Method for calculating head loss along pressure water supply pipeline

Abstract

This invention discloses a method for calculating the head loss along the flow path of pressurized water pipelines. From the perspective of energy loss, the head loss along the flow path of pressurized water pipelines is redefined to include energy loss between the water body and the flow boundary, as well as energy loss within the water body. The friction coefficient in the Darcy-Weisbach formula is used... λ This parameter, which is related to the relative roughness of the wall and the Reynolds number of the flow, and which usually needs to be determined experimentally, can be converted into a constant that can be directly determined based on the physical properties of the pressurized water pipeline wall and the hydraulic properties of the water body. This eliminates the experimental steps and avoids the uncertainty of the calculation. The method of this invention does not require iteration and can be directly programmed for calculation, which greatly improves the calculation speed. It is suitable for large-scale pipeline hydraulic calculations, real-time simulations, and embedded systems. It solves the problem of engineers repeatedly calculating λ in variable flow design and can be easily applied to various design, optimization, and analysis software.

Description

Technical Field

[0001] This invention relates to the field of water conservancy and hydropower pipeline engineering technology, and is particularly applicable to the method of calculating head loss along pressurized water transmission pipelines. Background Technology

[0002] Pressurized water pipelines are widely used in water conservancy, hydropower, municipal engineering, and agriculture. The pipeline's water conveyance capacity is a crucial aspect of its design, and head loss is a key factor affecting this capacity. Head loss in pressurized water pipelines is typically divided into friction head loss and local head loss. In practical engineering projects, pressurized water pipelines are usually quite long, and friction head loss constitutes a significant proportion of the total head loss, thus having a substantial impact on the pipeline's water conveyance capacity. Therefore, the accurate calculation of friction head loss in pressurized water pipelines is of great importance for both the design and operation of pressurized water pipeline projects.

[0003] German engineer Weisbach first proposed the formula for calculating head loss along the friction path in 1850: French engineer Darcy experimentally verified the formula in 1858, and it is commonly known as the Darcy-Weisbach formula. However, the friction coefficient in this formula... λ It is not a fixed constant; it depends not only on the relative roughness of the wall surface but also on the flow Reynolds number, and usually needs to be determined experimentally. In engineering design, the appropriate friction coefficient is selected for different water flow rates. λ It's not easy. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the head loss along the pressure of pressurized water pipelines, in order to solve the problem that the head loss along the pressure of pressurized water pipelines is difficult to determine and has weak applicability.

[0005] To achieve the above objectives, the method for calculating the head loss along the pressure of a pressurized water transmission pipeline as described in this invention specifically includes: head loss along the pressure of a pressurized water transmission pipeline. This includes energy loss between the water body and the flow boundary, as well as energy loss within the water body; obtaining the wall loss coefficient of pressurized water transmission pipelines. wet perimeter of pressurized water pipelines Length of pressurized water pipeline Water density Local gravitational acceleration Cross-sectional area of ​​pressurized water pipeline Internal loss coefficient of water flow Water flow rate The head loss along the pressurized water pipeline was obtained. Based on the obtained head loss along the pressurized water pipeline, determine the pipe diameter and pump head of the pressurized water pipeline; assess the risk of pipe roughness, scale buildup, or leakage; and provide a basis for pump station speed regulation and valve adjustment.

[0006] Furthermore, the wall loss coefficient of the pressurized water pipeline The energy loss between the water flow and the wall surface is considered; for a given pressurized water pipeline wall and water body, the pressurized water pipeline wall loss coefficient is a constant.

[0007] Furthermore, the internal loss coefficient of the water flow The energy loss characteristics within the water body are reflected. For a given water body, the energy loss coefficient within the water body is constant.

[0008] The advantage of this invention lies in redefining the head loss along the pipeline in pressurized water supply from the perspective of energy loss. It also addresses the friction coefficient in the Darcy-Weisbach formula. λ This parameter, which is related to the relative roughness of the wall and the Reynolds number of the flow, and which usually needs to be determined experimentally, can be converted into a constant that can be directly determined based on the physical properties of the pressurized water pipeline wall and the hydraulic properties of the water body. This eliminates the experimental steps and avoids the uncertainty of the calculation. The method of this invention does not require iteration and can be directly programmed for calculation, which greatly improves the calculation speed. It is suitable for large-scale pipeline hydraulic calculations, real-time simulations, and embedded systems. It solves the problem of engineers repeatedly calculating λ in variable flow design and can be easily applied to various design, optimization, and analysis software. Attached Figure Description

[0009] Figure 1 This is a schematic diagram of the research object in the method for calculating head loss along a pressurized water pipeline as described in this invention.

[0010] Figure 2 The graph shows the calculation results of the pressure head loss calculation method for pressurized water transmission pipelines described in this invention, the experimental results of pressure head loss for pressurized water transmission pipelines, and the relationship between the calculation results of the Darcy-Weisbach formula and the flow rate. Detailed Implementation

[0011] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0012] The principle underlying the method for calculating head loss along a pressurized water pipeline as described in this invention is as follows: The head loss along the flow path in a pressurized water pipeline is essentially a form of energy loss. This energy loss in a pressurized water pipeline can be divided into two parts: energy loss between the water body and the flow boundary, and energy loss within the water body itself.

[0013] like Figure 1 As shown, a body of water of length b inside a pressurized water pipeline is taken as the research object, and the mass of the water body is denoted as m, with gravitational acceleration as... When the flow distance is L, the energy loss is W, and the corresponding head loss is W. Then we have: (2) Let the cross-sectional area of ​​the pressurized water pipeline be A, and the density of the water be... Then we have: (3) The head loss can be obtained from equations (2) and (3). With energy loss The relationship between them is: (4) In equation (4) This includes energy loss W1 generated between the water body and the flow boundary, and energy loss W2 generated within the water body, namely: (5) Assuming frictional force per unit area of ​​the flow boundary It is proportional to the square of the average flow velocity across the cross section, that is: (6) In the formula The wall loss coefficient is... The average flow velocity is the cross-sectional velocity.

[0014] The wall loss coefficient reflects the energy loss characteristics between the water flow and the wall. It is related to the physical properties of the wall and the water body, and the wall loss coefficient may differ for different walls and water bodies. For a given wall and water body, the wall loss coefficient can be considered a constant.

[0015] The resultant force F of the interfacial friction on the water body under study is: (7) In the formula, C is the wetted perimeter of the flow section, and b is the length of the water body under study.

[0016] When the distance the water body travels is L, the energy loss W1 between the water body and the flow boundary is: (8) Assuming energy loss within a unit volume of water per unit time It is proportional to the square of the average flow velocity across the cross section, that is: (9) In the formula This is the internal loss coefficient of the water body.

[0017] The internal loss coefficient of a water body reflects the energy loss characteristics within the water body, and it is related to the physical and mechanical properties of the water body. For a given water body, the internal loss coefficient can be considered a constant.

[0018] Let A be the cross-sectional area of ​​the pressurized water pipeline, and b be the length. Then, consider the energy loss within the water body of the study object per unit time. for: (10) The time T required for the water body to flow a distance L is: (11) When the water body under study flows a distance L, the energy loss W2 inside the water body is: (12) Based on equations (5), (8), and (12), the total energy loss W of the water body when the distance the water body travels is L is: (13) Based on equations (4) and (13), the formula for calculating the head loss along a pressurized water pipeline can be obtained: (14) If the average cross-sectional velocity is expressed in terms of flow rate, then: (15) In equations (15) and (16): -Head loss along pressurized water pipelines, m; - Wall loss coefficient of pressurized water transmission pipeline, kg / m 3 ; -Water body internal loss coefficient, kg / m³ 3 / s; -Wet perimeter of pressurized water pipeline, m; -Cross-sectional area of ​​pressurized water supply pipeline, m² 2 ; - Length of pressurized water pipeline, in meters; -Water density, kg / m³ 3 ; - Gravitational acceleration, m / s² 2 ; -Water flow rate, m 3 / s.

[0019] Therefore, the wall loss coefficient of pressurized water transmission pipelines is obtained. wet perimeter of pressurized water pipelines Length of pressurized water pipeline Water density Local gravitational acceleration Cross-sectional area of ​​pressurized water pipeline Internal loss coefficient of water flow Water flow rate According to formula (15), the head loss along the pressurized water pipeline can be obtained.

[0020] The pipe diameter and pump head of the pressurized water transmission pipeline are determined based on the obtained head loss along the pipeline; the pipeline roughness, scale buildup or leakage risk are assessed; and the basis for pump station speed regulation and valve adjustment is provided.

[0021] To verify the effectiveness of the method described in this invention, this invention selects the test results of head loss along the flow path of pressurized water transmission pipelines from the literature (Ma Di. Study on hydraulic characteristics of pressurized water transmission pipelines [D]. North China University of Water Resources and Electric Power, 2018.). Taking the pressurized water transmission pipeline used in the test as an example, the head loss along the flow path of pressurized water transmission pipelines calculated by the method described in this invention is used to calculate the head loss along the flow path under different flow rates. Specifically, as follows: The density of water in the pressurized water pipeline used in the test Local gravitational acceleration The pressurized water supply pipeline is a cement-lined ductile iron pipe; length The cross-section is circular, with a diameter of Cross-sectional area wet perimeter of cross section ; Wall loss coefficient of pressurized water transmission pipeline Internal loss coefficient of water flow The head loss along the pressurized water transmission pipeline is calculated using formula (15) according to the present invention. And in the literature (Ma Di. Study on hydraulic characteristics of pressurized water conveyance pipelines [D]. North China University of Water Resources and Electric Power, 2018.), different water conveyance flow rates were experimentally determined. Head loss data along the route As shown in Table 1.

[0022] Table 1 For comparison, Table 1 also provides the calculation results of the head loss along the pressurized water pipeline used in the experiment using the Darcy-Weisbach formula, denoted as... .

[0023] Figure 2 The figure shown is the test results of head loss along the pipeline from the literature (Ma Di. Study on hydraulic characteristics of pressurized water transmission pipelines [D]. North China University of Water Resources and Electric Power, 2018.). h T Calculation results of this invention h f and the results of Darcy-Weisbach formula calculation h D Respectively with traffic Q Relationship curves. Curve 1 represents the experimental results from the literature. h T Curve 2 represents the calculation results of this invention. h f Curve 3 represents the result calculated using the Darcy-Weisbach formula. h D .

[0024] Table 1 shows the relative errors of the calculation results of this invention. The relative error of the Darcy-Weisbach formula calculation results The calculations were performed using the following formulas respectively. from Figure 1 It can be seen that the calculation results of the present invention fit the experimental results well. As shown in Table 1, the maximum absolute value of the relative error of the calculation results of the present invention is 4.32%, and the maximum absolute value of the relative error of the calculation results of the Darcy-Weisbach formula is 21.18%. The calculation results show that the calculation results of the present invention are in good agreement with the experimental results.

[0025] This method allows for the rapid and accurate calculation of head loss for different candidate pipe diameters at various design flow rates. By adding this head loss value to the geometric elevation difference and terminal pressure requirements, the theoretical head required by the pump can be precisely determined. By comparing the pipeline construction costs and long-term operating energy consumption of pumping stations under different schemes, the "economical pipe diameter" with the lowest total life-cycle cost and the matching "high-efficiency pump type" can be scientifically selected, achieving energy and cost savings from the source.

[0026] For pipelines already in service, the theoretical head loss calculated using this method can be continuously compared with the actual head loss measured by on-site pressure and flow sensors. If the actual value is significantly and consistently higher than the theoretical value during long-term operation, it strongly indicates an increase in the roughness of the pipeline's inner wall (such as scaling and corrosion product deposition), leading to deterioration of hydraulic conditions. If the actual head loss suddenly increases abnormally and is accompanied by abnormal flow, it may indicate a leak. This deviation analysis based on a precise model provides quantitative and forward-looking decision support for preventative maintenance (such as cleaning and descaling) and safety early warning (such as leak location).

[0027] Simultaneously, by embedding the method of this invention into the hydraulic model of the control system, it is possible to predict in real time the head loss and pressure distribution of key nodes throughout the network under different flow distributions or valve openings. Based on this, the control system can dynamically calculate the optimal pump group combination, speed regulation scheme, and valve opening to meet water supply demand, ensuring water supply safety while always keeping the system operating at the lowest energy consumption point, thereby achieving an upgrade from "experience-based control" to "model predictive optimization control".

Claims

1. A method for calculating head loss along a pressurized water pipeline, characterized in that: Head loss along pressurized water pipelines This includes energy loss between the water body and the flow boundary, as well as energy loss within the water body; obtaining the wall loss coefficient of pressurized water transmission pipelines. wet perimeter of pressurized water pipelines Length of pressurized water pipeline Water density Local gravitational acceleration Cross-sectional area of ​​pressurized water pipeline Internal loss coefficient of water flow Water flow rate The head loss along the pressurized water pipeline was obtained. Based on the obtained head loss along the pressurized water pipeline, determine the pipe diameter and pump head of the pressurized water pipeline; assess the risk of pipe roughness, scale buildup, or leakage; and provide a basis for pump station speed regulation and valve adjustment.

2. The method for calculating head loss along a pressurized water transmission pipeline according to claim 1, characterized in that: The wall loss coefficient of the pressurized water pipeline The energy loss between the water flow and the wall surface is considered; for a given pressurized water pipeline wall and water body, the pressurized water pipeline wall loss coefficient is a constant.

3. The method for calculating head loss along a pressurized water transmission pipeline according to claim 1, characterized in that: The internal loss coefficient of water flow The energy loss characteristics within the water body are reflected. For a given water body, the energy loss coefficient within the water body is constant.

Images