With reference to Figure 8‑26 and Figure 8‑27, unit 3 should be as long enough to ensure that the hydraulic jump occurs within the culvert.

For a given total drop, the resulting length of unit 2 is short, but this may cause the slope of unit 2 to be very steep.

Provided that unit 1 is on a mild slope, its length has no effect on the outlet velocity of any downstream hydraulic function. It is recommended that unit 1 either not be used or be very short; the result is additional latitude for adjustment in the profiles of units 2 and 3.

A longer unit 3 and a milder (but still steep) slope in unit 2 together enhance the possibility of a hydraulic jump within the culvert. However, these two conditions are contradictory and usually not feasible for a given culvert location. Make some compromise between the length of unit 3 and the slope of unit 2. Unit 3 must be on a mild slope (d

u

> d

c

). This slope should be no greater than necessary to prevent ponding of water in the unit. Do not use an adverse (negative) slope.

If a unit 1 is used, the headwater will most likely result from the backwater effect of critical depth between units 1 and 2.

If a unit 1 is not used, the headwater will most likely result from inlet control.

Critical depth will not change from one unit to the next, but uniform depth will vary with the slope of the unit.

The increment, δ d, should be such that the change in adjacent velocities is not more than 10%.

The depth in unit 2 should tend to decrease towards uniform depth, so δ d should be negative. The resulting profile is termed an S2 curve.

Also, δ d should be small enough when approaching unit 3 such that the cumulative length does not far exceed the beginning of unit 3.

For hand computations, an acceptable expedient is to omit the profile calculation in unit 2 and assume that the exit depth from unit 2 is equal to uniform depth in unit 2.

Because uniform depth is now greater than critical depth (mild slope), and flow depth is lower than critical depth, the flow depth tends to increase towards critical depth. Therefore, in unit 3, δ d should be positive.

The starting depth for unit 3 is the calculated depth at the end of unit 2.

Reset the cumulative length, Σ L, to zero.

The resulting water surface profile is termed an M3 curve.

As each depth is calculated along unit 3, calculate the sequent depth, d

s

. For more information, see the , , and subsections in Section 3.

Calculate the elevation of sequent depth (d

s

+ flow line elevation) and compare it with the tailwater elevation. Tailwater elevation may be a natural stream flow elevation, or may produced artificially by installing a sill on the downstream apron between wingwalls. Design Division Hydraulics does not recommend the use of sills. (see ). If sills are used, the total vertical dimension of the artificial tailwater is determined by adding the elevation at the top of the sill and the critical depth of design discharge flow over the sill. Base this critical depth on the rectangular section formed by the top of the sill and the two vertical wingwalls. If the elevation of sequent depth is lower than the tailwater elevation, the following points apply; go to Step 5:

Hydraulic jump is likely to occur within the culvert.
Outlet velocity is based on the lower of tailwater depth, TW, and barrel height, D.
Profile calculations may cease even though the end of the barrel has not been reached.

If the computed profile tends towards critical depth before reaching the end of the culvert, the following apply and you should go to Step 5:

Hydraulic jump is likely to occur within the culvert.
Outlet depth will be equal to critical depth and outlet velocity is based on critical depth.
Profile calculations may cease even though the end of the barrel has not been reached.

Compare the cumulative length, Σ L, to unit 3 length. If Σ L ≥ length of unit 3, the following apply:

Hydraulic jump does not form within the length of unit 3.
Exit depth is the present value of d.
Exit velocity is based on exit depth.
The broken-back culvert configuration is ineffective as a velocity control device and should be changed in some manner. Alternatives include rearrangement of the culvert profile, addition of a sill, and investigation of another device. If the profile is reconfigured, go back to step 3. Otherwise, skip step 5 and seek alternative measures.

If tailwater is very sensitive to varying downstream conditions, it may be appropriate to check the occurrence of the hydraulic jump based on the lowest tailwater that is likely to occur.

The hydraulic jump may not occur within the barrel under other flow conditions. It is wise to check the sensitivity of the hydraulic jump to varying flow conditions to help assess the risk of excessive velocities.

If a sill has been employed to force an artificial tailwater, and the hydraulic jump has formed, the outlet velocity calculated represents the velocity of water as it exits the barrel. However, the velocity at which water re-enters the channel is the crucial velocity. This velocity would be the critical velocity of sill overflow.