Losses through junctions

Introduction

Modeling the head losses through a junction can be tricky because the losses are not directly captured by the differential equations that govern the flow through pipes. Therefore, it is up to each software package to decide how the losses are accounted for.

HEC-22

One of the most widely used method is documented in Federal Highway Administration (FHWA) hydraulic Engineering circular №22 (HEC-22) Chapter 7.1.6 Energy Losses.

  • The friction losses for open channel flow are already accounted for by the governing equations in SWMM and ICM, which can be derived from manning’s equation.
  • The exit losses referred in HEC-22 is for the situation discharging to a channel instead of a junction.
  • Bend losses is just a function of one velocity in the pipe. However, transition losses and exit losses will require two velocities.
  • The entrance loss: Eai — Ei
  • The junction loss: Ea — Eai
  • The exit loss: E0-Ea

SWMM5

According to the SWMM5 reference manual, the two governing equations are applied to the network in this manner.

  • The continuity equation is done for each manhole and two half pipes
  • The momentum equation is applied to each pipe
  • The junction has only one depth
  • The connected pipes share the same depth as the junction
  • The losses through a junction will result higher level in the pipe on the upstream end (the same as the junction depth)

ICM

In comparison, ICM has more spatial resolution. Each pipe is divided into smaller segments, as a direct result, for each pipes the upstream and downstream end has different flow and depth values.

Examples

To illustrate how losses are calculated in ICM/SWMM5, here is a simple example.

  • No Loss: no loss for any of the pipes
  • EN5EX4: only the middle pipe (Loss) has losses, entrance: 5, Exit 4

SWMM5 Results

For the no loss scenario, it reaches steady state with a depth of 0.443 ft at all junctions.

ICM Results

For ICM it is much easier to check the calculations because the entrance and exit losses are calculated for each junction, and it can be estimated from the modeling results by comparing the junction level and the connection pipe depth. The calculation is straightforward as shown below, the level difference between the node and the pipe is the minor losses.

XPSWMM Results

XPSWMM shows similar results as SWMM5.

Conclusion

Calculating the losses through a junction can be tricky. ICM has clear advantage over SWMM5 and XPSWMM, as ICM explicitly calculates head losses through the junction, which can be visually shown on a profile. While XPSWMM/SWMM5 lumps the head losses into the friction loss of the pipe, therefore, there is no head loss calculated on the entrance and exit side of the manholes.

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