JP2006057407A - Pipe network analysis method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a pipe network analysis method which is accurately carried out in a short time. <P>SOLUTION: The pipe network PN comprises a network of a water source S1, nodes N1-N4 to be mutual intersections of conduits and the conduits K1-K5 with one end or the other end connected to the water source S1 or the nodes N1-N4. A water amount to be taken out from the conduit by water demand is reduced from a water amount in the pipe network PN, and a flow rate in the conduits K1-K5 constituting the pipe network PN and a water head to be water pressure in the nodes N1-N4 are calculated in the pipe network analysis method. The water amount to be taken out from at least one part in the conduit where water demand exists is taken out when the water amount to be taken out is reduced from the water amount in the pipe network PN. The flow rate in the conduit where the water demand exists is made to be varied in steps, and a conduit flow rate q<SB>s</SB>, Ki on the start point side to be a flow rate on the upperstream side and a conduit flow rate q<SB>e</SB>, Ki on the end point side to be a flow rate on the downstream side in the conduit are calculated as the flow rate in the conduit. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a pipe network analysis method.

  In recent years, in the water supply business, to grasp the state of the pipeline network buried in the ground (hereinafter referred to as the pipeline network), and to perform maintenance management such as making an update plan for the pipelines that make up this pipeline network Is extremely important.

  Under such circumstances, the head of the reservoir that supplies water to the pipe network (height from the sea level to 0 [m] to the surface of the reservoir), the location of the pipeline, the diameter of the pipeline, the intersection of the pipelines ( The so-called pipe network analysis is carried out to calculate the flow rate of each pipeline and the head of each node under given conditions such as the amount of water taken out from the node (hereinafter referred to as the amount of removed water). . By obtaining data on the flow rate of each pipe and the head of each node from the results of such pipe network analysis, for example, it is possible to grasp pipes with a high flow rate, nodes with low heads, and the importance of pipes. Since it can be grasped, it can be used for a pipeline renewal plan.

  When the pipe network analysis as described above is performed on a pipe network in which, for example, a water source S1 and nodes N1 to N4 are connected by pipe lines K1 to K5 as shown in FIG. If it is a net | network, as shown in FIG. 16, for example, water supply pipes P1-P7 are connected to a house etc. from each pipe line, and arbitrary water quantities V1-V7 are taken out from these pipes. When the pipe network analysis including the pipes P1 to P7 is performed, it is necessary to handle the intersection of the water supply pipe and the pipe line as a node, and the water pipe is also subject to the pipe network analysis. The number of nodes and the number of nodes will increase dramatically, and the amount of calculations performed at the time of analysis will become very large.

  Therefore, the water supply pipes P1 to P7 are not handled at the time of analysis, the water supply pipes P1 to P7 are not subjected to pipe network analysis, and only the amount of water taken out from these water supply pipes P1 to P7 is handled separately. The amount of calculation required at the time of analysis is reduced.

  As shown in Fig. 17 (a), regarding the handling of the amount of water taken out during pipe network analysis, the amount of water taken out from the pipeline by the water supply pipe is collected at each node, and a fixed amount of water is discharged from these nodes. A node extraction model in which extraction is performed, and a pipe extraction model in which, as shown in FIG. 18 (a), a constant amount of water is extracted uniformly from the pipe along the length direction. There is.

  In the case of the nodal extraction model shown in FIG. 17A, as described above, since water is taken out from each node instead of from the pipeline, for example, as shown in FIG. The flow rate of the water flowing in the pipe line reaching the node B is constant.

  Further, in the case of the pipeline extraction model shown in FIG. 18A, as described above, since water is handled in such a way that a certain amount is uniformly extracted from the pipeline over its length direction, for example, As shown in FIG. 18B, the flow rate of the water flowing in the pipe line from the node A to the node B gradually decreases at a constant rate.

In each model, the amount of water taken out is handled as described above, so that the amount of calculation to be performed at the time of analysis is reduced and pipe network analysis can be performed quickly. In addition, as a pipe network analysis method using the pipe extraction model, for example, there is one described in Non-Patent Document 1.
Uto, Nishikawa, Izumi “Analysis and design of water distribution pipe network by mesh flow method”, Measurement and Control, Society of Instrument and Control Engineers, August 1989, Vol. 28, no. 8, p. 45-58

  In pipe network analysis in recent years, if the effective head represented by the difference between the head of the node and the ground height at that node is used, and the effective head at that node is smaller than a predetermined size, the drainage of water at that node is poor. There is an increasing demand for considering the pressure dependency of the amount of water taken out, which expresses that. This is because in the conventional pipe network analysis, the amount of water to be taken out is always treated as constant, and as a result of the pipe network analysis, there is no effect on the water output regardless of the size of the effective head of the node. Because it is not in reality.

  When considering the pressure dependency of the amount of water to be taken out, as shown in FIG. 17 (b), if it is a nodal point extraction model in which the flow rate of water flowing in the pipeline is constant, the calculation performed at the time of analysis is performed for the convenience of calculation. Since the amount does not increase so much, it is possible to perform an analysis considering the pressure dependency of the amount of water taken out. On the other hand, as shown in FIG. 18 (b), in the case of a pipe extraction model in which the flow rate of water in the pipe gradually decreases at a constant rate, it is theoretically necessary to consider the pressure dependence of the amount of extracted water. Even if it is possible, since the amount of calculation when actually performing the analysis becomes very large, practical implementation becomes very difficult.

  As described above, when performing a pipe network analysis in consideration of the pressure dependency of the amount of water to be taken out, the node take-out model is preferable to the pipe take-out model. As it is, it is handled to take out from each node, and we do not consider taking out water from the pipe like the actual pipe network or pipe take-out model. There is a risk that the accuracy will be inferior.

  Therefore, an object of the present invention is to provide a pipe network analysis method that can solve such problems and can be performed accurately and in a short time.

  In order to solve the above-mentioned problem, the invention described in claim 1 is constituted by a network relationship between a water source, a node that is an intersection of pipes, and a pipe line to which the water source or the node is connected to one end and the other end. The amount of water taken out from the pipe due to demand for water is subtracted from the amount of water in the pipe network, and then the flow rate in each pipe constituting the pipe network and the water pressure at each node. In the pipe network analysis method for calculating a certain head, when the amount of water to be taken out is subtracted from the amount of water in the pipe network, the amount of water taken out is taken out from at least one place in a pipeline where the water is in demand, The flow rate in the pipeline with demand is changed stepwise, and then the flow rate in the pipeline is the upstream flow rate in the pipeline and the downstream flow rate. And calculates the end point pipeline flow.

  In this way, for example, when water is taken out from the pipe line from a water supply pipe connected to the pipe line, by setting the amount of water taken out from the pipe line according to the amount of water taken out from the water pipe, Compared to the case of taking out the amount of water taken out from the node as in the nodal extraction model, or the case of taking out a constant amount of water from the pipe in the length direction as in the case of the pipe extraction model. Is close to reality, and pipe network analysis can be performed more realistically. Thereby, the accuracy of pipe network analysis can be improved. In addition, since the start-point side pipe flow rate and the end-point side pipe flow rate are calculated as the flow rate in the pipe line where there is a demand for water, it is possible to calculate the pipe flow rate according to reality. Furthermore, even if water is extracted from at least one location in a pipeline where there is demand for water, and the pipe network analysis is performed, the number of pipelines and nodes to be analyzed is the same as the node extraction model and the pipeline extraction model. Therefore, pipe network analysis can be performed in a short time.

  The invention according to claim 2 is the pipe network analysis method according to claim 1, wherein the initial value of the head of each node in the pipe network is set, and based on the initial value of the water head, A lower limit value and an upper limit value of the start point side pipe flow rate are set, an initial value of the start point side pipe flow rate is set based on the lower limit value and the upper limit value of the start point side pipe flow rate, and the start point side pipe flow rate A node calculated based on the updated initial value and the initial value of the starting-side pipe flow rate updated based on the head of the node calculated based on the initial value of the flow rate and the initial value of the head of the set node. And a convergence calculation for updating the updated initial value based on the initial value of the head of the set node, and calculating the convergence value as a starting side pipe flow rate, and calculating the calculated starting point side pipe The end point side pipe flow rate corresponding to the flow rate is calculated.

  In this way, since the convergence calculation is performed to calculate the value of the starting point side pipe flow rate, the value of the starting point side pipe flow rate can be calculated accurately, and the end point side pipe flow corresponding to the starting point side pipe flow rate is calculated. The flow rate can also be calculated with high accuracy.

  According to a third aspect of the present invention, in the pipe network analyzing method according to the first or second aspect, the water head of each node set based on the start side pipe flow rate and the end side pipe flow rate in a pipe having water demand The initial value of each of the nodes is updated based on the updated value of the head of water, the start side pipe flow rate and the end side pipe flow rate in the pipe having the water demand are calculated, and the calculated start side pipe Based on the channel flow rate and the end side pipe flow rate, a convergence calculation is performed to further update the updated head values of the nodes, and the convergence value of the start side pipe flow rate and the end point side pipe flow rate The value of the start point side pipe flow rate and the value of the end point side pipe flow rate in a certain pipe line are calculated, and the convergence value of the head of the node is calculated as the value of the head of the node.

  In this way, based on the starting point side pipe flow rate and the end point side pipe flow rate in pipes where water is in demand, the set initial value of the head of each node is updated, and the updated value of the head of each node is updated. Based on the above, the starting point side pipe flow rate and the end point side pipe flow rate in the pipe having the demand for water are calculated, and the updated each of the updated start point side pipe flow rate and the end point side pipe flow rate are calculated based on the calculated starting point side pipe flow rate and end point side pipe flow rate. By performing a convergence calculation that further updates the value of the head of the node, the value of the start side pipe flow rate, the value of the end side pipe flow rate, and the value of the head of the node can be accurately calculated.

  The invention according to claim 4 is the pipe network analysis method according to any one of claims 1 to 3, wherein the amount of water taken out from at least one place in the pipe where water is in demand is taken out of the water in the pipe. It changes according to the size of the pressure head, which is a value obtained by subtracting the ground height of the place where the water is taken out from the head of the place where the water is taken out.

  In this way, by making the amount of water taken out dependent on the size of the pressure head, for example, it can be expressed that the drainage of water becomes worse at the peak of demand or the area on the hill where the pressure head decreases, Pipe network analysis can be performed with higher accuracy than the conventional pipe network analysis in which the amount of water taken out is constant.

  As described above, according to the present invention, for example, when water is taken out from a pipe from a water supply pipe connected to the pipe, the quantity of water taken out from the pipe is set according to the quantity of water taken out from the water pipe. By setting, compared to the case of taking out the amount of water taken out from the node as in the nodal extraction model, or the case of taking out a constant amount from the pipe along the length direction as in the pipe extraction model. The water extraction situation is close to reality, and a more realistic pipe network analysis can be performed. Thereby, the accuracy of pipe network analysis can be improved. In addition, since the start-point side pipe flow rate and the end-point side pipe flow rate are calculated as the flow rate in the pipe line where there is a demand for water, it is possible to calculate the pipe flow rate according to reality. Furthermore, even if water is extracted from at least one location in a pipeline where there is demand for water, and the pipe network analysis is performed, the number of pipelines and nodes to be analyzed is the same as the node extraction model and the pipeline extraction model. Therefore, pipe network analysis can be performed in a short time.

A method for performing a pipe network analysis on the pipe network shown in FIG. 1A by the pipe network analysis method according to the embodiment of the present invention will be described.
In this embodiment, as shown in FIG. 1 (a), the water taken out from the pipeline by the water supply pipe is taken out from at least one location in each pipeline, in this case, a fixed amount from any plurality of locations. Thus, for example, as shown in FIG. 1 (b), in the pipeline from the node A to the node B, a constant flow of q1 [m ³ / s] of water flows in the section AB1, and the point B1 (Q1-q2) [m ³ / s] of water is taken out in section B1B2, q2 [m ³ / s] of constant flow flows, and (q2-q3) [m ³ / s] at point B2 The amount of water taken out can be handled, and the flow rate of the water flowing in the pipe line from the node A to the node B is stepwise along the water flow direction. It can be handled to decrease. Hereinafter, a model that handles the amount of extracted water as described above is referred to as a discrete extraction model.

Further, in the present embodiment, when performing the pipe network analysis on the pipe network shown in FIG. 1A, various initial data are given as shown in FIGS.
Specifically, as shown in FIG. 2, the water source S1 is given a value A [m] of LWL (Low Water Level) as the head of the water source and a ground height H (S1) [m] of the water source S1. Yes. Further, in the present embodiment, since water is not taken out from each node, each of the nodes N1 to N4 is given a value of 0.0 [m ³ / s]. Further, the ground heights H (N1) to H (N4) [m] are given to the nodes N1 to N4.

In addition, as shown in FIG. 3, the pipes K1 to K5 have a start point, an end point, a flow velocity coefficient CH, pipe lengths L (K1) to L (K5) [m], pipe inner diameters D (K1) to D ( K5) [mm] is given. In the present embodiment, for example, a case where water is taken out from the pipes K3 and K4 and the water is not taken out from the pipes K1, K2, and K5 among the pipes K1 to K5 will be described. To do. For this reason, the pipes K1, K2, and K5 are provided with a take-out water amount of 0.0 [m ³ / s], and the pipes K3 and K4 are provided with a take-out water amount V [m ³ / s].

  In the pipe network analysis described below, as described above, the water taken out from the pipe line by the water supply pipe is handled in such a manner that a certain amount is taken out from a plurality of arbitrary locations in each pipe line. The analysis procedure is based on the known nodal head method.

  Further, in the present embodiment, the Hazen Williams empirical formula (shown in Equation 1) is used to find the loss head when water flows from one end side to the other end side of the pipe.

In Equation 1, h is a head loss [m], q is a flow rate [m ³ / s], CH is a flow velocity coefficient, D is a pipe inner diameter [m], and L is a pipe length [m]. The resistance coefficient of the road (hereinafter referred to as pipe resistance). The pipe resistance r is a constant determined by the flow velocity coefficient CH, the pipe inner diameter D, and the pipe length L. In addition, as shown in FIG. 4, the height represented by the sum of the effective head e [m], which is the pressure head at the node, and the ground height H [m] is indicated as the head P of the node (hereinafter referred to as the node head P). ) [M], the loss head h represented by the above equation 1 is expressed by the following equation (2): the node head P _S (LWL in the case of a water source) and the node head P at the end of the pipeline _Expressed by the difference from _e .

  In addition, an equation obtained by solving Equation 1 for q, Equation 3

Where g is a partial derivative of loss head h, and g is expressed by the following equation (4). In the following, g is referred to as variational conductance for the pipe.

  In order to perform a pipe network analysis on the pipe network shown in FIG. 1A under the above conditions, first, as shown in FIG. 5, step 1 (S001) is performed as shown in FIGS. Read the initial network data as shown.

  Next, as shown in FIG. 5, as step 2 (S002), based on the data read in step 1, the water source S1, nodes N1 to N4, and pipelines K1 to K5 are connected, and network relations in the pipeline network Build up. At this time, the theory of the electric network is applied in the calculation of the pipe network analysis.

Specifically, as shown in FIG. 6, graph processing is performed on the pipe network PN. That is, a reference node N5 (water head = 0 [m]) corresponding to the ground of the electric network is provided, and this reference node N5 is connected to a node (water source) where water flows in and out. In the case of the present embodiment, the water is handled as being taken out from the pipe, but as described above, the analysis procedure is performed based on the known nodal head method, so the flow rate is 0 [m ³ / s] here. These nodes N1 to N4 and the reference node N5 are connected by reference node connection branches b1 to b4. Then, the water source S1 and the reference node N5 are connected by the reference node connection branch b5.

At this time, the flow rates of the reference node connection branches b1 to b4 are constant at the amount of water taken out at the nodes N1 to N4, that is, 0 [m ³ / s]. In such a case, the reference node connection branches b1 to b4 are made publicly known. By release removal, it can be removed as shown in FIG. However, since the flow rate of the reference node connection branch b5 is unknown, the reference node connection branch b5 cannot be removed.

  In addition, the arrow in FIG. 7 has shown the flow direction of the water in the pipe lines K1-K4 and the reference | standard node connection branch b5. The water flow direction in the pipe lines K1 to K4 may be set arbitrarily, but the water flow direction in the reference node connection branch b5 is set in a direction toward the reference node N5. Further, data on the reference node connection branch b5 is shown in FIG. As shown in FIG. 8, the starting point of the reference node connection branch b5 is the water source S1, the end point is the reference node N5, and the head of this reference node N5 is set to 0 [m]. The difference is A [m] which is the value of LWL of the water source S1.

  Next, as shown in FIG. 5, in step 3 (S003), a breadth-priority tree is searched based on the graph theory. In general, a tree in graph theory is defined as a subgraph (here, corresponding to a pipe line) that includes all points (nodes) and does not have a closed circuit (loop). , A tree obtained by searching so as to branch as much as possible from the root (reference node).

  Since the search for the breadth-first tree can be performed by a known method, a detailed description of the method is omitted here. The result of the breadth-first tree search performed in step 3 is shown in FIG. As shown in FIG. 9, as a result of the search, pipes K1 to K3 and K5 with a breadth-priority tree are represented by solid lines as tree branches, and pipe K4 without a breadth-priority tree is a complementary tree branch. As a broken line.

  When the pipe network analysis is performed by the nodal head method, the nodal head P at each node is set as an unknown, and the initial value of the nodal head P required in the subsequent calculation is shown in Step 4 (S004) in FIG. As described above, the determination is made in advance using the search result of the breadth priority tree.

  More specifically, in the case of the pipe network PN shown in FIG. 9, the depth ne in the breadth-first tree search, that is, the branch (pipe line) from the node N3 that is the terminal end of the breadth-priority tree to the reference node N5 that is the root. ) Is 4, and from FIG. 2, the LWL of the water source S1 is A [m], and the ground height of the node N3 is H (N3) [m], so that it is on the way from the water source S1 to the node N3. , The average head drop Δh per pipe line can be expressed as:

Here, for example, when the LWL of the water source S1 is A = 30.0 [m] and the ground height of the node N3 is H (N3) = 18.0 [m], the above-described drop amount Δh is expressed by the following equation (5). As a result, 4.0 [m] is obtained. Therefore, the initial value P _{(N1) 0} of the node hydrocephalus P node N1, 30.0-4.0 = 26.0 [m], the initial value P _(N2) of the node hydrocephalus P at the node N2 and N4 ₀ and P (N4) ₀ is set to 26.0−4.0 = 22.0 [m]. At this time, if the initial values of the node heads of adjacent nodes become the same, the loss head in the pipe connecting the nodes may become zero, so this is prevented. Therefore, the average drop amount Δh of the water head in each pipe line is varied by a random number, and the initial values of the node heads of the nodes N1 to N4 are set as shown in, for example, Equation 6.

Next, as shown in FIG. 5, the process proceeds to step 5 (S005) to determine a Jacobian matrix J to be used for calculation in a later process. In the present embodiment, since there are four nodes in the pipe network PN, the Jacobian matrix J is a 4 × 4 matrix. Also, the value of j _ii that is a diagonal element of the Jacobian matrix J is the sum of the variational conductance g of the pipe connected to the node Ni, and the value of the non-diagonal element j _{ij is} the value of the node Ni and the node Nj. And the variable conductance value of the pipe line directly connected to each other is attached with a negative sign, and j _ij = 0 if there is no pipe line directly connected. Thereby, the Jacobian matrix J used at the time of the calculation of a subsequent process can be expressed as in Expression 7.

At this time, for example, the value of j ₃₃ which is a diagonal element of the Jacobian matrix J is (g _K3 + g _K4 ) because it is the sum of the variational conductances g of the pipes K3 and K4 connected to the node N3. In addition, the value of the off-diagonal element j ₂₃ is a pipe that directly connects the node N2 and the node N3, in this case, a variational conductance g _K3 of the pipe K3 is given a negative sign (−g _K3 ). Become. However, at this point, the variational conductance value of each pipeline is unknown.

  Therefore, in Step 7 (S007) and Step 8 (S008) to Step 10 (S010), variational conductances of the pipelines K1 to K5 are obtained. In the pipelines K1 to K5, there are a pipeline with water extraction from the pipeline and a pipeline without it, and the calculation method of variational conductance is different in each case. Therefore, as shown in FIG. 6 (S006), in the case of all the pipes to be subjected to pipe network analysis, that is, in the case of the present embodiment, whether or not water is taken out from the pipes for the pipes K1 to K5. Find out about.

  For pipelines (pipelines K3, K4) where water is taken out from the pipelines, the process of step 8 (S008) to step 10 (S010) is performed to calculate the variational conductance of the pipelines K3, K4. For the pipes (pipe lines K1, K2, K5) from which no water is taken out from the pipe lines, the process of step 7 (S007) is performed to calculate the variational conductances of the pipe lines K1, K2, K5.

Here, first, a method for calculating the variation conductances g _K3 and g _K4 for the pipes K3 and K4 where water is taken out from the pipe will be described. Hereinafter, a case where the process is performed on the pipe line K3 will be described.

Since the water is taken out from the pipe K3 where the water is taken out from the pipe, the amount of water flowing from the node N2 into the pipe K3 is different from the amount of water flowing out from the pipe K3 to the node N3. That is, the starting point side pipe flow rate and the end point side pipe flow rate of the pipe line K3 are different. Therefore, in step 8, the starting point side pipe flow rate of the pipe line K3 is set to q _{s, K3} , and the end point side flow rate of the pipe line K3 is set to q _{e, K3} (in the case of the pipe line K4, the starting point side pipe flow rate is set to q _{s. , K4} , and the end side flow rate as qe _{, K4} ), the lower limit value and the upper limit value of the start point side pipe flow rate of the pipe line K3 necessary for calculating the variational conductance are set.

For the pipe line K3, as shown in FIG. 10, the pipe line K3 of the pipe length L (K3) is divided into n equal parts, and CL ₁ , CL ₂ ,. Treated as having _n-1 and CL _n water withdrawals. Table 1 shows the characters used in the following calculations. In the following, the demand amount is the amount that a person or the like requests water, and the supply amount is the amount of water that can be supplied from a pipeline.

  Note that the amount of water supplied in the i-th section is expressed based on the demand water volume in the i-th section and the water extraction possibility (ease of water extraction) according to the size of the effective head in the i-th section. (See FIG. 13).

Here, when r ^* = 10.666CH− ^1.85 · D− ^4.87 , in FIG. 10, the head P _{1_mid at} the midpoint of the first section is the initial value P (N2) of the node head of the node N2. It is a value obtained by subtracting the loss head when water flows from ₀ to the middle point of the first section, and the loss head when water flows to the middle point of the first section can be calculated from Equation 1. The water head P _{1_mid} at the midpoint of the first section can be expressed as in _Expression 8.

The effective hydrocephalus _{e 1_Mid} at the midpoint of the first section, from hydrocephalus _{P 1_Mid,} a value obtained by subtracting the ground elevation gL ₁ at its midpoint, the ground elevation gL ₁ intermediate point, ground elevation at the start Since it suffices to _add the half height of the ground height increase gL _add to gL _s , the effective water head e _{1_mid at} the midpoint of the first section can be expressed as in _Equation 9.

Further, the flow rate q _{1_mid at} the midpoint of the first section can be expressed as in Equation 10 because the amount of water supplied in the first section may be reduced from the starting point side pipe flow rate q _s .

Similarly, the water head P _{k_mid at} the middle point of the k-th section (2 ≦ k ≦ n) is the middle of the (k−1) _-th section from the value of the water head P _{k-1_mid} of the (k−1) _-th section. This is a value obtained by subtracting the loss head when only one section flows from the point to the middle point of the k-th section, and can be expressed as Equation 11.

Further, the effective head e _{k_mid at} the midpoint of the k-th section is a value _obtained by subtracting the ground height gL _{k_mid} at this midpoint from the nodal head _{Pk_mid at} the midpoint of the k-th section, and is expressed as in _Expression 12. be able to.

Furthermore, the flow rate q _{k_mid at} the middle point of the _k-th section is obtained by subtracting the amount of water supplied in the k-th section from the flow rate q _{k-1_mid at} the middle point of the (k−1) _-th section. Can be expressed as

Assuming that the node head at the end point of the pipe K3 is P _{pre, e} , the node head head P _{pre, e} at this end point is the loss when water flows for only a half section from the head P _{n_mid at} the midpoint of the nth section. Since it is a value obtained by subtracting the water head, it can be expressed as in Expression 14.

Then, the value P _{pre, e} of the head at the end point in the pipe K3 is the value of the node head P (N3) ₀ = P _e of the node N3 that is the end point of the pipe K3 set in Step 4 (a step described later) 22, if the value of the nodal head is updated, the convergence calculation is performed so as to be within a predetermined error range with respect to the updated value of the nodal head), and the starting side pipe flow rate of the pipe K3 The values of q _{s and K3} are calculated.

As a method for obtaining such a q _{s, K3} is dichotomy, pincer attack method, because there are such secant, to calculate the value of the start point side conduit flow q _{s, K3} due dichotomy is the starting point side conduit flow _{q s, K3} lower limit _{q s_min,} it is necessary to set the upper limit value _{q s_max.} In the following description, for example, the case of using the bisection method will be described.

When setting the lower limit q _{s_min} of the starting point side pipe flow rate q _{s, K3} , it is assumed that the amount of water taken out from the pipe 3 is 0 [m ³ / s], q _{s, K3} = yh / | h When ^1−β is set to a constant flow rate, the nodal head of the end point at this time is P (N3) ₀ = P _e (the initial value set in Step 4), but q _{s_min} = q _{s, where K s If} there is an amount of water taken out from _K3, since CLi ≧ 0, the flow rate reaching the node N3 on the end point side is smaller than _{qs, K3} . According to Equation 1, the loss head h is proportional to the 1.85th power of the flow rate of the pipeline, so that the start side pipeline flow rate is q _{s, K3} = yh / | h | ^1-β (where h = P (N2) −P (N3)) and the head loss h ^* when the amount of extracted water is 0 or more, h ≧ h ^* . Therefore, from Equation 2, the starting side pipe flow rate a _{q s, K3 = yh / |} h | 1-β and to the node water head _{P e} of the end point of the time was, nodal water head _{P pre} of the end point of the time taken out of water is greater than or equal to _0, and the _{e, P pre, e} ≧ the P _e.

Next, the upper limit value q _{s_max} of the starting point side pipe flow rate q _{s, K3} is set. Here, for example, assuming that the amount of water taken out from the pipeline is 0 [m ³ / s], the flow rate is q _{s, K3} = yh / | h | ^1−β, and the upper limit value of the start side pipeline flow rate Q _{s_max} = q _{s, K3} + (CL / 2), and as shown in FIG. 11, the line K3 is 2 between the section A and the section B at the intermediate point C (= L (K3) / 2). Consider a case where the water is divided into sections and the supply water amount and the demand water amount are equal.

In such a case, the flow rate in the A section is q _{s, K3} + (CL / 2), and if the supply water amount is CL, the flow rate in the B section is q _{s, K3-} (CL / 2). Here, FIG. 12 shows the function expressed by the equation (1).

As shown in FIG. 12, _{assuming that} the loss head when the flow rate is q _{s, K3} + (CL / 2) is h _A , and the loss head when the flow rate is q _{s, K3} − (CL / 2) is h _B. The loss head h ^* in the pipe K3 can be expressed as the sum of the loss head in the A section and the loss head in the B section, and the A section is half of the pipe length L (K3). The head loss in the A section is h _A / 2, and the head loss in the B section is h _B / 2, so the head loss h ^* in the pipe K3 is h ^* = (h _A + h _B ) / 2. It becomes.

In FIG. 12, h ^* is the midpoint of the straight line ab, and the function h = r · q · | q | ^0.85 is a downward convex function. Since it is on the lower side (negative region), the above-described loss head h ^* and the loss head h when the flow rate in the entire section is qs _{and K3} are h ^* > h.

Therefore, from Equation 2, when the starting point side pipe flow rate is qs _{, K3} = yh / | h | ^1-β + (CL / 2) (where h = P (N2) −P (N3)), P _{pre, e} ≦ P _e .
From the above, so that the starting point side pipe flow _{q s, K3} is sandwiched between the lower limit value _{q s_min} and the upper limit value _{q s_max.} Therefore, to set the lower limit of the start point-side flow rate _{q s, K3 q s_min = q} s, K3, the upper limit value _q s_max _{= q} s, K3 + a (CL / 2).

Start side conduit flow limit value _{q s_min,} and setting the upper limit value _{q s_max,} then, in step 9 (S009), from the number 8 to number 14, when the start point side conduit flow rate is the lower limit value _{q s_min} endpoint node hydrocephalus _{P e_min} the calculated end point side conduit channel _{q e_min,} and end point at the start point side conduit flow rate is an upper limit value _{q s_max} node hydrocephalus _{P E_max,} the end point side conduit channel _{q E_max} .

Here, by using a value such as the nodes N2, N3 initial value P of the node water head _{(N2) 0, P (N3} ) 0 calculated in the above, the case of performing the calculation of step 8 and step 9 . For the water source S1, the nodes N1 to N4, and the pipelines K1 to K5, initial conditions as shown in Tables 2 and 3 are given.

The calculation performed in step 8 is as follows. In the case of the pipe K3, the start point is the node N2 and the end point is N3, and the initial values set in step 4 are P (N2) ₀ = 20.01818 and P (N3) ₀ = 16.41315. Therefore, as described above, the lower limit value of the starting point side pipe flow rate q _s can be calculated from q _{s_min} = q _{s and K3} = yh / | h | ^1−β. lower limit _{q s_min} side pipe flow _{q s is} a q s_min = 0.08162373.

The upper limit value of the originating side conduit flow _{q s, K3} is _{q s_max = q s, K3 +} (CL / 2) = yh / | h | 1-β + (CL / 2) can be calculated from, here, from Table 3, the pipe length of the conduit K3 L (K3) is 100 [m], total CL = 0.03 eject water from line K3 (supply water amount) ^[m 3 / s] _Yes , if the number of sections for dividing the pipe K3 is n = 20 _, the upper limit q _{s_max} of the starting-point-side pipe flow _{qs , K3} is q _{s_max} = 0.096662373.

Here, from Table 3, the flow velocity coefficient CH = 110 and the pipe inner diameter D = 0.2 [m]. From the above, the length of one section in the pipe line K3 is 5 [m] (100 [m] / 20. = 5 [m]), the calculation performed in step 9 is as follows. That is, the head of the midpoint of the first section is P _{1_mid} = 20.692179929 [m] from _Equation 8. In addition, the ground height gL ₁ of the first section is gL ₁ = 15.1428 [m] by interpolation between the ground height gL _{s at the} start point and the ground height gL _{e at the} end point using the conditions in Table 2. Become. Furthermore, the effective head e _{1_mid at} the midpoint of the first section is e _{1_mid} = 5.549337929 [m] from _Equation 9.

At this time, the pressure dependency of the amount of extracted water in the first section is taken into consideration, that is, the amount of supplied water corresponding to the value of the effective head e _{1_mid at} the midpoint in the first section is _obtained . FIG. 13 shows a characteristic curve of the effective water head and the takeout rate. In this case, the effective hydrocephalus _{e 1_Mid} at the midpoint of the first section is because about 5.5 [m], the removable rate at this time, and FIG. 13 than 0.057.

Therefore, the amount of water (supply water amount) CL ₁ that can be taken out in the first section is obtained as shown in Equation 15.

Next, hydrocephalus _{P 1_Mid} at the midpoint of the first section, with a lower limit _{q s_min} effective hydrocephalus _{e 1_Mid,} and the start point side conduit flow _{q s, K3,} and by using the number 11 to number 14, and the In the same procedure, the head P _{2_mid} , the ground height gL ₂ , and the effective head e _{2_mid at} the midpoint of the second section are obtained, and the third section, the fourth section,... calculated by performing, starting side conduit flow _{q s, K3} end point side conduit flow _{q e_min} corresponding to the lower limit value _{q s_min} of calculating the nodal hydrocephalus _{P e_min} endpoint.

Furthermore, the same procedure, for the upper limit value _{q s_max} the starting side conduit flow _{q s, K3,} the upper limit value _{q s_max} the corresponding end point side conduit flow _{q E_max,} calculates the nodal hydrocephalus _{P E_max} endpoint. Equation 16 shows the calculated result.

Next, as shown in FIG. 5, as step 10 (S010), the variational conductance gK3 of the pipe line _K3 is calculated. Usually, if there is no water removal from the pipeline, the variation conductance of the pipeline can be calculated using Equation 4, but the pipeline K3 takes into account the removal of water from the pipeline. Since it is a pipeline, the variational conductance of the pipeline cannot be calculated using Equation 4.

Therefore, for example, the value of the variational conductance g _K3 of the pipeline K3 is calculated by _Expression 17 representing the relationship between the average value of the starting-side pipe flow rate and the ending-point-side pipe flow rate and the nodal head of the end point.

From Equations 16 and 17, g _K3 = 0.009355086.
Next, as step 11 (S011), the initial values qs _{and K3 (0)} of the starting point side pipe flow rate are expressed by the following _{equation (} 18 ₎

In step 12 (S012) to step 17 (S017), as described above, the iterative calculation by the bisection method is performed.
Specifically, as step 12, start point side pipe flow rate qs _{, K3 (0)} determined in step 11 ₍ if the value of the start point side pipe flow rate is updated in step 17 described later, after the update ) And the initial value P (N2) ₀ of the node head of the node N2 set in step 4 (or the updated value if the node head is updated in step 22 described later), From Equations 8 to 14, the end point side pipe flow rates q _{e and K3 (0)} and the end point heads _{Pe and N3} when the start point side pipe flow rate is q _{s and K3 (0)} are calculated.

Then, as Step 13 (S013), the end point heads _{Pe and N3} calculated in Step 12 and the node head set in Step 4, in this case, the initial point head of the node N3 serving as the end point of the pipe line K3 The difference from the value P (N3) ₀ (or the updated value if the value of the nodal head is updated in step 22 (S022) described later) is within an error range, for example, 1.0 × 10 ⁻⁶ . Calculate whether it is within range. At this time, if the difference does not fall within the error range, the process proceeds to step 14 (S014).

Step 14 includes the values of the end point heads _{Pe and N3} calculated in Step 12 and the initial value P (N3) ₀ of the nodal point head of the node N3 set in Step 4 (the value of the nodal point head in Step 22 described later). If you update compares the magnitude of its value after update), when the calculated value of the water head P _{e, N3} endpoint is larger than the initial value P (N3) ₀ of the node hydrocephalus set is Then, the process proceeds to step 15 (S015). In step 15, as q _{s_min} = q _{s, K3 (0)} , that is, the lower limit value q _{s_min} of the starting point side pipe flow rate is the initial value q _s of the starting point side pipe flow rate. _, The value of q _{s_min} is corrected so as to be _{K3 (0),} and the process proceeds to step 17 (S017).

The value of the water head _{P e, N3} of the calculated end point is smaller than the initial value P _{(N3) 0} of the node hydrocephalus set, the process proceeds to step 16 (S016), in step _{16, q s_max} = q _s, as _{K3 (0),} i.e. the value of the upper limit value _{q s_max} the starting side conduit flow, so that the initial value _{q s} of the start point side conduit _{flow, K3 (0),} to modify the value of _{q s_max} Then, the process proceeds to Step 17.

In step 17, the value of _{q s_min} was modified in step 15 or, _using the values of _{q s_max} was modified in step 16, as _{q s, K3 (1) =} 0.5 · (q s_min + q s_max), Update the value of the starting pipe flow rate. Note that q _{s and Ki (k)} indicate that the value of the starting point side pipe flow rate of the pipe Ki has been updated K times.

Then, the process returns to step 12, and the calculations of step 12 to step 17 are repeated using the values of the starting point side pipe flow rate q _{s and K3 (1)} updated in step 17, and the calculation in step 12 is performed in step 13. The value of the end point head _{Pe, N3} and the node head set in step 4, in this case, the initial value P (N3) ₀ of the node head of the node N3 that is the end point of the pipe K3 (the node head in step 22 described later) If the difference between the updated value and the updated value is within the error range, the process proceeds to step 18 (S018).

In step 18, the values of the start point side pipe flow rate qs _{, K3 (k)} and the end point side pipe flow rate qe _{, K3 (k)} when the difference falls within the error range are determined as the pipe K3. _Are determined to be the values of the starting point side pipe flow rate qs _{, K3} and the end point side pipe flow rate qe _{, K3} . At this time, each of the values and the ending point side conduit flow value of the calculated start point side conduit with a flow rate value of the number 16 of _the, q _s, K3 _{= 0.08189067,} and q e, K3 = 0.08154781 Become. Then, the process proceeds to Step 19 (S019). Note that the same calculation as in steps 8 to 18 is performed for the pipe K4. In addition, in the above description, the calculation using the bisection method has been described in Step 12 to Step 17, but not limited to this, the scissors method, the secant method, or the like can be used.

Assuming that the number of sections for dividing the pipeline K4 is n = 20, the pipeline length K (100) is 100 [m] from Table 3 and the amount of water taken out from the pipeline K4 is similar to the pipeline K3. The total is CL = 0.03 [m ³ / s], flow velocity coefficient CH = 110, pipe inner diameter D = 0.2 [m], and the length of one section in the pipe K4 is 5 [m] (100 [ m] / 20 = 5 [m]), the variational conductance is g _K4 , the start side pipe flow rates q _{s and K 4 in} the pipe _{K 4} , and the end side pipe flow rates q _{e and K 4} are expressed by _Equation 19. Value.

  Moreover, in the above, although the case where the process of step 8-step 18 was performed in step 6 with respect to the pipeline (pipeline K3, K4) with extraction of the water from a pipeline was demonstrated in step 6 For the pipelines (ducts K1, K2, K5) where no water is taken out from the pipeline, the process proceeds to step 7.

In step 7, the pipes K1, K2, and K5 are pipes from which water is not taken out from the pipe, and the flow rate in the pipe is constant. , K5 variation conductances g _K1 , g _K2 , and g _K5 are calculated. Here, for example, from Tables 2 and 3, the flow velocity coefficient of each of the pipes K1, K2, and K5 is CH = 110, the pipe length is L = 100 [m], and the pipe inner diameter is D = 0.2 [ m], LWL of the water source S1 = 30.0 [m], and the initial values of the nodes N1, N2, and N5 set in Step 4 are P (N1) ₀ = 25.40, P (N2) ₀ = 20 80118, P (N4) ₀ = 20.84996, the variational conductances g _K1 , g _K2 , g _K5 , lines K 1, K 2, K 5 of the lines K 1, K 2, K 5 are obtained from Equations 1 to 3. The flow rates q _K1 , q _K2 , and q _K5 of FIG.

Thus, when the variational conductances g _K1 , g _K2 , g _K5 , and the flow rates q _K1 , q _K2 , q _K5 of the conduits K1, K2, and _K5 are calculated, step 19 (S019). Proceed to

In step 19, the Jacobian matrix J determined as shown in Equation 7 in Step 5 is added to the variation conductance g _K3 of the conduit K3 calculated by _Equation 17, the variation conductance g _{K4 of} the conduit K4 shown in Equation 19, Substituting the values of the variational conductances g _K1 , g _K2 , and g _K5 of the pipelines K1, K2, and K5 shown in Expression 20, the Jacobian matrix J is calculated as shown in Expression 21, and the process proceeds to Step 20 (S020). .

In step 20, first, a continuous flow rate system is established at each of the nodes N1 to N4. For example, as shown in FIG. 14, the flow rate continuous expression is such that at a certain node N, the amount of water flowing out from the node N to the pipe line is q ₃ , q ₄ , and the amount of water flowing into the node N is −q ₁ , − q ₂ , and the amount of water taken out from the node is c (as described above, since the procedure of the pipe network analysis in the present embodiment is performed based on the known nodal head method, c = 0 [m ³ / s]), the sum of these values is 0 as shown in Equation 22.

Therefore, the continuous flow rates f _N1 (Q) to f _N4 (Q) for the nodes _{N1 to N4} are as shown in Equation 23. At this time, the water head of the water source S1 is LWL = A [m], the water head of the reference node N5 is 0 [m], and the values of these water heads are known, so here the water source S1 and the reference node N5 The continuous flow type is not considered.

In this embodiment, since c = 0, the flow rates q _K1 , q _K2 , q _{K5 of} the pipelines K1, K2, and K5 calculated in step 7 and the pipeline K3 calculated in step 18 are calculated. Substitute the values of the start point side pipe flow rates q _{s and K3} , the end point side pipe flow rates q _{e and K3} , the start point side pipe flow rates q _{s and K4} , and the end point side pipe flow rates q _{e and K4} into Equation 23. And the number 24 is obtained.

Here, it is determined whether or not the absolute values of f _N1 (Q) to f _N4 (Q) are smaller than a threshold, for example, 1.0 × 10 ⁻⁶ . As the values shown in Expression _24, since the absolute value of each of _{f N1 (Q) ~f N4 (} Q) is not less than the threshold value 1.0 × ^{10 -6,} not satisfied flow continuous, step 21 ( The process proceeds to S021).

  In order to obtain the value of the pipe flow rate such that the above equation 23 satisfies the continuous flow rate equation, iterative calculation is performed by the Newton-Raphson method using the Jacobian matrix J calculated in step 19. Therefore, in step 21, first, simultaneous linear equations used for the above iterative calculation are established.

In Equation 23, q _K1 , q _K2 , and q _K5 can be expressed using the node head P from Equation 3 and Equation 2. Further, q _{s, K 3} , q _{s, K 4} , q _{e, K 3} , q _{e, and K} 4 in Expression 23 are the initial values P (N 1) _{0 to} P (N 4) of the node heads of the nodes N 1 to N 4 set in Step 4. ) Since it is obtained by performing the processing of step 8 to step 18 using a value of ₀ , it can be said that it is a function of the nodal head P. Therefore, f _N1 (Q) to f _N4 (Q) are set as shown in Equation 25. be able to.

  Therefore, simultaneous linear equations used for the iterative calculation by the Newton-Raphson method can be expressed as shown in Equation 26.

Here, ΔP = (ΔP _N1 , ΔP _N2 , ΔP _N3 , ΔP _N4 ) ^T (T is a transposed matrix) is a correction value for correcting the value of P, and J ^k , ΔP ^k , F (P ^k ), Each of P ^k is a value used in the k-th iteration of the Newton-Raphson method. Further, P ^{k + 1} can be obtained by the equation shown in Equation 27.

  From Equation 7 and Equation 25, Equation 26 can be expressed as Equation 28.

_However, f ^N1 (P ₀₎ is _~f N4 respectively ^{(P 0),} the initial value of the node hydrocephalus at node N1-N4. In addition, from Equation 21 and Equation 24, Equation 29 is derived,

Multiply the inverse matrix of the Jacobian matrix J from the left side of Equation 29 to calculate ΔP.
When the simultaneous linear equations are solved as described above, the process proceeds to step 22 next. In step 22, the value of the nodal head used for the next iterative calculation is updated by adding the calculated correction value to the value of the nodal head used for the current iterative calculation from Equation 27. Then, the process returns to step 6, the processes of step 6 to step 19 are performed again, and the processes of step 21, step 22, and step 6 to step 19 are repeated until the flow rate continuity formula in step 20 is satisfied.

When the flow rate continuous type is satisfied in step 20, the process proceeds to step 23, where the flow rates q _K1 , q _K2 , q _K5 , and the starting point side pipe line in the pipe K3 when the flow rate continuous type is satisfied. Flow rate q _{s, K3} , end point side pipe flow rate q _{e, K3} , start point side pipe flow rate q _{s, K4} , end point side pipe flow rate q _{e, K4} , and when continuous flow rate is satisfied Record the value of the nodal head used at the time of calculation, and finish the work.

Then, using the results of the above-described pipe network analysis, an important pipe line that has a great influence on the entire pipe network is formulated, and the result is used for maintenance management such as a pipe renewal plan.
As described above, according to the present invention, by setting the amount of water to be taken out from the pipeline according to the amount of water to be taken out from the water supply pipe, the amount of water to be taken out from the node as in the node taking out model, or the pipe taking out model Compared to the case where a constant amount is taken out from the pipe along the length of the water as in the case where the water is taken out, the state of taking out the water becomes closer to reality, and a more realistic pipe network analysis can be performed. . Thereby, the accuracy of pipe network analysis can be improved.

  In addition, since the value of the starting point side pipe flow rate is calculated using a bisection method, the value of the starting point side pipe flow rate can be calculated with high accuracy, and the end point side pipe flow rate corresponding to the starting point side pipe flow rate. Can also be calculated with high accuracy.

In addition, by performing convergence calculation using the Newton-Raphson method, it is possible to accurately calculate the value of the starting point side pipe flow rate, the value of the end point side pipe flow rate, and the value of the nodal head.
Furthermore, by making the amount of water taken out dependent on the size of the effective head, for example, it can be expressed that the amount of water taken out becomes worse at peak times of demand where the pressure head falls or in areas on high ground. The pipe network analysis can be performed with higher accuracy than the conventional pipe network analysis which is a fixed case.

  Note that the above pipe network analysis method can be calculated in combination with a node extraction model.

(A) is a figure explaining the discrete extraction model in the pipe network analysis method of this invention, (b) is a figure which shows the flow volume in a pipe line in the case shown to Fig.1 (a). It is a figure which shows the initial data provided to the water source and node in the pipe network shown to Fig.1 (a). It is a figure which shows the initial data provided to the pipe line in the pipe network shown to Fig.1 (a). It is a figure which shows the relationship between LWL, dynamic water level, loss head, ground height, and effective head. It is a figure which shows the pipe network analysis method of this invention. It is a figure which shows the state which formed the reference | standard node connection branch. It is a figure which shows the state which removed the reference | standard node connection branch which can be removed open. It is a figure which shows the data of the reference | standard node connection branch b5 in FIG. It is a figure which shows the search result of the breadth priority tree with respect to the pipe network shown in FIG. It is a figure which shows the method of the calculation performed in the discrete extraction model shown in FIG. FIG. 2 is a diagram showing a flow rate in a pipeline when determining an upper limit value of a start-side pipeline flow rate in the discrete extraction model shown in FIG. 1. It is a figure which compares the magnitude | size of the loss head in the case shown in FIG. 11 with the magnitude | size of the loss head in the case where pipe flow volume is constant. It is a figure which shows the characteristic curve showing the relationship between an effective water head (pressure) and the extraction possibility rate (flow rate). It is a figure which shows the flow volume continuous type in a node. It is a figure which shows the pipe network used as the object of pipe network analysis. It is a figure which shows that water is taken out from the pipe line by the water supply pipe in the actual pipe network. (A) is a figure which shows the node extraction model which takes out fixed amount of water from each node, (b) is a figure which shows the flow volume in the pipe line in a node extraction model. (A) is a figure which shows the pipe | tube extraction model which takes out a fixed amount of water uniformly from each pipe | tube along the length direction, (b) is a figure which shows the flow volume in the pipe line in a pipe | tube extraction model. is there.

Explanation of symbols

S1 Water source N1 to N4 Nodes K1 to K5 Pipe line PN Pipe network q _{s, Ki} start side pipe flow rate q _{e, Ki} end side pipe flow rate

Claims (4)

With respect to a pipe network composed of a network relationship between a water source, a node that is an intersection of the pipes, and a pipe to which the water source or the node is connected to one end and the other end, In the pipe network analysis method for calculating the water head which is the flow rate in each pipe line constituting the pipe network and the water pressure at each node after subtracting the water quantity taken out from the pipe network, the quantity of water taken out Is subtracted from the amount of water in the pipe network, the amount of water taken out is taken out from at least one place in the pipeline where the water is demanded so that the flow rate in the pipeline where the water is demanded changes stepwise. And a starting point side pipe flow rate which is an upstream side flow rate and a downstream side flow rate which is a downstream side flow rate are calculated as a flow rate in the pipe. Analysis method. Set the initial value of the head of each node in the pipe network, and based on the initial value of the head, set the lower limit value and the upper limit value of the start side pipe flow rate in the pipe where water is demanded, the start side An initial value of the starting point side pipe flow rate is set based on the lower limit value and the upper limit value of the pipe flow rate, the head of the node calculated based on the initial value of the starting point side pipe flow rate, and the set nodal point The initial value of the starting-point-side pipe flow rate is updated based on the initial value of the head, and the update is performed based on the head of the node calculated based on the updated initial value and the initial value of the head of the set node The convergence calculation for updating the initial value is performed, the convergence value is calculated as the starting point side pipe flow rate, and the end point side pipe flow rate corresponding to the calculated starting point side pipe flow rate is calculated. The pipe network analysis method according to 1. Based on the start point side pipe flow rate and the end point side pipe flow rate in the pipe where water is demanded, the initial value of the head of each set node is updated, and based on the updated head value of each node, Calculate the starting point side pipe flow rate and the end point side pipe flow rate in the pipe with the demand for water, and based on the calculated starting point side pipe flow rate and end point side pipe flow rate, the updated head value of each node The convergence calculation for further updating is performed, and the convergence value of the start point side pipe flow rate and the end point side pipe flow rate is set to the value of the start point side pipe flow rate and the end point side pipe flow rate in the pipe having the water demand, 3. The pipe network analysis method according to claim 1, wherein a convergence value of the water head of the node is calculated as a value of the water head of the node. The amount of water taken from at least one location in a pipeline where water is in demand is the size of the pressure head, which is a value obtained by subtracting the ground height of the location where the water is taken out from the location where the water is taken out in the pipeline. The pipe network analysis method according to any one of claims 1 to 3, wherein the pipe network analysis method changes according to the method.

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