Three reasons exist for initiating a synoptic, system-wide collection of hydraulic and operational data. First, after conducting preliminary simulations using an equivalent network representation of the water-distribution system, results indicated higher than expected pressures, exceeding 125 psi in some locations (in the southernmost areas of Dover Township including the borough of South Toms River and Berkeley Township). Measured data were not available to either confirm or negate these initial simulation results. Second, to understand the present-day distribution of water from points of entry (sources) to locations throughout the distribution system, a calibrated model of the distribution system needed to be developed; however, a database of spatially and temporally varying data by which to characterize the distribution system was not available. Third, to reconstruct historical characteristics of the water-distribution system, a synoptic, system-wide characterization of the water-distribution system, based on measured data, was required. Neither present-day nor historical system-wide pressure measurements were available for the water-distribution system being investigated. Hence, ATSDR investigators decided to obtain present-day measurements to accurately characterize the water-distribution system.

ATSDR, in coordination with NJDHSS and the water utility, developed a protocol to collect pressure data and operational information during winter- and peak-demand periods of the year March and August 1998, respectively. Details of the protocol are provided in a report by Maslia and Sautner (1998a) and are briefly described below.

Hydrant Selection
Twenty-five hydrants (out of a system total of 2,127 in 1997) were initially selected as test hydrants (designated as H-1, H-2, etc.) on which continuous pressure recording-equipment (described below) would be installed. The number and location of the proposed test hydrants (H-1, H-2, etc., shown in Plate 4) were selected based on the following:

1. Hydrant locations were selected to help determine the system pressures that exist in the southern Dover Township, Berkeley Township, and the borough of South Toms River areas that were initially simulated as having unusually high pressures, as described above.

 
2. Hydrant locations were also selected to provide a thorough, system-wide coverage so that effects from storage tanks filling or emptying and pumps turning on or off could be characterized by pressure changes at these hydrants.

 
3. ATSDR used additional hydrants for quality assurance in the event that data- collection devices failed to operate properly or that hydrants became inoperable or unusable during the test.

 
4. ATSDR responds to and attempts to accommodate stakeholder input when conducting site activities. In the case of modeling the water-distribution system serving Dover Township, area residents wanted assurances that a sufficient number of measuring locations would be available to accurately characterize the distribution system. When ATSDR investigators determined that additional data-collection locations would not abrogate the scientific merits of the field test, additional monitoring locations requested by area residents were also included.

could not be used to monitor pressure during the test periods (see Plate 5 for location of alternate test hydrants). During installation of the data-gathering equipment on the hydrants, it was determined that 5 of the designated test hydrants (H-5, H-6, H-14, H-19, and H-22; Plate 4) were not suitable for use as measuring points. Therefore, associated alternate hydrants (AH-5, AH-6, AH-14, AH-19, and AH-22; Plate 5) were used instead. The 5 hydrants (H-5, H-6, H-14, H-19, and H-22) were not used because when they were identified and turned on, investigators noticed excessive leakage flowing from the bolts joining the hydrant base to the underlying pipeline. Investigators felt that the excessive leakage would worsen with a pressure gauge or pressure recording device attached to the hydrant, resulting in erroneous pressure measurements. The final set of test hydrants used for both the March and August 1998 tests is shown in Plate 6. These 25 hydrants are connected to network pipelines that: (1) were installed between 1963 and 1996, (2) are constructed of asbestos cement (14 hydrants), plastic (PVC, 10 hydrants), and ductile iron (1 hydrant) materials, and (3) range in diameter size from 6 in. to 12 in.

Table 2. Identification, coordinates, and location of test hydrants used for the March and August 1998 pressure tests,
Dover Township area, New Jersey
 

ATSDR  Hydrant ID1	2UWTR Hydrant ID	2Pipe Diameter (inches)	2Year Installed	Hydrant Location					5Land Surface Elevation (feet)
				3Geodetic Coordinates NAD 1927		New Jersey State Plane Coordinates, NAD 1927		Street Identification4
				Latitude (decimal degrees)	Longitude (decimal degrees)	Northing (feet)	Easting (feet)
H-1	6-075	8	1993	39.953265	-74.286958	408142.264	2106457.294	Millbrook Dr. & Westbrook Dr., NW corner	49.42
H-2	6-014	8	1983	39.977381	-74.283213	416931.503	2107469.462	Costa Mesa Dr. & Pine Valley Dr., SE corner	55.77
H-3	1-863	12	1989	39.989508	-74.265614	421370.722	2112381.845	Route 37, W. Floracraft @ no. 1600	59.91
H-4	6-173	8	1974	39.964666	-74.245314	412347.723	2118112.826	Pembroke Ln. & Fort de France Ave., SE corner	29.92
AH-5	6-227	12	1988	39.945245	-74.240738	405279.324	2119429.296	Prince Charles Dr. & Davenport Rd, NE corner	51.60
AH-6	1-156	6	1960	39.971423	-74.221675	414841.283	2124726.787	Oakside Dr. & Shady Nook Dr., NW corner	44.14
H-7	1-304	12	1966	39.957666	-74.212299	409843.256	2127380.239	Lakehurst Rd. & Edgewood Dr., SW corner	32.86
H-8	5-012	10	1988	39.950151	-74.199608	407124.136	2130952.345	South Main St. & Flint Rd., SE corner	6.92
H-9	1-061	6	1991	39.952620	-74.193779	408032.128	2132581.850	Washington St. & Hooper Ave., NE corner	32.68
H-10	1-078	12	1976	39.953508	-74.170042	408391.758	2139234.937	Washington St., across from Pine St.	35.68
H-11	1-731	8	1988	39.947713	-74.145932	406319.347	2146006.636	Elizabeth Ave. & Berkeley Ave., NW corner	13.91
H-12	1-702	8	1988	39.944769	-74.121910	405287.147	2152748.462	Minturn Rd. & Bay Shore Dr., NW corner	4.26
H-13	1-665	12	1988	39.952430	-74.118217	408084.170	2153766.796	Marshall Rd. across from Maritime Dr.	6.56
AH-14	1-762	8	1985	39.958156	-74.146045	410123.244	2145952.755	Windsor Ave. & Huckleberry Ln., SW corner	28.27
H-15	1-591	12	1986	39.968498	-74.122447	413930.025	2152545.164	Bay Ave. & Bermuda Dr., SE corner	6.18
H-16	1-973	8	1996	39.973560	-74.206719	415640.998	2128914.673	S. Dakota Ave. & N. Carolina Ave., NE corner	38.66
H-17	2-332	6	1987	39.992107	-74.206319	422397.734	2128991.902	Indian Head Rd. & Hill Grass Ct., NW corner	89.30
H-18	2-124	12	1984	39.999978	-74.228648	425233.402	2122721.279	Whitesville Rd. & Clayton Ave., N corner	46.76
AH-19	2-348	12	1987	40.020870	-74.220673	432854.892	2124917.511	Route 9 Hwy. & Riverwood Dr., NW corner	71.78
H-20	2-720	12	1996	40.050572	-74.250934	443633.608	2116391.508	Whitesville Rd. & Clear Lake Blvd., NW corner	82.68
H-21	2-171	12	1974	40.009504	-74.215593	428721.714	2126361.277	Church Rd. & Rte 9 , NE corner	71.24
AH-22	2-025	8	1965	40.018729	-74.154675	432174.358	2143406.735	Hovsons Blvd. & Adirondack Pl., NE corner	14.17
H-23	2-093	12	1963	40.003062	-74.154607	426467.378	2143458.575	Fisher Blvd. & Hooper Ave., SE corner	10.50
H-24	1-400	12	1971	39.992985	-74.173007	422767.509	2138324.083	Indian Hill Rd. & 300 ft South of Hooper Ave.	88.89
H-25	1-308	8	1988	39.975514	-74.176163	416398.421	2137474.800	Brookside Dr. & Bay Ave., SW corner	42.81

¹Refer to Plate 6 for hydrant locations.
²Data obtained from United Water Toms River, Inc., November 1997.
³Geodetic data obtained by ATSDR staff using global positioning system (GPS) equipment, January 1998; refer to Sautner, et al. (1998).
⁴Refer to Appendix A for photographs showing hydrant location referenced to street corners.
⁵Land surface elevation, referenced to sea level datum, determined by use of GPS equipment. For hydrants H-2, AH-6, H-11, H-12, and H-18, GPS data were determined to be in error. Therefore, elevations were determined from U.S. Geological Survey digital elevation model (DEM), 7 ½-minute quadrangles for the Dover Township area.

The location of the final set of test hydrants, described by: (1) geodetic coordinates, (2) New Jersey state plane coordinates, and (3) street location, is listed in Table 2. Photographs showing the location of the test hydrants with reference to street corners are provided in Appendix A. The geodetic locations were determined using global positioning system (GPS) equipment⁽³⁾. Details pertaining to determining hydrant locations are provided in Sautner, et al. (1998). Land surface elevation at the hydrant locations was also determined using GPS equipment by placing the top of the receiving antenna on the ground next to the hydrant (see photograph of hydrant H-8 in Appendix A), and subtracting the length of the antenna (1.83 feet [ft]) from the recorded GPS elevation. Because elevations of the measuring points will be used in the calibration process to assess the reliability of the model (see section on "Hydraulic Model Calibration"), elevations determined by use of the GPS equipment were further verified by using land surface elevations obtained from 7½-minute U.S. Geological Survey (USGS) digital elevation model (DEM) quadrangles for the Dover Township area. For six hydrants (H-2, AH-6, H-11, H-12, and H-18; Table 2) the GPS elevations were found to be in error, although the cause of the error was unknown. Therefore, elevations for these hydrants were derived using the DEM data instead. (For these hydrants, field verification of land surface elevations indicated that the GPS-determined elevations were in error.)

Data Recording Equipment

To record system pressures continuously over the 48-hour duration of the tests, each test hydrant was equipped with a RADCOM Lolog LL™ continuous recording pressure data logger that sampled pressures at one-minute intervals. Components that made up the hydrant pressure measurement configuration were (Figures 2 and 3): (a) a hydrant adapter kit, (b) a brass lever handle shut-off valve, (c) a coiled pressure hose with a quick release coupling, and (d) the RADCOM Lolog LL™ pressure data logger. The pressure data recording equipment was chosen because of:

1. a factory calibration to 150 psi (see Appendix B);

 
2. a pressure range of 0 psi to 300 psi and accuracy of +/- 0.2% of the pressure range;

 
3. the variable sampling rate of 1, 5, 15, 30, and 60 minutes;

 
4. the compact size of the device (5.5 in. x 3.3 in. x 1.3 in.) that would allow its attachment directly to a hydrant; and

 
5. the reliability of the device with respect to environmental factors such as precipitation and cold because the device is constructed of die-cast aluminum and IP68 sealing (fully submersible).

Figure 2. Components of hydrant pressure measurement configuration.
 

(A) Dickinson A7983 Hydrant Adapter Kit	(B) Dickson brass lever handle shut-off valve, 1/4 NPTF x 1/4 NPTF, shown in "off" position
(C) Coiled Pressure Hose with a quick release coupling	(D) RADCOMM Lolog LL™ pressure data logger

Figure 3: Assembly of hydrant pressure measurement configuration: (A) hydrant adapter kit, (B) brass shut-off valve in "on" position, (C) coiled pressure hose with quick release coupling, and (D) RADCOM LoLog LL™ pressure data logger.

Test Protocol

ATSDR established a test protocol or workplan (Maslia and Sautner 1998a) to ensure that successful data-gathering would occur during the test and to establish quality-assurance procedures that would be followed for each hydrant monitored. Because a large number of hydrants were to be monitored on a continuous basis, two installation teams were used. As part of the test protocol and quality-assurance procedure, each logger was identified by a hydrant number (H-1, H-2, etc.) and a logger serial number. Table 3 lists hydrant identifications and the associated pressure data logger serial numbers used for the March and August 1998 tests. Before conducting the tests, the loggers were factory calibrated to 150 psi, and, therefore, did not need field calibration (a letter from the manufacturer indicating the loggers were calibrated is provided in Appendix B). However, as part of the quality-assurance procedure, logger pressure during installation was verified with a manual pressure gauge, as described below. Installation teams were composed of ATSDR, NJDHSS, and water-utility staff. The following 7-step procedure was used to install and quality-assure the pressure data logger installation on each of the 25 hydrants:

1. Water utility staff opened a hydrant and flushed it to remove debris (Figure 5); the water utility staff determined the length of time required to flush each hydrant so that clear running water would be observed. At that point, the hydrant was shut off.

 
2. ATSDR and NJDHSS staff installed a hydrant adapter kit, brass lever handle shut-off valve, and Ashcroft Duralife industrial pressure gauge on the test hydrant (Figure 6).

Table 3. Hydrant identification and corresponding data logger serial numbers used for the March and August 1998 pressure tests, Dover Township area, New Jersey
 

Hydrant Identification	Data Logger Serial Number	Hydrant Identification	Data Logger Serial Number
H-1	294	AH-14	307
H-2	295	H-15	308
H-3	296	H-16	309
H-4	297	H-17	310
AH-5	298	H-18	311
AH-6	299	AH-19	312
H-7	300	H-20	313
H-8	301	H-21	1314, 222
H-9	302	AH-22	315
H-10	303	H-23	316
H-11	304	H-24	317
H-12	305	H-25	318
H-13	306

¹ Logger 314 was determined to be defective during installation of the March 1998 test. The manufacturer supplied a replacement logger (number 222) that was installed on hydrant H-21at approximately 10:34 hours on March 24, 1998 and used for the remainder of the March 1998 test and for the August 1998 test.
 
 

3. With the shut-off valve in the "off" position, the hydrant was reopened, the shut-off valve was moved to the "on" position, and a check was made for any leaks occurring around the pressure gauge connection and the hydrant adapter kit. At this point, a pressure reading was obtained from the pressure gauge (Figure 6) and recorded in a field book. An example of the entry form used to record installation information for hydrant H-1 is provided in Appendix C. After the pressure was recorded, the shut-off valve was turned to the "off" position, and the pressure gauge was disconnected from the shut-off valve and hydrant adapter kit

 
4. The RADCOM Lolog LL™ pressure data logger (Figure 2D) was now attached to the hydrant by means of a nylon cable tie (Figure 7). A coiled pressure hose with a quick release coupling (Figure 3) was then attached to the data logger and the shut-off valve. The shut-off valve was then placed in the "on" position, and the data logger started recording water pressure at the hydrant. A piece of duct tape was wrapped around the shut-off valve handle to ensure that it remained in the "on" position. A photograph showing the attachment of the pressure data logger installation to test hydrant H-23 is provided in Figure 7.

 
5. Because the logger is a continuous recording device, it was "zeroed" and the date and time initialized during installation. For a quality assurance check, an instantaneous pressure reading from the pressure data logger was obtained (Figure 8), and this was compared with the manual gauge pressure recorded earlier (see field book sheet in Appendix C). The pressure from the data logger was obtained within about one minute of installation by using the Psion HC-120 ™ hand-held computer to query the data logger by attaching an RS232C cable from the infra-red port on the data logger to the hand-held computer (Figure 8).

 
6. After the installation was completed, the hydrant was enclosed in a black, heavy-duty plastic bag (0.003 in.) to indicate that the hydrant was out of service, as required by local ordinance (Figure 9).

 
7. ATSDR stationed staff in the water utility's operations control room for the duration of the tests. The staff recorded the operational history of wells and booster pumps. They also recorded instantaneous system-production data and storage tank water levels registered by the water utility's SCADA system.

Figure 6. (A) hydrant adapter kit, brass lever handle shut-off valve in "off" position, and Ashcroft Duralife industrial pressure gauge, and (B)

Figure 8. ATSDR staff querying pressure data logger attached to test hydrant H-11 for parameters of date, time, and pressure using the Psion HC-120™ hand-held computer.

Figure 9. ATSDR staff covering test hydrant H-11 with a heavy-duty (0.003 in.) plastic bag to indicate "out-of-service" condition.

Figure 10. Data being downloaded from the Psion HC-120™ hand-held computer to a laptop computer using the RS232 ports on both computers.

Review of installation pressure data indicated that all data logger and gauge pressures were within 3 psi for both the March and August 1998 tests (e.g., Appendix C) with the exception of the logger installed on hydrant H-21 (Plate 6; Table 3) during the March 1998 test. Because of the quality-assurance procedures in place, the logger at this test hydrant location, was determined to be defective and a new logger was flown in overnight and installed the next morning. Therefore, the first 10 hours of data for the March 1998 test were not recorded for hydrant H-21 (see pressure graph for test hydrant H-21 in Appendix D). For the duration of the March and August 1998 tests, ATSDR and NJDHSS staff routinely checked each test hydrant and pressure data logger and, using the Psion HC-120™ hand-held computer to observe instantaneous pressure readings at each hydrant, assured that the loggers were functioning properly (e.g., Appendix C). Additionally, routine checks of each test hydrant were made to assure that no significant water leaks, potentially affecting the pressure measurements, had developed. After the tests were concluded, loggers were removed in a process that was the reverse of the one described in steps 1-6 above. The recorded data in the data loggers were downloaded to and stored in the Psion HC-120™ hand-held computer (Figure 4) for post-test analysis. After all data loggers were removed from the test hydrants, data in the Psion HC-120™ hand-held computer were downloaded, as an additional quality assurance step, to a laptop computer in the manner shown in Figure 10.

Analysis of Pressure Data

Because data from the tests were gathered at one-minute sampling intervals, the pressure graphs show transients or "spikes" in the data (Appendix D and E). To use the measured pressure data as a reference for calibrating a model, the data should be averaged over one-hour time periods--the smallest time step for which the water-distribution system model is valid (see section on "Requirements for Model Input"). Therefore, the measured pressure data from the tests, shown in Appendix D for the March 1998 test and in Appendix E for the August 1998 test, were averaged over one-hour time periods for use with model calibration. From this point in the report, all pressure data will be referenced to the one-hour average values of the measured pressure data. Graphs of the one-hour average of measured pressure values along with graphs of measured storage tank levels and well and pump flows will be presented and discussed later in the report in the section on "Hydraulic Model Calibration."

Analysis of pressure data from both tests indicates that pressures throughout the water-distribution system generally range from a minimum of approximately 40 psi (test hydrant H-24, Table 4) to a maximum of about 108 psi (test hydrant H-12, Table 4). Because of higher demand conditions existing in August 1998 (Figure 1), maximum one-hour averages of measured pressures for the August test are lower than that those for the March test. For example, at test hydrant H-12, the maximum one-hour average measured pressure of 93.0 psi for the August test is more than 15 psi lower than the maximum one-hour average measured pressure of 108.2 psi for the March test. In the southern Dover Township, Berkeley Township, and the borough of South Toms River areas, where initial model simulation indicated areas of questionably high pressure (some in excess of 125 psi--see section on "Initial Model Simulation"), test results indicate that for March 1998, hourly averages of measured pressures ranged from about 50 psi to 104 psi (test hydrants H-1 - H-10, Table 4 and Plate 6) and for August 1998, pressures ranged from 48 psi to 93 psi (for test hydrants H-1 - H-10). Specific details for the tests and results for each test are provided in reports by Sautner and Maslia (1998) and Maslia and Sautner (1998b).

Table 4. Comparison of maximum and minimum pressures obtained from the March and August 1998 pressure tests, Dover Township area, New Jersey
 
 

Hydrant Identification1	2Pressure, in Pounds Per Square Inch
	March 1998 Test		August 1998 Test
	Maximum	Minimum	Maximum	Minimum
H-1	92.1	55.8	79.1	48.1
H-2	90.7	50.0	80.0	50.4
H-3	87.3	51.8	76.5	47.6
H-4	103.4	66.0	93.1	63.1
AH-5	98.6	58.7	87.8	55.4
AH-6	97.8	61.6	80.1	55.8
H-7	102.0	66.4	89.8	66.5
H-8	103.8	74.4	92.4	76.2
H-9	99.0	65.4	82.2	63.4
H-10	90.5	59.2	78.7	62.9
H-11	101.8	68.9	88.2	70.6
H-12	108.2	71.3	93.0	72.8
H-13	107.6	71.6	91.4	73.7
AH-14	94.3	62.4	82.9	66.8
H-15	103.1	70.9	90.0	74.0
H-16	91.9	62.7	78.9	62.1
H-17	72.0	45.6	61.6	44.3
H-18	87.9	62.8	76.3	59.5
AH-19	71.6	52.7	61.7	46.2
H-20	61.9	50.4	57.3	42.8
H-21	72.8	50.2	63.6	47.2
AH-22	97.4	68.9	80.1	63.0
H-23	102.5	71.1	84.3	70.5
H-24	68.9	39.6	53.8	39.8
H-25	89.0	58.5	74.1	59.1

¹See Plate 6 for hydrant locations.
²Pressure values are hourly averages derived from one-minute sampling measurements.
 
 

Historical Background

Mathematical modeling has been used for more than 60 years to analyze flow in water-distribution system networks since the concept was proposed by Cross (1936). Using computers for conducting analyses of flow in pipe networks originated in the early 1960s and was greatly expanded during the ensuing decade of the 1970s with the advent of enhanced solution algorithms (Epp and Fowler 1970, Wood and Charles 1972) and the implementation of modeling techniques for devices such as pumps and valves (Jeppson and Davis 1976). In the late 1970s, single-time-period simulations were advanced to extended period simulations with techniques developed by Rao and Bree (1977). Hydraulic models can be used to analyze systems where demand and operating conditions are static or are time varying. The former type of model is a 'steady-state' model, and the latter is referred to as an 'extended period simulation' or EPS model.

Modeling the spatial distribution of water quality in pipelines first began with a steady-state modeling approach as suggested by Wood (1980) who studied slurry flow. Other researchers developing steady-state water-quality models in the 1980s and early 1990s include Chun and Selznick (1985), Metzger (1985), Males et al. (1985), Clark et al. (1988), Grayman et al. (1988a), Wood and Ormsbee (1989), and Clark (1993). The representation of temporally varying conditions for contaminant movement in a distribution system or 'dynamic' water-quality models began to be used in the mid-1980s. Investigators developing such models include Clark et al. (1986), Liou and Kroon (1986), Grayman et al. (1988b), and Hart (1991). With the widespread use and relatively low cost of personal computers and desktop workstations during the mid-1980s and 1990s, many models, both proprietary and public domain, can now be used to conduct hydraulic and water-quality analyses. Two such models in use today are the proprietary model Piccolo (SAFEGE Consulting Engineers 1994) and the public domain model, EPANET (Rossman 1994, Rossman et al. 1994) developed by the U.S. Environmental Protection Agency. The reader is referred to Rossman (1999) and Clark (1999) for a thorough discussion on the evolution and development of hydraulic and water-quality models.

Hydraulic Simulation Model

Hydraulic modeling of water-distribution systems can be conducted by solving mathematical equations that characterize the pipe network of the distribution system. The EPANET water-distribution system model was chosen to conduct an extended period simulation of the hydraulic behavior within the water-distribution system. EPANET solves the following set of equations for each storage node s (tank or reservoir) in the system (Rossman 1994, Rossman et al. 1994):
 

	(1)
	(2)
	(3)
and the following equations for each link (between nodes i and j) and each node k:
	(4)
	(5)
where the unknown quantities are: ys     =   height of water stored at node s, (L); qs     =   flow into storage node s, (L3 T-1); qij    =   flow in link connecting nodes i and j, (L3 T-1); hi     =   hydraulic grade line elevation at node i, (L); and
the known constants are: As     =   cross-sectional area of storage node s, (L2); Zs     =   elevation of node s, (L); Qk    =   flow consumed (+) or supplied (-) at node k, (L3 T-1); and f( . )  =   functional relation between head loss and flow in a link.

Equation (1) expresses conservation of water volume at a storage node while equations (3) and (5) do the same for pipe junctions. Equation (4) represents the energy loss or gain due to flow within a link. For known initial storage node levels y_s at time zero, Equations (4) and (5) are solved for all flows q_ij and heads h_i using equation (2) as a boundary condition. The system of equations is solved using a technique known as the gradient method, and the reader is referred to Todini and Pilati (1987), Salgado et al. (1988), and Rossman (1994) for details.

Water-Quality Simulation Model

The fate of a dissolved substance flowing through a distribution network over time is tracked by EPANET's dynamic water-quality simulator. To model water quality of a distribution system, EPANET uses flow information computed from the hydraulic simulation as input to the water-quality model. The water-quality model uses the computed flows to solve the equation for conservation of mass for a substance within each link connecting nodes i and j, such that:

(6)

where:
 

cij  = concentration of a substance in link i, j as a function of distance and time (i.e., cij = cij(xij,t)), (ML-3); xij  = distance along link i, j, (L); qij  = flow rate in link i, j at time t, (L3T-1); Aij  = cross-sectional area of link i, j, (L2); and (cij)  = rate of reaction of constituents within link i, j, (ML-3T-1 ).

Equation 6 must be solved with a known initial condition at time zero and the following boundary condition at the beginning of a link (i.e, at node i) where x_ij = 0:
 

(7)

where:
 

Cki lkivZt  =    concentration at end node of link k, i, of length Lki, (ML-3); Lki           =    the length of link k, i, (L); Mi            =    the mass of a substance introduced by any external source at node i, (M); and Qsi           =    the flow rate of the source, (L3T-1).

The summations are made over all links k, i that have flow into the head node i, of link i, j. Note, the boundary condition for link i, j depends on the end node concentrations of all links k, i that deliver flow to link i, j. Hence, Equations (6) and (7) form a coupled set of differential and algebraic equations over all the links in the network. These equations are solved using a numerical method called the Discrete Volume-Element Method; for details the reader is referred to Rossman et al. (1993) and Rossman (1994).

The EPANET water-quality simulator provides a mechanism to account for the gain or loss of a substance by considering its reaction as it travels through the distribution system ((c_ij) in Equation (6)). For the intended use of the present study, however, the transport of conservative constituents (no reaction, transformation, or decay) will be analyzed. Therefore, the reaction rate, (c_ij), is set equal to zero for all simulations.

Identifying the source of delivered water in a distribution system has become a necessity when trying to determine the location of a source that may supply water that exceeds a given level of a chemical or biologic constituent. Wood and Ormsbee (1989) developed an explicit method to calculate the percentage of flow, under steady flow conditions, originating at various source points at a specific location in a distribution system. EPANET also has the ability to track the percentage of water reaching any point in the distribution network over time from a specified location (source) in the network (i.e., the "proportionate contribution" of water from a specified source). In this case, the value of c_ij in Equation (7) is set at 100 percent for the source location and the value of c_ij in Equation (6) becomes the percentage of flow the source location has contributed to the location of interest. Given the multiple number of points of entry to the water-distribution system serving the residents of Dover Township, the ability to track the percentage of water originating from a point of entry becomes a very useful analysis tool for this investigation.