**When the f=
low in a conduit** becomes pressurized the free surface condition is=
maintained by using a fictitious slot (i.e., the Preissmann slot) to accou=
nt for compressibility effects during surcharging. The width of the narrow =
slot characterizes the elastic properties of the water and sewer walls. The=
slot width is calculated by assuming a speed for the surcharged flow. A fe=
w examples used by other models include 50 m/s [Sjoberg, 1981]. The default=
value in EXTRAN is 0.005=C2=B7W, where W is the conduit width.

Surcharge is a condition i= n which closed conduit flows full and under pressure. Sewer simulation is t= he prediction of the heads, velocities, and flows in an existing or predete= rmined network. Sewer design is the sizing of new sewer diameters that will= not allow surcharging. The prevention of street flooding has a longer retu= rn period than the design of a sewer system which has the goal of preventin= g surcharge.

The solution of the condui= t momentum equation and junction continuity equation when surcharge occurs = has changed often between the different versions of EXTRAN:

=20

- =20
- E= XTRAN 2 =20
- E= XTRAN 3 =20
- E= XTRAN 4 =20
- EXTRAN 5 (EXTRAN-XP) =20

A surge tank was used at s= urcharged nodes. This maintained the flow continuity at nodes at the cost o= f failing to predict surcharge and flood elevations realistically.

A surcharge iteration was = implemented to realistically predict surcharge heads. The assumptions were:= (1) the nodal surface was zero when the node was surcharged, and (2) the n= et flow into the node was zero. The conduit flow was calculated as though t= he water surface extended to the surface with zero surface width. A Taylor = series expansion was used to estimate =C2=B6H/=C2=B6Q for conduits and dive= rsion structures. Drawbacks to this solution included convoluted rules for = setting the junction surcharge level.

A default surface area for= all nodes was included in the model to alleviate strictures on the junctio= n surcharge level. This was used in all solutions. One solution in EXTRAN a= voided the application of a different set of governing equations during sur= charge by retaining a small pseudo-surface area for each conduit. A transit= ion of conduit surface area is provided between the "almost full" conduit a= nd a small "Priessmann slot" to maintain free-surface flow.

The transition zone is fro= m the 96 percent conduit depth to a point 1.25 times conduit diameter above= the top. The conduit width (W) decreases quadratically from the conduit wi= dth at 0.96=C2=B7W to a width equal to 0.01=C2=B7W at a depth of 1.25 diame= ters. The conduit cross sectional area increases but the hydraulic radius r= emains equal to Rf.

When the junction head is = greater than 1.25 times the junction crown elevation the width stays consta= nt at 0.5 percent of the conduit width (or vertical dimension) allowing the= same free-surface flow equations 12 and 18 to be used during the entire si= mulation.

The surcharge iteration us= ed in EXTRAN 3 and continued in EXTRAN 4 was discontinued. A "Priessmann sl= ot" technique for linking open channel and surcharged flow is used exclusiv= ely by the model. Warning messages concerning gaps between conduits at a no= de were eliminated.

Special conditions account= ed for are surcharged closed conduits, overtopping open channels, and recta= ngular culvert calculations for wetted perimeter.

When a closed conduit is s= urcharged EXTRAN assumes that a vertical slot is present at the top of the = conduit. This Priessmann slot allows the same conduit momentum equation to = be used during both surcharged and non-surcharged flow. The width of the sl= ot is given by the product of the conduit width (WIDE) and the parameter WS= LOT described above. When the depth is greater than 1.25 the conduit depth = (DEEP) is used. When the depth is between 1.25*DEEP and DEEP the width of t= he slot is a quadratic function of the top width and WSLOT*WIDE.

Open channels that overtop= their banks are modeled as weir flow over the sides of the channel. The ov= erflow is assigned to the upstream junction and is listed in the summary ou= tput as weir discharge. This replaces the HYDRAD messages of previous versi= ons of EXTRAN, which simply set the depth of the open channel to the maximu= m conduit depth.

Two results are now possib= le when the water surface elevation of the junction breaks the ground eleva= tion, a flooded junction with surface outflow of excess water, and a ponded= junction that allows the flooded water access to the network when capacity= is available. These parameters are defined in the "Junction Defaults" dial= og under Job Control.