’s Equation to Equation 6-24.
    EquationObject218239
    Equation 6-24.
    where:
    • S
      f
       = friction slope (ft./ft. or m/m)
    • Q = discharge (cfs or m
      3
      /s)
    • n = Manning’s roughness coefficient
    • z = 1.486 for use with English measurements only.
    • A = cross-sectional area of flow (sq. ft. or m
      2
      )
    • R = hydraulic radius (ft. or m) = A / WP
    • WP = wetted perimeter of flow (the length of the channel boundary in direct contact with the water) (ft. or m).
Combining Equation 6-23 with Equation 6-24 yields Equation 6-25 for friction loss.
EquationObject219240
Equation 6-25.
where:
  • z = 1.486 for use with English measurements units only.
  • L = length of pipe (ft. or m).
For a circular pipe flowing full, Equation 6-25 becomes Equation 6-26.
EquationObject220241
Equation 6-26.
where:
  • z = 0.4644 for English measurement or 0.3116 for metric.
  • D = Pipe diameter (ft. or m).
For partial flow, you could use Equation 6-25 to approximate the friction slope. However, the backwater methods, such as the
(Standard) Step Backwater Method
outlined in Chapter 7, provide better estimates of the hydraulic grade line.
  1. Using the downstream Hydraulic Grade Line elevation as a base, add the computed friction loss h
    f
    . This will be the tentative elevation of the Hydraulic Grade Line at the upstream end of the conduit segment.
  2. Compare the tentative elevation of the Hydraulic Grade Line as computed above to the elevation represented by uniform depth of flow added to the upstream flow line elevation of the subject conduit.
  3. The higher of the two elevations from step 2 above will be the controlling Hydraulic Grade Line elevation (HGL
    us
    ) at the upstream node of the conduit run. (If you perform backwater calculations, the computed elevation at the upstream end becomes the Hydraulic Grade Line at that point).
  4. If other losses are significant, calculate them using the procedures outlined below. Use Equation 6-27 to determine the effect of the sum of minor losses (h
    m
    ) on the Hydraulic Grade Line.
    EquationObject221242
    Equation 6-27.
  5. If the upstream conduit is on a mild slope (i.e., critical depth is lower than uniform depth), set the starting Hydraulic Grade Line for the next conduit run (HGL
    ds
    ) to be the higher of critical depth and the Hydraulic Grade Line from step 3 (or 4 if minor losses were considered).
  6. Go back to step 2 and continue the computations in an upstream direction into all branches of the conduit system. The objective is to compare the level of the Hydraulic Grade Line to all critical elevations in the storm drain system.
  7. Check all laterals for possible entrance control head as described in the subsection below.
  8. If the Hydraulic Grade Line level exceeds a critical elevation, you must adjust the system so that a revised Hydraulic Grade Line level does not submerge the critical elevation (this condition is sometimes referred to as a “blowout.”) Most adjustments are made with the objective of increasing capacity of those conduit segments causing the most significant friction losses. If the developed Hydraulic Grade Line does not rise above the top of any manhole or above the gutter invert of any inlet, the conduit system is satisfactory.
NOTE: If the conduit system does not include any pressure flow segments but the outlet channel elevation is higher than the top of the conduit at the system exit, compute the Hydraulic Grade Line through the system until the Hydraulic Grade Line level is no higher than the soffit of the conduit. At this point, continuance of the Hydraulic Grade Line is unnecessary, unless other losses are likely to be significant.