FM Question

It has been brought to my attention that several users do not believe
that SWMM 5 is correctly simulating the behavior of a long, pumped force
main during times when the pump rapidly cycles on and off. When the pump
shuts off, SWMM shows that flow continues to exit from the end of the
force main for several minutes at a decreasing rate. This causes it to
de-pressurize at some point along its length since flow is leaving but
not entering the main during this period of time. When the pump starts
up again, there is a lag and then a gradual increase in flow out of the
main for several minutes until such time as the main completely re-fills
and re-pressurizes once again. The net result is that the initial flow
rate seen at the pump when it turns on again is significantly attenuated
at the outlet of the main.

The input data for an example showing this behavior is listed below. It
has a 50,000 foot long flat force main divided into 10 conduit sections
of 5,000 feet each. A fixed downstream boundary condition with water
level 0.1 ft above the top of the force main is used. A typical diurnal
DWF pattern is fed into the pump's wet well and the Type 3 pump turns on
at 5 feet and turns off at 1 feet. If you run this example, graph the
time series of flows for the pump and the last force main segment with
the X-axis interval adjusted to focus on the period from 16 to 18 hours
so you can more easily observe the behavior just described. Note that
during periods of prolonged pumping, when the main remains fully
pressurized, the outflow from the main is perfectly matching the varying
inflow from the pump.

An objection has been raised about this behavior, based on the belief
that once the main is pressurized, the outflow should equal the inflow
at every instance of time, including those times when the pump is turned
off (implying that the main will not de-pressurize during such times).
SWMM begs to differ. When the pump shuts off, the water in the main is
moving at about 2 ft/sec. The momentum contained in this column of
water will continue to carry it out of the downstream end, until such
time that frictional forces dissipate its forward motion. This is simply
Newton's Second Law at work (a body in motion tends to stay in motion
unless subjected to an opposing force). During the time that the pump is
off but the main keeps discharging water, mass continuity says that
somewhere along the main there must be empty volume that becomes
available to make up for the volume being discharged. Thus the main no
longer remains full throughout its length, so when the pump cycles on
again, the flow at the pump will not be immediately seen at the outlet
since the main is no longer pressurized throughout. Instead, some period
of time will elapse before the main refills and can then start obeying
"outflow equals inflow".

The question being put to the group is: Is SWMM 5 modeling this scenario
correctly? Has anyone has observed this type of behavior in actual
practice (i.e., flow continuing to issue from the end of a long (e.g.
several miles) force main after the pump feeding it has been shut off
and then gradually ramping back up over several minutes to match the
pump flow once the pump turns on again)?

==========================================================================

[TITLE]

[OPTIONS]
FLOW_UNITS              CFS
INFILTRATION            GREEN_AMPT
FLOW_ROUTING            DYNWAVE
START_DATE              07/01/1999
START_TIME              00:00:00
REPORT_START_DATE       07/02/1999
REPORT_START_TIME       00:00:00
END_DATE                07/03/1999
END_TIME                00:00:00
SWEEP_START             01/01
SWEEP_END               12/31
DRY_DAYS                0
REPORT_STEP             00:00:30
WET_STEP                00:05:00
DRY_STEP                01:00:00
ROUTING_STEP            0:00:05
ALLOW_PONDING           NO
INERTIAL_DAMPING        NONE
VARIABLE_STEP           0.00
LENGTHENING_STEP        0
MIN_SURFAREA            0
NORMAL_FLOW_LIMITED     SLOPE
SKIP_STEADY_STATE       NO
IGNORE_RAINFALL         NO
FORCE_MAIN_EQUATION     H-W
LINK_OFFSETS            DEPTH

[JUNCTIONS]
;;                Invert      Max.        Init.       Surcharge   Ponded
;;Name            Elev.       Depth       Depth       Depth       Area
;;--------------  ----------  ----------  ----------  ----------
----------
2                 0           0           0           1000        0
3                 0           0           0           1000        0
4                 0           0           0           1000        0
5                 0           0           0           1000        0
6                 0           0           0           1000        0
7                 0           0           0           1000        0
8                 0           0           0           1000        0
9                 0           0           0           1000        0
10                0           0           0           1000        0
11                0           0           0           1000        0

[OUTFALLS]
;;                Invert      Outfall     Stage/Table       Tide
;;Name            Elev.       Type        Time Series       Gate
;;--------------  ----------  ----------  ----------------  ----
Outfall           0           FIXED       3.1               NO

[STORAGE]
;;                Invert      Max.        Init.       Shape       Shape
                              Ponded      Evap.
;;Name            Elev.       Depth       Depth       Curve       Params
                              Area        Frac.
;;--------------  --------    --------    --------    ----------
--------    --------    --------    --------    --------
1                 -10         22          0           FUNCTIONAL  800
      0           0           0           0

[CONDUITS]
;;                Inlet             Outlet
Manning     Inlet       Outlet      Init.       Max.
;;Name            Node              Node              Length      N
      Offset      Offset      Flow        Flow
;;--------------  ----------------  ----------------  ----------
----------  ----------  ----------  ----------  ----------
2                 2                 3                 5000        0.013
      0           0           0           0
3                 3                 4                 5000        0.013
      0           0           0           0
4                 4                 5                 5000        0.013
      0           0           0           0
5                 5                 6                 5000        0.013
      0           0           0           0
6                 6                 7                 5000        0.013
      0           0           0           0
7                 7                 8                 5000        0.013
      0           0           0           0
8                 8                 9                 5000        0.013
      0           0           0           0
9                 9                 10                5000        0.013
      0           0           0           0
10                10                11                5000        0.013
      0           0           0           0
11                11                Outfall           5000        0.013
      0           0           0           0

[PUMPS]
;;                Inlet             Outlet            Pump
Init.       Startup     Shutoff
;;Name            Node              Node              Curve
Status      Depth       Depth
;;--------------  ----------------  ----------------  ----------------
------      --------    --------
1                 1                 2                 InfluentPump
ON          5           1

[XSECTIONS]
;;Link            Shape             Geom1             Geom2       Geom3
      Geom4       Barrels
;;--------------  ------------      ----------------  ----------
----------  ----------  ----------
2                 FORCE_MAIN        3                 130         0
      0           1
3                 FORCE_MAIN        3                 130         0
      0           1
4                 FORCE_MAIN        3                 130         0
      0           1
5                 FORCE_MAIN        3                 130         0
      0           1
6                 FORCE_MAIN        3                 130         0
      0           1
7                 FORCE_MAIN        3                 130         0
      0           1
8                 FORCE_MAIN        3                 130         0
      0           1
9                 FORCE_MAIN        3                 130         0
      0           1
10                FORCE_MAIN        3                 130         0
      0           1
11                FORCE_MAIN        3                 130         0
      0           1

[LOSSES]
;;Link            Inlet       Outlet      Average     Flap Gate
;;--------------  ----------  ----------  ----------  ----------

[DWF]
;;                                  Average     Time
;;Node            Parameter         Value       Patterns
;;--------------  ----------------  ----------  ----------
1                 FLOW              15          "diurnalcurve"

[CURVES]
;;Name            Type        X-Value     Y-Value
;;--------------  ----------  ----------  ----------
InfluentPump      Pump3       10          30
InfluentPump                  20          25
InfluentPump                  30          20
InfluentPump                  40          10
InfluentPump                  50          0

[PATTERNS]
;;Name            Type        Multipliers
;;--------------  ----------  -----------
diurnalcurve      HOURLY      .5    .4    .3    .2    .1    .1
diurnalcurve                  .5    1     1.2   1.1   1.0   1.4
diurnalcurve                  1.7   1.5   1.2   1.1   .8    1.1
diurnalcurve                  1.6   1.7   1.3   1.1   .9    .7

[REPORT]
INPUT       NO
CONTROLS    NO

[TAGS]

[MAP]
DIMENSIONS  -139.899    39986.136   2937.878    40003.401
Units       Feet

[COORDINATES]
;;Node            X-Coord                 Y-Coord
;;--------------  ------------------      ------------------
2                 500.691                 39998.450
3                 663.377                 39997.384
4                 809.869                 39997.384
5                 992.985                 39997.384
6                 1155.172                39997.384
7                 1338.288                39997.384
8                 1504.527                39998.450
9                 1720.214                39997.384
10                1978.220                39998.450
11                2250.655                39998.450
Outfall           2589.358                39998.450
1                 7.363                   40000.904

[VERTICES]
;;Link            X-Coord                 Y-Coord
;;--------------  ------------------      ------------------

[LABELS]
;;X-Coord               Y-Coord                 Label
-2029.817               43740.130               "Influent pump 1" 1
"Arial"     10    0     0

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