JP4308641B2 - Pipeline evaluation method - Google Patents

Description

  The present invention relates to a pipeline evaluation method.

  In recent years, in the water supply business, it has become extremely important to perform maintenance management such as grasping the state of an existing pipe network and making an update plan for the pipe network. For example, in consulting services related to pipe networks, we evaluate which important pipes have a major impact on the entire pipe network due to the occurrence of water leaks, etc., and provide the results to customers. ing.

  The above-mentioned important pipelines can be evaluated based on the result of pipe network calculation performed on the pipe network. Pipe network calculation means each condition under given conditions such as the head of the water source, the arrangement of the pipe, the diameter of the pipe, the demand of water taken from the node as the demand point of water (hereinafter referred to as the quantity of water taken out). It means calculating the flow rate of the pipeline and the head of each node.

  Here, a method for evaluating a pipe line based on the result of pipe network calculation will be described with reference to FIGS. This evaluation method includes a preparatory process for performing an evaluation, a calculation process for calculating an evaluation value to be used for evaluation using the result of the preparatory process, and an evaluation for setting a pipeline to be evaluated after the calculation process. It has a setting process of an object pipe line, and an evaluation process of evaluating each pipe line based on the calculated evaluation value. For example, when performing the pipe network calculation for the pipe network constituted by the network relationship of the water source S1, the pipe lines K1 to K8 and the nodes N1 to N6 as shown in FIG. 3, FIG. 4 and FIG. Various initial data are given as shown.

That is, for the water source S1, the LWL (Low Water Level) [m] as the head of the water source, the ground height [m] that is the head of the installation height of the water source S1, and the nodes N1 to N6, the amount of water [m ³ / S] and the ground height [m], which is the head of the node, and the pipe lines K1 to K8, the start point, the end point, the flow velocity coefficient, the pipe length [m], and the pipe inner diameter [mm] are given.

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

数１において、ｈは損失水頭〔ｍ〕、ｑは流量〔ｍ^３／ｓ〕、Ｃ_０は流速係数、Ｄは管内径〔ｍ〕、Ｌは管路長さ〔ｍ〕であり、ｒを管路の抵抗係数とする（以下、管路抵抗と記す）。この管路抵抗ｒは、流速係数Ｃ_０、管内径Ｄおよび管路長さＬにより決定する定数である。また、損失水頭ｈ〔ｍ〕を流量ｑ〔ｍ^３／ｓ〕で偏微分したときの値をｒ´とすると、ｒ´は数２で表される。

In Equation 1, h is a head loss [m], q is a flow rate [m ³ / s], C ₀ is a flow velocity coefficient, D is a pipe inner diameter [m], L is a pipe length [m], and r is The resistance coefficient of the pipe (hereinafter referred to as pipe resistance). The pipe resistance r is a constant determined by the flow velocity coefficient C ₀ , the pipe inner diameter D, and the pipe length L. Further, r ′ is expressed by Equation 2 when a value obtained by partial differentiation of the loss head h [m] with the flow rate q [m ³ / s] is r ′.

なお、以下において、このｒ´を変分抵抗と記す。

In the following, this r ′ is referred to as variation resistance.

  Under the conditions as described above, in order to perform the pipe network calculation by the mesh flow method for the pipe network shown in FIG. 3, first, as shown in FIG. The initial data of the pipe network is read as shown in FIGS. At this time, the read data is, for example, numerical data as shown in FIGS.

  Next, as step 2 (S002), based on the data read in step 1, as shown in FIG. 7, the water source S1, the nodes N1 to N6, and the pipelines K1 to K8 are connected, and the network relationship in the pipeline network Build up.

  At this time, the node N7 connected to the water source S1 through the pipe E1 is used to apply the calculation theory of the electric network to the pipe network calculation in which the amount c of water taken out from the nodes N1 to N6 is constant. The reference node is virtually provided (water head = 0), and the reference node N7 and the pipe line E1 that are virtually provided can be created by a known method. For this reason, detailed description about creation of the reference node N7 and the pipe E1 is avoided here. In addition, the arrow in a figure has shown the direction of the pipe lines K1-K8 and the pipe line E1. At this time, the direction of the pipelines K1 to K8 may be arbitrary, but the direction of the pipeline E1 is set so as to be directed to the reference node N7. Moreover, the data about the pipe line E1 are shown in FIG. As shown in FIG. 8, the starting point of the pipe E1 is the water source S1, the end point is the reference node N7, and the head of this reference node N7 is set to 0 [m], so the head difference between the start point and the end point is A [m].

  Next, as shown in FIG. 6, as step 3 (S003), a breadth-first 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 this breadth priority tree search can also be performed by a known method, a detailed description of the method is avoided here. The result of the breadth-first tree search performed in step 3 is shown in FIG. As shown in FIG. 9, a pipe line with a breadth-priority tree is represented by a solid line as a tree branch, and a pipe line without a breadth-priority tree is represented by a broken line as a complementary tree branch.

  Next, in step 4 (S004), it is assumed that water does not flow through the pipelines K4 and K5 that have been complemented in step 3, and the amount of water taken out from the nodes N1 to N6 is c (= constant). Based on this, the fixed flow rate a (= constant) of the pipe lines K1 to K3, K6 to K8, and E1, which are tree branches, is set. At this time, for example, the fixed flow rate a (K1) of the pipe line K1 is represented by the sum of the amounts c of water taken out from all nodes on the downstream side of the pipe line K1. In addition, there is no amount of water taken out from the reference node N7, and conversely, the sum of the taken-out water amounts c of all the nodes N is supplied from the water source S1, so that the fixed flow rate a (E1) of the pipeline E1 is And a negative sign. Accordingly, the fixed flow rates a (K1) to a (K8) and a (E1) of the pipelines K1 to K8 and E1 are as shown in Equation 3. The fixed flow rate a is a set value not related to the pipe resistance r of each pipe line. Further, in the following, when it is not necessary to specify for which explanation the fixed flow rate of the pipe line is, it is referred to as a fixed flow rate a.

次に、ステップ５（Ｓ００５）として、管網内に形成されたメッシュどうしの隣接関係を検索する。ここでいうメッシュとは、平面グラフにおいて枝（木枝、補木枝）に囲まれ、かつ、内部に枝を含まない領域である。

Next, in step 5 (S005), the adjacent relationship between the meshes formed in the pipe network is searched. The mesh here is a region that is surrounded by branches (tree branches, complementary tree branches) in the plane graph and does not include branches inside.

  From the conditions shown in FIGS. 4 and 5 and the result of step 2, the meshes in the pipe network are mesh 1 and mesh 2 as shown in FIG. 10, and mesh 1 and mesh 2 are pipeline K8. Recognize that they are adjacent to each other.

Then, it is assumed that a flow is generated in the mesh 1 and the mesh 2 in an arbitrary direction (clockwise direction in the drawing), and a circulation flow rate circulating through the mesh at that time (hereinafter referred to as a mesh flow rate). Are m1 and m2 [m ³ / s] (= variable). The mesh flow rates m1 and m2 are also set values that are not related to the pipe resistance r of each pipe, as in the case of the fixed flow rate a. Further, in the following, when there is no need to specify which mesh flow rate is in the description, it is referred to as a mesh flow rate m.

  Since the flow rate q of each branch (pipe) is the sum of the fixed flow rate a and the mesh flow rate m, the flow rate q (K1) in each branch (pipe) is determined from the values of the fixed flow rate a and the mesh flow rate m. -Q (K8) and q (E1) are derived. If the direction of the fixed flow rate a and the direction of the mesh flow rate m are the same when deriving the flow rate q, the value of the mesh flow rate m is added to the value of the fixed flow rate a, and the direction of the fixed flow rate a and the direction of the mesh flow rate m are reversed. If it is oriented, the value of the mesh flow rate m is subtracted from the value of the fixed flow rate a. If it does in this way, flow volume q of each pipe line will be expressed like a number 4 using mesh flow volume m1 and m2. In addition, when it is not necessary to specify which branch (pipeline) the flow rate is in the description, the flow rate is indicated as q.

ここで、図１１に示すように、メッシュに任意の方向（図示においては右回り方向）に流れが発生していると仮定したとき、これと同じ向きの流れの管路の損失水頭ｈに正、逆向きの流れの管路の損失水頭ｈに負の符号を与えると、このメッシュを構成する各管路の損失水頭の総和Σｈは０となることから、図１０に示すように、メッシュ１およびメッシュ２に関しては数５が成り立つ。

Here, as shown in FIG. 11, when it is assumed that the flow is generated in an arbitrary direction (clockwise direction in the drawing) in the mesh, the flow head has a positive flow head h in the same direction. When a negative sign is given to the loss head h of the reverse flow pipe, the total sum Σh of the loss heads of the pipes constituting this mesh becomes 0. Therefore, as shown in FIG. For the mesh 2, Equation 5 holds.

このとき、数１より、数５にて表した式を数６のように表現する。

At this time, the formula expressed by Formula 5 is expressed as Formula 6 from Formula 1.

数３より、取り出し水量ｃおよび固定流量ａは定数であることから、数６で表される式は、メッシュ１のメッシュ流量ｍ１およびメッシュ２のメッシュ流量ｍ２を変数とする非線形連立方程式となる。

From Equation 3, since the amount of extracted water c and the fixed flow rate a are constants, the equation represented by Equation 6 is a nonlinear simultaneous equation with the mesh flow rate m1 of the mesh 1 and the mesh flow rate m2 of the mesh 2 as variables.

  The solution of the nonlinear simultaneous equations is obtained by iterative calculation by the Newton-Raphson method in a later calculation process. At this time, it is already known to use the calculation formula shown in Equation 7.

Ｊはヤコビ行列であり、ΔＭはＭ＝（ｍ１、ｍ２）^Ｔ（Ｔは転置行列を表す）の値を修正する修正ベクトルである。このとき、このヤコビ行列Ｊの成分〔ｊ_ｉｊ〕は、数８に示す式

J is a Jacobian matrix, and ΔM is a correction vector for correcting the value of M = (m1, m2) ^T (T represents a transposed matrix). At this time, the component [j _ij ] of the Jacobian matrix J is expressed by the equation shown in Equation 8.

により求められるが、特にメッシュ流量法を用いた管網計算時におけるヤコビ行列Ｊの成分〔ｊ_ｉｊ〕は、経験上、上記において検索したメッシュどうしの隣接関係、つまりステップ２で構築したネットワーク関係に基づいて求めることができる。したがって、ステップ６(Ｓ００６)においては、ステップ５の結果より、ヤコビ行列Ｊを、数９に示すように決定する。

In particular, the component [j _ij ] of the Jacobian matrix J at the time of calculation of the pipe network using the mesh flow rate method is based on experience that the adjacent relationship between the meshes searched above, that is, the network relationship constructed in step 2 is Can be based on. Accordingly, in step 6 (S006), from the result of step 5, the Jacobian matrix J is determined as shown in equation (9).

詳細には、管網内に形成されているメッシュの数が２個であるから、ヤコビ行列Ｊを２×２の行列と決定し、そして、このヤコビ行列Ｊの対角成分であるｊ_１１の値を、メッシュ１を構成している管路Ｋ２、Ｋ３、Ｋ４、Ｋ８の変分抵抗の和とし、かつ、ｊ_２２の値を、メッシュ２を構成している管路Ｋ５、Ｋ６、Ｋ７、Ｋ８の変分抵抗の和とする。

Specifically, since the number of meshes formed in the pipe network is two, the Jacobian matrix J is determined to be a 2 × 2 matrix, and the diagonal component j ₁₁ of the Jacobian matrix J is determined. values, line K2 constituting the mesh 1, K3, K4, Shun Kazu of variation resistance K8, _and the value of _{j 22,} conduit K5 constituting the mesh 2, K6, K7, The sum of the variation resistance of K8.

Further, j ₁₂ and j ₂₁ values which are non-diagonal components of the Jacobian matrix J are used as the values of variation resistances of the pipe K8 shared by the mesh 1 and the mesh 2 (the number of shared pipes is plural. In this case, the sum of those variational resistances is set to 0, or 0 if not shared, and since the flow direction of the mesh 1 and the flow direction of the mesh 2 are opposite, the sign is negative ( If it is the same direction, make it positive). The Jacobian matrix J is determined as described above, and the calculation formula shown in Equation 7 is determined. However, at this point, the variation resistance of each pipeline is unknown.

Here, in order to make it easier to calculate the inverse matrix J ⁻¹ of the Jacobian matrix J determined in step 6 in a later step, a commonly used LU decomposition or the like may be applied to the Jacobian matrix J.

  Although the preparatory process for evaluating the pipeline by the above steps 1 to 6 was performed, the above preparatory process is a process that can be performed based on the network relation of the water source, the pipe line, and the node. In particular, this is a process that can be performed regardless of the pipe resistance r of each pipe.

  Next, as shown in FIG. 6, as a calculation process, as step 7 (S007), arbitrary initial values for starting iterative calculation by the Newton-Raphson method are set in the mesh flow rates m1 and m2, and step 8 In (S008), the value of the flow rate q in each pipeline is calculated from Equation 4.

  Next, when the value of the flow rate q in each pipeline is obtained, the variation resistance r ′ in each pipeline is obtained from Equation 2 as step 9 (S009). In step 11 (S010), F (M) is calculated by substituting the flow rate q of each pipeline into Equation 6.

Next, in step 11 (S011), the absolute value of each value of f1 (m) and f2 (m) obtained in step 10 is, for example, larger than 1.0 × 10 ⁻⁶ set as a threshold value. Determine if it is small.

At this time, if the absolute value of each value of f1 (m) and f2 (m) is not smaller than the threshold value 10 ⁻⁶ , the value of the mesh flow rate m is larger than the value of the mesh flow rate m satisfying Equation 5. The process proceeds to step 12 (S012) assuming that there is a large deviation.

In Step 12, the value of the variation resistance r ′ of each pipeline calculated in Step 9 is substituted into the Jacobian matrix J determined in Step 6, and based on this, the inverse matrix J ⁻¹ of the Jacobian matrix J is calculated. , Equation 10 is derived.

そして、数１０に示す連立１次方程式を解いて、修正ベクトルΔＭの値を算出する。

Then, the simultaneous linear equation shown in Equation 10 is solved to calculate the value of the correction vector ΔM.

Next, in step 13 (S013), the values of the mesh flow rates m1 and m2 used for the current calculation (initial values in the case of the first calculation) are corrected by the calculated correction values Δm1 and Δm2, that is, k When M at the time of the second calculation is expressed as M ^k , M ^{k + 1} used in the next calculation is M ^{k + 1} = M ^k + ΔM ^k .

Then, returning to step 8, the mesh flow rate is set to M ^{k + 1} which is a corrected value, and the calculation of step 8 to step 11 is performed. Until f1 (m) and f2 (m) satisfy the threshold condition, Newton · Performs iterative calculations using the Rafson method.

In step 11, when each value of f1 (m) and f2 (m) becomes smaller than the threshold value 10 ⁻⁶ , the value of the mesh flow rate m used in the calculation at this time satisfies Equation 5. The iterative calculation is terminated assuming that the solution is sufficiently close, and the process proceeds to step 14 (S014).

  In step 14, the values of the mesh flow rates m1 and m2 used for the current calculation are set as solutions of the nonlinear simultaneous equations. Then, using the values of the mesh flow rates m1 and m2, the flow rate q in each pipeline is obtained, and the loss heads h (K1) to h (K8) in each pipeline are obtained from Equation 1. In addition, when it is not necessary to specify for which explanation it is a loss head of which pipe line, it is described as the loss head h.

  Then, as shown in FIG. 12, since the difference between the LWL and the dynamic water level is the loss head, and the difference between the dynamic water level and the ground height is the effective head as the pressure head, the LWL given in advance and the ground height From the calculated value of the loss head h, for example, the effective heads P (N1) to P (N6) [m] at the nodes N1 to N6, the LWL of the water source S1, and the ground height H (S1) of the water source S1 From the difference, the effective head P (S1) of the water source S1 is calculated as an evaluation value. Then, values such as the flow rate q, the loss head h, and the effective head P obtained by calculation are recorded. In addition, when it is not necessary to specify the effective head at which node, it is indicated as effective head P.

  Next, as an evaluation target pipeline setting process, in step 15 (S015), if the pipeline to be evaluated is erased, it is returned to the original position, but the first calculation is the evaluation target. Since the process is performed for the complete pipe network without deleting the pipe line, the process proceeds to step 16 (S016).

  In step 16, it is determined whether there is another pipeline to be evaluated. As described above, the first calculation of the pipe network is performed on the pipe network in a complete state without deleting the pipes, and each pipe line must be evaluated next. Proceeding to step 17 (S017) assuming that there is a pipeline.

In step 17, if the pipe to be evaluated is, for example, pipe K2, the pipe K2 is deleted from the pipe network as shown in FIG.
When the pipe K2 to be evaluated is deleted from the pipe network in the complete state, the connection relation of the water source S, the node N, and the pipe K after the pipe 2 is deleted, that is, the network relation of the pipe network is newly constructed. Therefore, the process returns to step 2 as shown in FIG.

  Then, for the pipe network in which the pipe K2 has been deleted, preparatory steps such as the construction of the network relation of the pipe network and the search for the width priority tree are performed, and the pipe network in which the pipe K2 has been deleted A calculation formula for calculating the evaluation value is derived.

  Then, the process proceeds to the calculation process, and the iterative calculation is performed by the Newton-Raphson method, and the flow rate q of each pipe, the loss head h, each node, and the effective head P of the water source S1 in the pipe network in which the pipe K2 is deleted. Ask for.

  Thereafter, if there are other pipelines to be evaluated, the same operation as the above-described pipeline K2 is performed through steps 16 and 17, and if there is no pipeline to be evaluated, step 18 (S018). )

  As an evaluation process, in step 18, in order to evaluate which of the important pipelines has a great influence on the entire pipe network, the flow rate q, the loss head h, and the effective head P that are the results recorded in step 14 above. Using these values, an index for evaluating each pipeline is calculated. Here, an average pressure change amount is obtained as an evaluation index.

  The average pressure change is an index representing the pressure fluctuation of the entire pipe network when the evaluation target pipe line is cut off. The larger the average pressure change amount, the larger the pressure fluctuation of the entire pipe network, that is, the entire pipe network. This means that the importance of the evaluation target pipeline is high. This average pressure change is the average value of the effective head of the node N or the water source S connected to one side of the pipe and the effective head of the node N or the water source S connected to the other side of the pipe. Is calculated as the value of the effective head of the pipe, the effective head of the specific pipe in the pipe network before setting the evaluation target pipe, and the specific pipe in the pipe network after setting the evaluation target pipe The value obtained by multiplying the difference from the effective head of the road by the capacity of the specific pipe is calculated for all the pipes to calculate the sum, and the sum is divided by the sum of the capacities of all the pipes. Can be calculated. Therefore, the value is calculated by substituting the effective head P as the evaluation value recorded in Step 14 and the necessary numerical value into Equation 11.

なお、Ｐ_ｎ、ｉは、完全な状態の管網における管路Ｋ_ｉの両端の節点または水源の有効水頭の平均値であり、Ｐ_ｄ、ｉは、評価対象管路を管網から取り除いた管網における管路Ｋ_ｉの両端の節点または水源の有効水頭の平均値であり、Ｖ_ｉは、管路Ｋ_ｉの管容量である。

Note that P _{n, i} is the average value of the effective heads of the nodes or water sources at both ends of the pipe K _i in the pipe network in a complete state, and P _{d, i} is the pipe to be evaluated removed from the pipe network It is the average value of the effective heads of the nodes or water sources at both ends of the pipe line K _i in the pipe network, and V _i is the pipe capacity of the pipe line K _i .

As described above, the average pressure change amount when each pipe line is set as the evaluation target pipe line is calculated, and it is evaluated that the calculated pipes are higher in importance in descending order of the calculated average pressure change amount. Japanese Patent Application Laid-Open No. 2004-228561 describes a technique that can perform pipe network analysis while efficiently using a computer memory that performs calculation on the pipe network.
JP-A-6-274576

  In the case of the pipeline evaluation method as shown in FIG. 6, first, the calculation is performed on the complete pipe network, and then the calculation is performed on the pipe network in which the evaluation target pipe is deleted. It must be made. At this time, for example, if the evaluation target pipe line K2 is deleted from the pipe network, the pipe network after the pipe line K2 is erased is used as a new pipe network, and a preparation process (excluding step 1), that is, step 2 to step It is necessary to perform the steps up to 6 again. Moreover, every time the evaluation target pipe is changed, this preparation process (except for step 1) must be performed. When the number of evaluation target pipes reaches several thousand, the same number of preparation processes must be performed. Therefore, it becomes a big hindrance for speeding up pipe evaluation.

  Therefore, the present invention solves such a problem, and in a pipe network composed of a network relationship of an arbitrary number of water sources, pipes, and water demand points, the evaluation of the pipes that affect the pipe network can be performed quickly. The purpose is to do.

  In order to solve the above-mentioned problem, the invention according to claim 1 is configured by a network relationship of an arbitrary number of water sources, a water demand point, and a pipe line to which the water source or the demand point is connected at both ends. In a pipe network, when evaluating a pipeline that affects the pipe network, a preparatory process for performing the evaluation, and a calculation for calculating an evaluation value used for the evaluation using the result of the preparatory process In the pipeline evaluation method for performing a process and a process for setting an evaluation target pipeline for setting the pipeline to be evaluated after the calculation step, the network relationship is established as the preparation step, and the pipe network The calculation formula for calculating the flow rate of each pipeline in the network is derived based on the constructed network relationship, and as the calculation step, the calculation formula is used to calculate the flow rate of each pipeline in the pipeline network, and the calculation is performed. The flow rate of each pipeline From the Hazen-Williams formula, which represents the head of loss when water flows from one end of the pipe to the other, the product of the flow rate at that time and the resistance coefficient of the pipe, And calculating an evaluation value to be used for the evaluation based on the calculated flow rate and loss head of each pipeline, and as a setting step for the evaluation target pipeline, From which the evaluation target pipe is determined, the resistance coefficient in the evaluation target pipe is set to be larger than the normal resistance coefficient of the pipe, and the evaluation target pipe is set to a pipe that is difficult to flow of water, Then, before returning to the calculation step, the flow rate of each pipe in the pipe network in the state where the resistance coefficient is increased, the loss head of each pipe, and the evaluation value are calculated, and the evaluation in the pipe network before changing the resistance coefficient Value and pipe network after increasing the resistance coefficient By using the definitive evaluation value, the evaluation object line is intended to evaluate the effect of the tube network.

  In this way, by setting the resistance coefficient in the evaluation target pipeline to be larger than the normal resistance coefficient of the pipe and changing the setting of the evaluation target pipeline to a pipeline that is difficult to flow of water, the evaluation target pipeline Even if it is not deleted from the pipe network, it is possible to cause the pipe network to have the same effect as when the evaluation target pipeline is deleted from the pipe network, and by performing the calculation process on the pipe network in this state, The evaluation value in the pipe network when the evaluation target pipeline is set can be calculated. Therefore, for example, if the evaluation target pipe is to be deleted from the pipe network when the evaluation target pipe is set, a preparatory process such as construction of a network relationship is performed on the pipe network after the evaluation target pipe is deleted. It is necessary to do this, but by changing the setting of the evaluation target pipe to a pipe that does not flow easily without erasing the evaluation target pipe, the network relation of the pipe network does not change, and based on the network relation Since the result of the preparatory process performed does not change, the preparatory process can be omitted when calculating the evaluation value in the pipe network when the evaluation target pipe is set to a pipe that is difficult to flow of water. .

  According to a second aspect of the present invention, in the pipe evaluation method according to the first aspect, the value of the head of the water source and the value of the head of each demand point are given as initial data. From the difference between the value of the head and the loss head of the pipe calculated during the calculation step, the value of the head at the demand point downstream of the pipe is further reduced, so that the pressure head at the demand point is effective. The value of the head is calculated as the evaluation value.

  The invention according to claim 3 is the pipe evaluation method according to claim 2, in addition to the value of the head of the water source and the value of the head of each demand point, the value of the head of the installation height of the water source is the initial data. In the calculation step, the effective head of the water source is calculated from the difference between the head of the water source and the head of the installation height of the water source, and the value of the effective head that is the pressure head at each demand point and the water source The average value of the effective head of the demand point or water source connected to one side of the pipeline and the effective head of the demand point or water source connected to the other side of the pipeline using the effective head value of Is calculated as the value of the effective head of the pipe, the effective head of the specific pipe in the pipe network before setting the evaluation target pipe, and the specific pipe in the pipe network after setting the evaluation target pipe A value obtained by multiplying the difference from the effective head of the road by the capacity of the specific pipe line, Calculating the total sum of the pipes and calculating the sum, dividing the sum by the sum of the capacities of all the pipes to calculate the average pressure change amount of the pipe network as an evaluation index; The evaluation target pipe line is evaluated based on the magnitude of the average pressure change amount.

  In this way, by calculating the average pressure change amount as an evaluation index, it is possible to easily evaluate the pipeline only by comparing the magnitude of this value. In addition, since the order of the magnitude of the average pressure change amount in the case of each evaluation target pipe represents the order of the magnitude of pressure fluctuation in the pipe network, from this result, the importance of each evaluation target pipe Can be judged.

  As described above, according to the present invention, since the preparation step can be omitted when calculating the evaluation value in the pipe network when the evaluation target pipe is set to a pipe that is difficult to flow of water, the evaluation target pipe The road can be evaluated quickly.

  In addition, by calculating the average pressure change amount as an evaluation index, it is possible to easily evaluate the pipeline only by comparing the magnitudes of the values. In addition, since the order of the magnitude of the average pressure change amount in the case of each evaluation target pipe represents the order of the magnitude of pressure fluctuation in the pipe network, from this result, the importance of each evaluation target pipe Can be judged.

  A method for evaluating a pipeline according to an embodiment of the present invention will be described. It should be noted that the pipe network to be subjected to the pipe network calculation when evaluating the pipe line by this method has the same configuration as the pipe network shown in FIG. 3, and the initial data given at the time of the pipe network calculation is also This is the same as the initial data shown in FIGS. Further, the pipe network calculation method in the following description uses a mesh flow rate method as in the conventional case.

  When evaluating pipes by the pipe line evaluation method according to the embodiment of the present invention, first, as in the prior art, first, a preparation process and a calculation process are performed on a pipe network in a normal state, and the flow rate of each pipe line q, loss head h, and effective head P as an evaluation value are calculated and recorded. The preparation process and the calculation process at this time, that is, the process of Step 1 (S001) to Step 14 (S014) shown in FIG. 1 is the same as the conventional Step 1 to Step 14 shown in FIG. Omitted.

  When the process of step 14 is completed, as shown in FIG. 1, the process proceeds to step 15 (S015) as a process for setting the evaluation target pipeline. At this point, since the evaluation target pipeline has not been set, the process proceeds to step 16 (S016), and then to step 17 (S017) in order to examine the influence of the evaluation target pipeline on the entire pipe network.

  In step 17, a pipe to be evaluated is determined, and the magnitude of the pipe resistance r in the pipe to be evaluated is set sufficiently larger than the normal pipe resistance r of the pipe to be evaluated. Change the pipeline to a pipeline that is difficult for water to flow.

  In this way, by changing the setting of the evaluation target pipe to a pipe that is difficult to flow of water, and expressing the evaluation target pipe as clogged as shown in FIG. 2, the evaluation target pipe is removed from the pipe network. Even if it is not deleted, it is possible to cause the pipe network to have the same effect as when the evaluation target pipeline is deleted from the pipe network. In addition, in this case, the network relationship of the pipe network does not change, and therefore the result of the preparation process performed based on the network relationship does not change. Thereby, when calculating the evaluation value in the pipe network in which the evaluation target pipe line is set, the preparation process which is performed based on the network relation and is not related to the magnitude of the pipe resistance r can be omitted. .

Thereby, when calculating the evaluation value in the pipe network in which the evaluation target pipe line is set, it can be performed from step 7 onward in which the calculation result varies depending on the magnitude of the pipe resistance r.
From the above, the process returns to Step 7 as shown in FIG. 1, and Steps 7 to 13 are performed as calculation processes as in the prior art. In step 11 (S011), if the absolute values of f1 (m) and f2 (m) are smaller than the threshold value 10 ⁻⁶ , the iterative calculation by the Newton-Raphson method is terminated, 14 (S014).

In step 14, the values of the mesh flow rates m1 and m2 used for the current calculation are set as the solution of the nonlinear simultaneous equations shown in Equation 6.
Then, using the values of the mesh flow rates m1 and m2, the flow rate q in each pipeline is obtained, and the effective head P at each node and water source is calculated as the loss head h in each pipeline and the evaluation value, for example. Then, the values of the flow rate q, the loss head h, and the effective head P obtained by calculation are recorded, and the process proceeds to Step 15 (S015).

In step 15, the pipe resistance r of the pipe to be evaluated, in this case the pipe K2, is returned to the normal value, and the process proceeds to step 16 (S016).
If there are other pipelines to be evaluated in step 16, the process proceeds to step 17 (S 017). Thereafter, calculation is performed in the same manner as in the case of pipeline K 2, and there are no other pipelines to be evaluated. If so, the process proceeds to step 18 (S018). In step 18, the average pressure change amount, which is an evaluation index for each pipeline, is obtained in the same manner as in the prior art, and each evaluation target pipeline is evaluated.

  As described above, the pipe resistance r in the pipe to be evaluated is set to be sufficiently larger than the pipe resistance r at the normal time of the pipe, and the pipe to be evaluated is changed to a pipe in which water does not easily flow. Therefore, even if the evaluation target pipeline is not deleted from the pipe network, the same effect as when the evaluation target pipe is deleted from the pipe network can be generated in the pipe network. By performing the process, it is possible to calculate the evaluation value in the pipe network when the evaluation target pipeline is set. Therefore, if the evaluation target pipe is to be deleted from the pipe network as in the conventional pipe line evaluation method, a preparatory process such as construction of a network relationship is performed on the pipe network after the evaluation target pipe is deleted. Although it is necessary to perform this, as in the method for evaluating pipelines in the present embodiment, the pipeline to be evaluated is changed to a pipeline that is difficult to flow of water without erasing the pipeline to be evaluated. No change occurs in the network relationship, and the result of the preparation process performed based on the network relationship does not change, so when calculating the evaluation value in the pipe network when setting the evaluation target pipeline, the preparation process Can be omitted. Thereby, the evaluation of the pipe line that affects the pipe network can be performed quickly.

It is a figure which shows the evaluation method of the pipe line of this invention. It is a figure which shows the state which carried out the setting change of the evaluation object pipe line to the pipe line where water does not flow easily. It is a figure which shows the pipe network used as the object of evaluation. It is a figure which shows the initial data provided to the water source and node in the pipe network shown in FIG. It is a figure which shows the initial data provided to the pipe line in the pipe network shown in FIG. It is a figure which shows the evaluation method of the conventional pipe line. It is a figure which shows the state which constructed | assembled the network relationship in a pipe network. It is a figure which shows the data of the pipe line E1 in FIG. It is a figure which shows the search result of a breadth priority tree. It is a figure which shows the mesh in a pipe network. It is a figure which shows the conditional expression of the loss head in the mesh of a pipe network. 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 state which deleted the pipe line K2 in the pipe network shown in FIG.

Explanation of symbols

S Water source K Pipe line N Node h Loss head r Pipe resistance q Flow rate C ₀ Flow coefficient D Pipe inner diameter L Pipe length

Claims (3)

In a pipe network composed of a network relationship between an arbitrary number of water sources, a water demand point, and a pipe line to which the water source or the demand point is connected at both ends, a pipe line that affects the pipe network When evaluating, a preparation step for performing the evaluation, a calculation step for calculating an evaluation value to be used for the evaluation using a result of the preparation step, and a pipeline to be subjected to the evaluation after the calculation step In the pipeline evaluation method for performing the evaluation target pipeline setting step for setting the network, as the preparation step, the network relationship is constructed, and the calculation formula for calculating the flow rate of each pipeline in the pipeline network is constructed. Derived based on the network relationship, as the calculation step, the flow rate of each pipeline in the pipe network is calculated using the calculation formula, and the calculated flow rate of each pipeline and water from one end side of the pipeline When it flows to the other end The loss head of each pipe in the pipe network is calculated from the Hezen-Williams equation, which represents the head of loss as the product of the current flow rate and the resistance coefficient of the pipe, and the calculated flow rate of each pipe and An evaluation value used for the evaluation is calculated based on the loss head, and the evaluation target pipeline is determined from the pipelines as the evaluation target pipeline setting step, and the resistance in the evaluation target pipeline is determined. The coefficient is set to be larger than the normal resistance coefficient of the pipe, and the evaluation target pipe is set to a pipe that is difficult to flow of water, and the state before the calculation step is returned and the resistance coefficient is increased. Calculate the flow rate of each pipe in the pipe network, the loss head of each pipe and the evaluation value, the evaluation value in the pipe network before changing the resistance coefficient, and the evaluation value in the pipe network after increasing the resistance coefficient And the evaluation target pipeline is a pipe. Conduit evaluation method characterized by evaluating the effect on. The value of the head of the water source and the value of the head of each demand point are given as initial data, and in the calculation process, the difference between the value of the head of the water source and the head loss of the pipe calculated during the calculation process. The value of the effective head that is the pressure head at the demand point is further calculated as the evaluation value by reducing the value of the head at the demand point on the downstream side of the pipe. Pipeline evaluation method. In addition to the value of the head of the water source and the value of the head of each demand point, the value of the head of the installation height of the water source is given as initial data, and the head of the water source and the installation height of the water source are calculated in the calculation process. The effective head of the water source is calculated from the difference from the head of the head and connected to one side of the pipeline using the effective head value which is the pressure head at each demand point and the effective head value of the water source. Calculate the average value of the effective head of the demand point or water source and the effective head of the demand point or water source connected to the other side of the pipe as the value of the effective head of the pipe, and set the evaluation target pipe A value obtained by multiplying the difference between the effective head of the specific pipe in the pipe network before the evaluation and the effective head of the specific pipe in the pipe network after setting the evaluation target pipe by the capacity of the specific pipe Is calculated for all pipelines and the sum is calculated. By dividing by the sum of the capacities of all the pipes, the average pressure change amount of the pipe network as an evaluation index is calculated, and the evaluation target pipe line is evaluated based on the magnitude of the average pressure change amount. The pipe line evaluation method according to claim 2.

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