Hydraulic Jump in Culverts

Figure 8-15 provides a sample plot of depth and momentum function and an associated specific energy plot. For a given discharge and given energy and momentum, there exist two possible depths, one less than critical depth (supercritical flow) a sequent (or conjugate) depth greater than critical depth (subcritical flow). With a proper configuration, the water flowing at the lower depth in supercritical flow can “jump” abruptly to its sequent depth in subcritical flow. This is called a hydraulic jump. With the abrupt change in flow depth comes a corresponding change in cross-sectional area of flow and a resulting decrease in average velocity.
By comparing the two curves at a supercritical depth and its sequent depth, it is apparent that the hydraulic jump involves a loss of energy. Also, the momentum function defines critical depth as the point at which minimum momentum is established.
Momentum Function and Specific Energy (click in image to see full-size image)
Figure 8-15. Momentum Function and Specific Energy
The balance of forces is represented using a momentum function (Equation 8-22):
EquationObject254287
Equation 8-22.
where:
  • M
     = momentum function
  • Q
     = discharge (cfs or m
    3
    /s)
  • g = gravitational constant = 32 ft./sec
    2
  • A
     = section area of flow (sq. ft. or m
    2
    )
  • InlineEquation34288 d_
    = distance from water surface to centroid of flow area (ft. or m).
InlineEquation34288The term A d_
represents the first moment of area about the water surface. Assuming no drag forces or frictional forces at the jump, conservation of momentum maintains that the momentum function at the approach depth, M
1
, is equal to the momentum function at the sequent depth, M
s
.
The potential occurrence of the hydraulic jump within the culvert is determined by comparing the outfall conditions with the sequent depth of the supercritical flow depth in the culvert. The conditions under which the hydraulic jump is likely to occur depend on the slope of the conduit.
Under mild slope conditions (d
c
 < d
u
) with supercritical flow in the upstream part of the culvert, the following two typical conditions could result in a hydraulic jump:
  • The potential backwater profile in the culvert due to the tailwater is higher than the sequent depth computed at any location in the culvert.
  • The supercritical profile reaches critical depth before the culvert outlet.
Under steep slope conditions, the hydraulic jump is likely only when the tailwater is higher than the sequent depth.