How is RHO computed for a Link in SWMM 5?

Subject:  How is RHO computed for a Link in SWMM 5?

SWMM 5 uses a sliding metric to calculate the cross sectional area and hydraulic radius used in the simulation for the link dynamic flow.  The area and hydraulic radius used moves from the Upstream End of the Link to the Midpoint of the Link based on the Froude number and a few other considerations (see Figure 1 for the other considerations).

The area and hydraulic radius used as a function of the Froude Number:

1.   Upstream cross sectional area and upstream hydraulic radius is used when the Froude Number > 1

2.   Midpoint sectional area and hydraulic radius is used then the Froude Number is < 0.5

3.   An area and hydraulic radius between the upstream and midpoint sections is used then the Froude Number is between 0.5 and 1

Figure 1:  How to compute RHO based on the Froude Number.

Figure 2:  The computed value of the Froude Number and the value of RHO over time.

Figure 3: Relationship between the upstream area, midpoint area and the actual area used during the simulation.