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2. ELEMENTS OF A WATER DISTRIBUTION SYSTEM To ALLWET, a water distribution system consists of six elements: nodes, pipes, reservoirs (a term to be precisely defined below), booster pumps, pressure reducing valves (PRVs) and check valves. This chapter of the manual describes the type of data associated with each of these elements. Later chapters contain detailed information for initially preparing and updating (interactively) the data. Figure 1 and Table 1 illustrate and describe a sample water distribution system to be referred to throughout this manual. 2-1 4 x Booster Water x <- Pump Tower x Station T-1 x x x 1 x x x x x x x x x x x x x 2 x x x x x x x x Figure 1 x x x x x x x x x CC x x x x x x x x x x x x x x x x x x x x 3 x x x AA x x x BB x x x x x x x x x x x x T-2 Pump Station ^ | Pressure Reducing Valve on pipe between nodes AA and 3 Figure 1 Sample System Configuration 2-2 Table 1: Sample Problem Data Units used: Pipe length - feet Pipe diameter - inches Flow - US gpm Head loss - feet Elevations - feet Pressure - psi Velocity - fps Node Data Class Node Elevation Demands A-D Coordinates Pressure 1 T-1 400 0,0,0,0 1000, 3000 1 T-2 375 0,0,0,0 4000, 500 3 1 385 0,50,50,0 1500, 3000 3 2 450 100,15,0,0 4000, 3000 2 3 350 75,25,0,0 500, 500 2 4 475 0,0,0,60 4000, 3500 1 AA 410 100,50,0,0 1000, 500 1 BB 410 175,0,0,0 1500, 500 1 CC 415 125,0,125,0 2750, 1750 30 psi Multiplicative factors for class 2 nodes: 1.3, 0.9, 1.0, 1.0 Pipe Data Number From Node To Node Diameter C Length 1 T-1 1 10 100 500 2 T-1 AA 10 100 2500 3 1 2 10 100 2500 4 4 CC 8 100 1964 5 1 BB 10 100 2500 6 2 T-2 10 100 2500 7 T-2 BB 10 100 2500 8 BB CC 8 100 1964 9 BB AA 10 100 500 10 AA 3 8 100 500 11 3 4 6 100 500 Pipe 4 has pseudonodes at 1978,2904; 2384,2634; 2655,2228 Pipe 8 has pseudonodes at 1978, 596; 2384, 866; 2655,1272 Water tank at node T-1 Water elevation = 475' Fraction of Supply = .3 Pump Station at node T-2 Pump elevation = 380' Fraction of Supply = .7 Head-discharge can be described by 5 points H: 145 135 120 100 75 Q: 200 600 1000 1400 1800 Booster pump on pipe 11 with head-discharge curve described by 5 points: H: 60 55 45 30 10 Q: 0 40 80 120 160 Pressure reducing valve on pipe 10 2 velocity heads lost when valve is inactive, valve set at 30 psi 2-3 2.1 Nodes and Calculation of Nodal Demands Nodes are located at pipe junctions, points where water can enter the distribution system, and any other points where the water pressure or hydraulic grade line should be known. By convention, flow out of the system through any node is positive, and flow into the system through a node is negative. For each node of the system, the following information must be provided: (a) Name. This should be unique and have one of four forms: (1) A numeric string having up to four characters (e.g. 1, 20, 500) (2) An alphabetic string of up to four characters followed by a numeric string of up to four characters, or vice versa (e.g. A1, 1A, 1B, 23CC, CC23, ABCD12, 12ABCD; but not numbers and letters interspersed, such as 12A1 or A3A) (3) Two alphanumeric character strings (i.e., either numbers or letters), separated by a hyphen and each containing no more than three characters (e.g. 1A-1, A1-1, CCC-A, A-CCC, 1-11, 1-12, 12-A) (4) An arbitrary alphanumeric string of up to eight characters not conforming with (1), (2) or (3) (e.g. A, 12345, 12Al, A3A) For output purposes, ALLWET orders the node names by the first string, and, when these are identical, the second string. Numeric strings come first, followed by all other strings in alphanumeric order (i.e., digits following letters). Thus the names in the above examples would be ordered: 1, 1-11, 1-12, 1A, 1B, 12-A, 12ABCD, 20, 23CC, 500, A, A1, ACCC, ABCD12, A1-1, A3A, CC23, CCC-A, 1A-1, 12A1, 12345. (b) Coordinates of the node. ALLWET uses this information for the selective output of nodes and pipes within a specified portion of the map during interactive use, and for the automatic calculation of pipe lengths. Users who don't wish to use these features can just enter zeros for all coor- dinate values. if coordinate values are used, the coordinate system must use the units in which pipe lengths are measured. (c) Elevation. All node elevations must refer to the same datum. This value is used solely to calculate the pressure at the node, after the hydraulic grade line has been determined. (d) Demand for water. Four values (designated A, B, C and D) for every node. Each value can designate a specific type of demand. For instance, type A might represent average daily residential demand at the node, while types B, C and D might represent average daily commercial demand, average daily industrial demands and miscellaneous demands respectively. (e) Pressure at a node. This may or may not be indicated. If a positive value is entered, during flow-pressure calculations ALLWET will calculate the flow into or out of the node necessary to maintain this pressure, and disregard the demand values. Changing the pressure to zero or any negative value will again allow ALLWET to use the four demands for the next flow-pressure calculation. 2-4 (f) An integer (1 through 10) to define the nodal classification. These classifications may have any significance the user desires. Possibilities include region in the distribution system, areas of high irrigation, or the identification of special demands at a node (hospital, theater, etc.). For most applications, no more than four or five nodal classifications would be necessary. (Using only classification 1 will often be adequate.) The four demands, the nodal classifications at each node, and the concept of multiplicative factors (described in the next paragraph) permit users of ALLWET to simulate specific demand patterns such as maximum day or maximum hour. For every nodal classification, ALLWET permits one multiplicative factor for each of the four demand types. Unspecified multiplicative factors are assumed equal to 1.0 (e.g., those for nodal classifications 1 and 3 in Table 1). For any analysis, ALLWET calculates total demand at each node by summing the products of each entered demand A through D with the corresponding multipli- cative factor. Thus, using the data in Table 1, the total flow at node 3 is 1.3 (75) + 0.9 (25) + 1.0 (0) + 1.0 (10) = 130. However, negative demands (flows into the system) are not multiplied by the factor before inclusion in the sum. This permits the modeling of fixed inflow sources. Therefore, if demand B for node 3 instead were -25, then the total flow would be 1.3 (75) + (-25) + 1.0 (0) + 1.0 (10) = 82.5. A system-wide factor PERC (default value equals 1.0) may also be speci- fied. In calculating nodal flows, all positive demands are multiplied by PERC as well as the corresponding multiplicative factor. Thus, in the second example just given, if PERC was 1.2 (representing a 20% increase in positive demands throughout the system), the total flow would be 1.3 (1.2) (75) + (-25) + 1.0 (1.2) (0) + 1.0 (1.2) (10) = 104. 2-5 2.2 Pipes Pipes require the following information: (a) Number to identify the pipe. (b) Two distinct nodes (a "from" node and a "to" node) which the pipe connects. Except for pipes containing booster pumps and PRVs, either node may be the "from" node. Pipe flows calculated by the computer will be negative if flow runs from the "to" node to the "from" node. (c) Diameter of the pipe. (d) Hazen-Williams roughness coefficient (also known as the C factor) or the Manning roughness factor. The same one of these must be used for all pipes in the system. (e) Length of pipe. (f) Coordinates of up to three pseudonodes. Pseudonodes permit the representation of curved pipes as up to four connected line segments. These may not be used if no coordinate system is used. 2-6 2.3 Reservoirs For the purpose of ALLWET, reservoirs are nodes at which water can enter the system, and, simultaneously, where the demand is not fixed. Discussion of the three types of nodes at which water can enter a distribution system should clarify the implications of this definition. Type 1: Nodes at which water enters the system at a fixed head, e.g., fixed head pumps or storage tanks "floating" on the system. For this type of reservoir, the user must indicate the node name and the HGL constant (i.e., the fixed value of the hydraulic gradient at the node). The calculated flow at a node having a type 1 reservoir equals the flow needed to maintain the indicated gradient. Flow leaving the distribution system (into a tank) will be positive while flow entering the distribution system (out of a tank) will be negative. During flow-pressure calculations, ALLWET places temporary Type 1 reservoirs at nodes with fixed pressures. Although the "floating" of a storage tank on the system implies that its elevation is allowed to vary freely, the HGL constant is a necessary input. ALLWET calculates flows and pressures in the system at a specific instant based upon what the elevations in storage tanks are at that instant. Separate analyses would have to be performed to evaluate how varying tank levels affect flows and pressures throughout the distribution system. As a practical matter, analyses at no more than two or three elevations would be sufficient. Type 2: Nodes with pump(s) that deliver water at a head dependent upon the flow. For these reservoirs ALLWET needs a relationship between the discharge of and the head generated by the pump, input as a series of points lying on the pump's head-discharge curve. Such a relationship will be referred to as an H-Q curve. (See section 2.5, "Notes Concerning H-Q Curves," later in this chapter.) 2-7 An HGL constant can also be entered for a type 2 reservoir. ALLWET adds this constant to the head values along the H-Q curve to determine the hy- draulic grade line at the node for a given value of flow. Thus, if the head values along the H-Q curve represent the actual hydraulic grade line of water leaving the pump (rather than the contribution to head made by the pump), then the HGL constant should be set to zero. However, if the head values along the H-Q curve represent the contribution of head made by the pump, then the HGL constant must be entered as the elevation of the pump with respect to the datum. The input data for a type 2 reservoir may be prepared in either way. Type 3: Nodes at which pumps (or something) deliver water at a fixed flow regardless of the hydraulic grade line. Such nodes are not reservoirs as defined above (since flow is fixed), but instead should be treated as nodes with a negative demand. This can be done by setting one of the node's demand to a negative number. Adequate accuracy can often be achieved (especially if one or more storage tanks "float" on the system) by considering type 2 reservoirs to be fixed input nodes. This will be necessary for older pumps whose H-Q curves are unknown. Engineers at pumping stations generally know or can measure the flow which a pumping station can generate. The user may optionally indicate a fraction of supply value for each type 1 and type 2 reservoir. Each such value represents the user's estimate of the fraction of the algebraic sum of all nodal demands which the corresponding reservoir will supply. ALLWET uses these values in defining the first iteration conditions when solving the system of nonlinear equations during pressure-flow calculations. Hence, prudent selection of these values can save computation time and insure convergence. If selected, these numbers may be positive or negative, but their sum must be one. A negative value for a type 2-8 1 reservoir (elevated tank) implies that water is expected to enter the tank (e.g., nighttime operation to replenish the tank for the next day's drawdown). If the fraction of supply values are not given or do not sum to one, ALLWET assumes each equal to 1/n, where n is the total number of type 1 reservoirs, type 2 reservoirs and nodes at which the pressure has been set. This default is adequate for most systems. However, an occasional problem will require user specified fraction of supply values in order for the solution to converge. Section 6.2.1 discusses this further. ALLWET constructs the set of nonlinear equations for the system starting from either a type 1 or type 2 reservoir, or from a node with a pressure set- ting. The node or reservoir selected for this purpose is referred to as the reference reservoir. Hence, every network to be studied must have at least one reservoir or pressure node. Usually, any reservoir or pressure node may be selected as the reference reservoir, so by default ALLWET uses the first reservoir or pressure node it finds. ALLWET will allow the user to override its choice, but this will be necessary only when ALLWET cannot otherwise reach a convergent solution. Section 6.2.2 discusses how to do this when necessary. Section 6.1 discusses the interpretation of calculated pressures at nodes having type 1 or type 2 reservoirs. 2-9 2.4 Booster Pump Stations Booster pump station descriptions consist of the pipe where the station is located and a description of the H-Q curve. The indicated pipe must be oriented so that the booster pump forces flow from the "from" node to the "to" node. The flow-head relationship (H-Q curve) is described by a series of points from the manufacturer's pump curve. 2.5 Notes Concerning H-Q Curves Figure 2 illustrates a typical head-flow relationship for a type 2 reservoir or booster pump. All such curves must be entered as from four to thirty (microcomputer version allows only up to twenty) points from the manufacturer's pump curve. ALLWET fits a third or fourth degree equation through the points using least squares (also called regression) techniques. H-Q curves should decrease in H as Q increases. Without this condition, ALLWET may have difficulty completing flow-pressure calculations. H-Q curves must represent the operating characteristics of the pump operating during a specific analysis. If a pump station consists of several identical pumps operating in parallel, the H-Q curve entered can be that for an individual pump with the user specifying the number of pumps operating in parallel. Testing a water distribution system with a different combination of pumps from the same location involves changing the number of parallel pumps or changing the H-Q curve. 2-10 │ │ x │ x │ x │ Head │ x (H) │ │ │ x │ │ │ x └─────────────────────────────────────────── Flow (Q) Figure 2 H-Q curves ┌─────────────┐ │ │ x────────<───────┤ PRV ├─────<────────x │ │ "Downstream" or └─────────────┘ "Upstream" or "to" node "from" node Figure 3 PRV Orientation 2-11 2.6 Pressure Reducing Valves (PRVs) Pressure reducing valves placed on pipes limit the pressure at the "to" node of the pipe. Three required and one optional inputs are necessary for PRVs. (a) Pipe on which PRV is located. (This pipe must be oriented with the "to" node on the downstream side of the PRV. See Figure 3.) The nominal diameter of the PRV is taken as the diameter of this pipe. (b) Maximum allowable pressure at "to" node of this pipe. (c) Resistance coefficient of the PRV (further explanation given below). (d) Associated reservoir for the PRV (further explanation follows). A partially closed PRV is "on" or "operating", i.e., the downstream pressure is being held fixed. A fully open PRV is "off" or "not operating" and the headloss, h, across such a PRV is governed by the equation h = kv**2/2g, where the resistance coefficient k is a dimensionless quantity representing the number of velocity heads lost across the PRV. PRVs act like check valves in that water is not allowed to flow backwards through them. The loss char- acteristics through a nonoperating PRV can be assumed part of "minor losses" by setting k to zero. In order that PRVs work properly, ALLWET must calculate the head at the "from" node of each PRV's pipe. This requires calculating the shortest path from an associated reservoir or pressure node to the "from" node of the PRV. ("Shortest" in this case means number of pipes rather than their length.) If this path crosses the PRV, ALLWET may not work properly. Thus, the user should specify for each PRV the node of an associated reservoir over pressure node of such that the shortest path to the upstream node of the valve does not cross the valve. If the user omits the selection or selects a node which lacks a reservoir or pressure node, ALLWET selects an arbitrary reservoir or pressure node. However, ALLWET's choice is not guaranteed to satisfy the 2-12 above requirement. 2.7 Check Valves Check valves placed on a pipe restrict the flow to be positive. Just as for PRVs, correct orientation of the pipe is essential. Section 6.1 discusses how ALLWET constrains flow in PRVs and check valves to be positive. 2-13