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.080 m3/s, then the input data and solution areInput Data SolutionDQ1U0.001DQ1 =- 0.01827DQ2U0.002DQ2 =149.2DQ3U0.003DQ3 =- 0.02508Qo1K0.124Qo1 =0.12Qo2K0.005Qo2 =0.00Qo3K0.096Qo3 =0.09Qo4K0.077Qo4 =0.07Qo5K0.048Qo5 =0.04Qo6K0.049Qo6 =0.04Qo7K0.081 0Qo7 =0.08Qo8K0.161 1Qo8 =0.16In this input file the initial discharge estimates Qoi have been altered from previousvalues so that all continuity equations remain satisfied with QJ5 = 0.080 m3/s.Thesolution values remind us that ∆ Q2 is actually the HGL at the downstream end of thePRV since it has closed, and FUNCT has set ∆ Q2 = - Qo5 and then used X(2) as theposition for HGL.The table lists the discharges and head losses for this situation:P i p e12345678Q, m3/s0.10170.02170.10830.07680.00.08000.05490.1851hL, m17.830.65219.986.400.011.471.88710.86The pump heads and local losses are hp1 = 8.02 m, hp2 = 3.69 m, hL1 = 0.638 m,hL2 = 7.25 m and hL3 = 1.211 m, with nodal heads of H1 = 177.4 m, H2 = 163.2 m,H3 = 160.7 m, H4 = 181.9 m, and H5 = 149.2 m.Now the PRV has closed entirely sothe flow in pipe 5 is zero, and the HGL at its downstream end is above its set point.* * *4.4.5.SYSTEMATIC SOLUTION OF THE Q - E Q U A T I O N SIn earlier sections we have developed the three systems of equations that can be used toanalyze pipe networks.We have written these equation systems for several smallnetworks, seen how the Newton method can be applied to any system of nonlinearequations and how to solve a problem by using a general purpose program that implements© 2000 by CRC Press LLCthe Newton method for all three equation systems, and finally we have carried out detailedcomputations by hand to obtain some solutions by iteration.In this section we will seehow this knowledge can be used in developing computer programs that will analyze anypipe network by using the Q-equations, and the programs will require only enoughinformation from the user to describe adequately the network and its connectivity.In thenext two sections similar programs will be developed for the solution of the H-equationsand the ∆ Q-equations.Let us begin by assuming that there are no local losses.If they exist, they can be mod-eled simply by assigning a larger equivalent sand roughness, or Hazen-Williams CHW, tothe pipes containing minor losses.Here we ignore the Manning equation.In describing any network of pipes, we need two types of information: (1) Pipe infor-mation consisting of the diameter, length, roughness coefficient, and end nodes for eachpipe.This information can be called pipe-oriented data, since we assemble it by goingthough a list of the pipes in the network; (2) Junction information, including the demandat the junction, its elevation, and possibly the pipes that join at the junction.Thisinformation is called node-oriented data, since it is assembled by moving through the nodesof the network.Actually the connectivity of the network can be defined either by givingthe nodes at the ends of each pipe, or by giving the pipe numbers that join at each node.We shall use this duplicative information to check that the user has not erred in definingthe network.Now we shall describe the input data that are required.Details on the form of this inputwill be provided subsequently.Prior to study of this section the reader should obtain alisting of the program SOLQEQS.FOR (or C if you prefer) from the text CD.The information that is required from the user is the following:1.A line that gives (a) the number of pipes, (b) the number of nodes, (c) the number ofreservoirs that supply the network, (d) the number of pumps, and (e) the optionswhich you wish to change from the default values.(The default options and howthese are changed will be described later.)2.For each pipe, list its (a) number, (b) upstream node, (c) downstream node, (d)length, (e) diameter, and (f) roughness coefficient.3.For each node, list its (a) number, (b) demand, and (c) elevation, and (d) a list ofpipes that join this node.4.For each reservoir, list (a) the pipe number that connects this reservoir to the net-work, and (b) the water surface elevation of the reservoir.5.For each pump, list (a) the number of the pipe that contains the pump, and (b) three( Q, hp) pairs of discharge vs.pump head that will allow its operating characteristicsto be defined.6.Finally, because the algorithms that could be used to determine the minimum set ofindependent loops for the energy equations are relatively complex, we require a listof pipe numbers around each loop (with a minus sign before a pipe number if themovement around the loop opposes the assumed direction of flow in that pipe).Werequire that pseudo loops be provided first, and then the real loops.The information in item one is used to dimension the arrays that will store theremaining information about the pipe network and to determine how many lines of eachinformation type will be read from the input data file.The information must be providedin the sequence that is listed above.The program must perform five major tasks:1.Read the input data that defines the network.2.Develop from this information the system of Q-equations, i.e., the junction contin-uity equations and the energy equations around pseudo and real loops of the network [ Pobierz całość w formacie PDF ]
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