When the flow in a conduit becomes pressurized the free surface condition is maintained by using a fictitious slot (i.e., the Preissmann slot) to account 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 few examples used by other models include 50 m/s [Sjoberg, 1981]. The default value in EXTRAN is 0.005·W, where W is the conduit width.
Surcharge is a condition in which closed conduit flows full and under pressure. Sewer simulation is the prediction of the heads, velocities, and flows in an existing or predetermined network. Sewer design is the sizing of new sewer diameters that will not allow surcharging. The prevention of street flooding has a longer return period than the design of a sewer system which has the goal of preventing surcharge.
The solution of the conduit momentum equation and junction continuity equation when surcharge occurs has changed often between the different versions of EXTRAN:
A surge tank was used at surcharged nodes. This maintained the flow continuity at nodes at the cost of 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 net flow into the node was zero. The conduit flow was calculated as though the water surface extended to the surface with zero surface width. A Taylor series expansion was used to estimate ¶H/¶Q for conduits and diversion 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 junction surcharge level. This was used in all solutions. One solution in EXTRAN avoided the application of a different set of governing equations during surcharge by retaining a small pseudo-surface area for each conduit. A transition of conduit surface area is provided between the "almost full" conduit and a small "Priessmann slot" to maintain free-surface flow.
The transition zone is from 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 width at 0.96·W to a width equal to 0.01·W at a depth of 1.25 diameters. The conduit cross sectional area increases but the hydraulic radius remains equal to Rf.
When the junction head is greater than 1.25 times the junction crown elevation the width stays constant 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 simulation.
EXTRAN 5 (EXTRAN-XP)
The surcharge iteration used in EXTRAN 3 and continued in EXTRAN 4 was discontinued. A "Priessmann slot" technique for linking open channel and surcharged flow is used exclusively by the model. Warning messages concerning gaps between conduits at a node were eliminated.
Special conditions accounted for are surcharged closed conduits, overtopping open channels, and rectangular culvert calculations for wetted perimeter.
When a closed conduit is surcharged 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 slot is given by the product of the conduit width (WIDE) and the parameter WSLOT 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 the 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 overflow is assigned to the upstream junction and is listed in the summary output as weir discharge. This replaces the HYDRAD messages of previous versions of EXTRAN, which simply set the depth of the open channel to the maximum conduit depth.
Two results are now possible when the water surface elevation of the junction breaks the ground elevation, 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" dialog under Job Control.