Hydraulic grade discontinuity at steep pipes or across nodes (frontwater analysis)

Product(s): SewerCAD, StormCAD, CivilStorm, SewerGEMS
Version(s): 10.00.xx.xx08.11.xx,xx
Area:  Calculations


Why do I see a jump in the hydraulic grade in the profile?

Typically, the StormCAD solver uses a backwater analysis. This type of analysis starts at the network outlet under free discharge, submerged, or tailwater control, and proceeds in the upstream direction.

Steep pipes, pipes with a profile description classified as S1, S2, S3, or some composite of these slopes,  tend to interrupt the backwater analysis, and reset the hydraulic control to critical depth at the upstream end of the steep pipe. At this point StormCAD performs a frontwater analysis for the steep profile, with the backwater analysis recommencing from the upstream structure.

An example of a steep pipe where frontwater analysis will take place: 

StormCAD will perform a frontwater analysis in a steep pipe operating under supercritical flow, since these pipes are typically entrance controlled. The hydraulic control is at the upstream end of the conduit and the gradually varied flow analysis will proceed in a downstream direction until either the normal depth is achieved, a hydraulic jump occurs, or the end of the pipe is reached. Even though outlet control rarely occurs in supercritical flow situations, the frontwater analysis is still performed for purposes of determining exit velocity. In a case such as this, the software will use inlet control at the upstream end of the steep pipe. A steep pipe with inlet control is able to transport a greater discharge than the inlet accepts. Since the control section is just inside the pipe at its entrance, the flow profile passes through critical depth at this location. The downstream pipe has no affect on the steep pipe.The flow in the steep pipe will approach normal depth as it moves along. There may be pressure flow at the downstream end of the pipe. This may cause a hydraulic jump just inside the end of the pipe. This will provide a transition between the supercritical and pressure flow.

StormCAD analyzes one pipe at a time as there could be headloss in the transition or there could be a slope change from one pipe to another.  If a user has two steeps pipes running continuously with the same characteristics, it would be better to make them one pipe.

Since the program's algorithm is fundamentally based on backwater analysis, a continuous frontwater analysis is not performed through two or more consecutive steep pipes.This is a performance trade-off that has little impact in evaluating performance of the collection system in most situations. The assumption of critical depth at the upstream end results in a conservative depth in all cases, and is exactly correct at the point of the steep run furthest upstream.

Discontinuity across a node structure

If the conditions warrant, a hydraulic jump can form in the middle of the pipe, which causes a slightly different situation because the backwater analysis continues through the node where the hydraulic jump occurs (see segments B and C and node Y below).

In the screen shot below a frontwater analysis is performed in all the arrows that start at the left and go to the right (>>>) and a backwater analysis is done for all arrows that start at the right and go to the left (<<<). When a hydraulic jump occurs, the location of the jump is essentially where the backwater analysis (which starts at the downstream node) stops. In the example below, a frontwater analysis would be performed at segment B and halt where the hydraulic jump occurs. A backwater analysis is performed from structure Y to the right side of the hydraulic jump, which can be see as segment C. Essentially, it's like StormCAD is treating this one pipe as two separate sections in order to create this profile because a frontwater analysis is done in part of the pipe and a backwater analysis is done in the other part. When you have conditions occur like this there is no "discontinuity" across structure Y and you will see entrance loss and headloss drawn as you would normally expect. This is because segment C starts at critical depth (at the downstream side of node Y) and moves to the left and segment D starts at critical depth and moves to the right, so we can draw a continuous profile line at the structure (critical depth - critical depth = continuous profile).

If we have a situation that occurs just upstream of this pipe where we see segment A, structure X, and segment B we'll see a discontinuous profile drawn at the structure (X). This occurs because segment A starts at critical depth on the left and approaches normal depth on the right and segment B starts at critical depth on the left and also approaches normal depth at the right side (approaching normal depth - critical depth = discontinuous profile). The profile at the structure is discontinuous and is drawn as you see at structure X.

If you'd like to further examine an area like structure X to see how changing the slope slightly might effect where the hydraulic jump would occur what you might try is this:

1) Note the Invert (Stop) elevation for the pipe containing segment A

2) Change the "Set Invert to stop?" property for pipe that contains segment A to "False"

3) Drop the invert by 1/10 and compute the model. What you're looking for is to see how much change in slope it takes to start seeing the hydraulic jump just upstream of structure X. Sometimes changing the stop invert by just 1/10 will be enough to see the change from the pipe having an S2 profile description to a composite S1/S2 profile description where you will see the jump occur.

4) Repeat 3 until you see the jump and note the change in the stop invert from the original value.

Doing this might provide you with a better understanding and feel for what is happening in that pipe and across the structure

Other considerations:

 Rapidly Varied Flow (Hydraulic jumps)

Rapidly varied flow is turbulent flow resulting from the abrupt and pronounced curvature of flow streamlines into or out of a hydraulic control structure.  Examples of rapidly varied flow include hydraulic jumps, bends, and bridge contractions.

The hydraulic phenomenon that occurs when the flow passes rapidly from supercritical to subcritical flow is called a hydraulic jump.  The most common occurrence of this within a gravity flow network occurs when there is a steep pipe charging into a particularly high tailwater.

Free Outfall

StormCAD allows you to define the tailwater condition at the outlet as either Free Outfall, Crown Elevation or User-Specified.

In a pipe with a hydraulically steep slope, the Free Outfall condition will yield a starting depth equal to normal depth in the pipe.  For a pipe with a hydraulically mild slope, the Free Outfall condition will yield a starting depth equal to critical depth.  If an outlet has multiple incoming pipes, the Free Outfall condition yields a starting elevation equal to the lowest of the individual computed elevations.

The Crown condition should be used when the pipe discharges to an outlet where the water surface elevation is equal to the elevation of the top of the pipe.

Structure Flooding

If you have flooding at manholes in SewerCAD or at inlets in StormCAD (the elevation of water is above the structure rim elevation), the backwater analysis will continue by resetting the hydraulic grade to the structure rim elevation or ground elevation, whichever is higher.  However, if a structure is defined with a bolted cover, the hydraulic grade is not reset to the rim elevation.

In actual flooding situations, flows may be diverted away from the junction structure and out of the system, or attenuated due to surcharged storage. In this program, even though the governing downstream boundary for the next conduit is artificially lowered to prevent the propagation of an incorrect backwater, the peak discharges at the structure are conserved and are not reduced by the occurrence of flooding at a junction.

See Also

What is the difference between the Hydraulic Grade and Energy Grade 'Structure Loss' calculation option?