A method and apparatus for optimizing flow distribution in a vehicle cooling system
By fitting the flow-pressure drop equation of the cooling system and combining the principles of flow conservation and pressure balance, the flow distribution of the commercial vehicle cooling system is optimized, solving the problem of uneven flow distribution and improving the calculation accuracy and the safety and performance of the vehicle cooling system.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- XUZHOU XUGONG AUTOMOBILE MFG CO LTD
- Filing Date
- 2026-03-02
- Publication Date
- 2026-06-09
AI Technical Summary
Existing theoretical calculation methods and one-dimensional simulation models cannot accurately calculate the flow resistance of pipelines, resulting in uneven flow distribution in the cooling system of commercial vehicles, leading to insufficient cooling of key high-temperature components and threatening the safety and performance of the entire vehicle.
The method of optimizing the flow distribution of the vehicle cooling system is adopted. By obtaining the flow-pressure drop data of the coolant pipeline model and components of the cooling system, a quadratic equation is fitted. Combining the principles of flow conservation and pressure balance, the calculation software is built independently using the planning and solving method, and the flow resistance coefficient or layout architecture is adjusted to optimize the flow distribution.
It enables rapid and accurate assessment of cooling system flow, improves calculation precision, and can quickly locate and optimize areas of insufficient flow, thereby enhancing the safety and performance of the vehicle's cooling system.
Smart Images

Figure CN122174729A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method and apparatus for optimizing flow distribution in a vehicle cooling system, belonging to the field of cooling system flow calculation technology. Background Technology
[0002] With the electrification transformation of commercial vehicles, their thermal management systems are becoming increasingly complex, expanding the cooling targets from traditional engines to key components such as motors, motor controllers, and power batteries. These components have extremely stringent requirements for cooling performance: the thermal safety and lifespan of power batteries are directly affected by temperature, and overheating may lead to thermal runaway, and their temperature uniformity requirements are high; the performance and reliability of motors and electronic controls are also strongly correlated with operating temperature, and overheating will lead to decreased efficiency, shortened lifespan, or even permanent damage.
[0003] In an integrated multi-loop cooling system, components are coupled through a complex fluid network. An imbalance in flow distribution can cause a "water-grabbing" phenomenon, resulting in insufficient cooling of critical high-temperature components (such as the battery and motor controller), which seriously threatens the safety and performance of the entire vehicle.
[0004] Existing theoretical calculation methods and one-dimensional simulation models cannot accurately calculate the flow resistance of pipelines, resulting in low calculation accuracy. Therefore, there is an urgent need in this field for a new method that can overcome this limitation and quickly and accurately evaluate and optimize system flow distribution to precisely meet the heat dissipation requirements of core components such as motors and batteries, ensuring the safety and efficiency of next-generation vehicles. Summary of the Invention
[0005] The purpose of this invention is to propose a method and apparatus for optimizing the flow distribution of a vehicle cooling system, which aims to quickly and scientifically assess the flow resistance of the pipeline and accurately calculate the flow rate of the cooling system.
[0006] To achieve the above objectives, the present invention is implemented using the following technical solution:
[0007] In a first aspect, the present invention proposes a method for optimizing the flow distribution of a vehicle cooling system, comprising:
[0008] Obtain the coolant piping model of the target vehicle's cooling system and its layout, including the main pipeline and several branch pipelines;
[0009] Acquire flow-pressure drop data for components of the cooling system, including a power source and a resistance element;
[0010] Extract the inner surface of the coolant pipeline model, segment the pipeline at each connection point on the inner surface, and seal both ends of each segment to obtain the pipeline model.
[0011] Based on the pipeline model, pressure drop data under different flow rates are obtained, and the relationship between pressure drop and flow rate is fitted into a quadratic equation with an intercept of 0.
[0012] The flow-pressure drop data based on the aforementioned components are fitted into a quadratic equation, wherein the power source pressure drop equation includes an intercept, and the resistance element pressure drop equation has an intercept of 0.
[0013] Based on the layout of the cooling system, for each branch, the equivalent flow resistance equation of the branch is obtained by summing the quadratic equation with zero intercept and the quadratic equation with intercept in the branch. Based on the principles of flow conservation and pressure balance, the equivalent flow resistance equation and flow relationship of the main pipeline and each branch are established simultaneously. The flow of the main pipeline and each branch is obtained by independently building a calculation software based on the planning and solving method.
[0014] If the flow rate of any branch is less than the minimum rated flow rate of the component being cooled, calculate the relative error between the actual branch flow rate and the minimum rated flow rate, and set an error threshold. If the relative error is lower than the error threshold, adjust the pipeline design to change the flow resistance coefficient. If the relative error is higher than the error threshold, adjust the layout of the cooling system or replace it with a high-lift power source until the flow rate of all branches is greater than or equal to the minimum rated flow rate.
[0015] Furthermore, the flow-pressure drop data of the components of the cooling system include head curves obtained based on the power source and flow-pressure drop curves of the radiator and each heat source obtained based on the resistance element.
[0016] Furthermore, the pressure drop data in the flow-pressure drop data is obtained by importing the pipeline model into CFD software for calculation.
[0017] Furthermore, the layout of the cooling system is analogous to an equivalent circuit network model; wherein, the power source, resistance element, pipeline and coolant flow rate in the cooling system are respectively equivalent to the battery, resistor, wire and current of the circuit, and the flow resistance generated when the coolant flows through the resistance element and pipeline is equivalent to the resistance.
[0018] Furthermore, when the cooling system is arranged in a series structure, the expression based on the principle of flow conservation and pressure balance is a quadratic equation in one variable concerning flow. After solving the equation to obtain the flow, the flow is substituted into the resistance equations of each component and pipeline to obtain the pressure drop of each component.
[0019] When the cooling system is arranged in a parallel structure, it is divided into a main pipeline and n parallel branches. The expression based on the principles of flow conservation and pressure balance is:
[0020]
[0021] In the formula, To control the traffic flow on the main road, For the flow of n parallel branches, The equivalent flow resistance of the main pipeline is a quadratic equation in one variable. The equivalent flow resistance quadratic equation for n parallel branches;
[0022] When the layout architecture is a hybrid structure, the hybrid structure is decomposed into a combined structure consisting of serial sub-modules and several parallel sub-modules, and the calculations are performed according to the above method.
[0023] Furthermore, the planning solution method is a nonlinear generalized reduced gradient method.
[0024] Furthermore, the adjustment methods for the pipeline flow resistance coefficient include adjusting the pipe diameter and the pipeline direction.
[0025] Furthermore, the calculation of all branch flow rates based on the planning solution method is achieved using calculation software developed with Python and PySide6; this software can freely assemble pipes and components according to the cooling system architecture and complete the calculation of all branch flow rates in one go.
[0026] The aforementioned further solution does not rely on externally purchased one-dimensional analysis software; instead, it develops computational software, eliminating potential procurement costs.
[0027] Secondly, the present invention proposes a vehicle cooling system flow distribution optimization device, including a cooling system data acquisition module, a cooling pipe flow resistance analysis module, a flow-pressure function establishment module, and a branch flow optimization module;
[0028] The cooling system data acquisition module is used to acquire the coolant piping model and layout architecture of the cooling system, as well as the flow-pressure drop data of the components of the cooling system;
[0029] The cooling pipeline flow resistance analysis module is used to obtain the flow rate-pressure drop data of the pipeline;
[0030] The flow-pressure function establishment module is used to fit the flow-pressure drop data of the component and the flow-pressure drop data of the pipeline into quadratic equations, and fit multiple quadratic equations, wherein the intercept of the other equations is 0, except for the equation corresponding to the power source.
[0031] The branch flow optimization module is used to solve for the flow of all branches based on the planning solution method. If the flow of any branch is less than the minimum rated flow of the corresponding component, the flow resistance coefficient is adjusted by changing the pipeline design, adjusting the layout of the cooling system, or replacing the high-head power source, until the flow of all branches is greater than or equal to the minimum rated flow.
[0032] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:
[0033] This invention segments the cooling system piping and uses CFD methods to calculate the flow resistance of each pipe at multiple flow rates, fitting a flow-pressure drop equation. Compared to theoretical calculations and one-dimensional calculation methods, this approach offers higher computational accuracy. By providing flow-pressure drop equations for each pipe and component, this invention can quickly identify locations causing insufficient flow and perform targeted optimizations, thus improving optimization speed. Furthermore, this invention offers flexible and efficient application advantages: on the one hand, it allows for rapid adjustment of component placement and simultaneous assessment of the compliance of total flow and flow rates in each branch; on the other hand, as the accumulated data volume in the database increases, the invention's dependence on CFD software will continuously decrease, effectively lowering the technical threshold for flow assessment. Simultaneously, this method is a virtual verification method, enabling rapid verification without relying on a prototype vehicle. Attached Figure Description
[0034] Figure 1 This is a flowchart of the vehicle cooling system flow distribution optimization method proposed in this embodiment of the invention;
[0035] Figure 2 This is the original architecture of the motor cooling system of a pure electric vehicle in an embodiment of the present invention;
[0036] Figure 3 This is the calculation result of the original architecture of the motor cooling system of a pure electric vehicle in an embodiment of the present invention;
[0037] Figure 4 This is an optimized architecture for the motor cooling system of a pure electric vehicle in an embodiment of the present invention;
[0038] Figure 5 This is the flow calculation result of the optimized architecture of the motor cooling system of a pure electric vehicle in an embodiment of the present invention. Detailed Implementation
[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use.
[0040] Example 1:
[0041] This embodiment proposes a method for optimizing the flow distribution of a vehicle cooling system, such as... Figure 1 As shown, it includes:
[0042] Obtain the coolant piping model of the target vehicle's cooling system and its layout, including the main pipeline and several branch pipelines;
[0043] Acquire flow-pressure drop data for components of the cooling system, including water pumps and resistance elements;
[0044] Extract the inner surface of the coolant piping model, segment the piping at each connection point on the inner surface, and seal both ends of each segment to obtain the piping model; the connection points include the inner surface of the tee and the inner surface of the connection points of other components.
[0045] Based on the pipeline model, pressure drop data under different flow rates were obtained, and the relationship between pressure drop and flow rate was fitted into a quadratic equation with an intercept of 0.
[0046] The flow-pressure drop data based on the aforementioned components are fitted into a quadratic equation, wherein the pump pressure drop equation includes an intercept, and the intercept of the resistance element pressure drop equation is 0.
[0047] Based on the layout of the cooling system, for each branch, the equivalent flow resistance equation of the branch is obtained by summing the quadratic equation with zero intercept and the quadratic equation with intercept in the branch. Based on the principles of flow conservation and pressure balance, the equivalent flow resistance equation and flow relationship of the main pipeline and each branch are established simultaneously. The flow rate of the main pipeline and each branch is obtained by independently building a calculation software based on the planning and solving method.
[0048] If the relative error is lower than the error threshold, the flow resistance coefficient is changed by adjusting the pipeline design. Adjusting the pipeline design includes adjusting the pipe diameter, pipeline direction, and valve opening. If the relative error is higher than or equal to the error threshold, the layout of the cooling system is adjusted or a high-lift water pump is replaced. Adjusting the layout of the cooling system includes changing the series structure to a parallel structure, increasing the number of branches, or adjusting components to other branches, until the flow rate of all branches is greater than or equal to the minimum rated flow rate. In this embodiment, the error threshold is set to 10%.
[0049] In this embodiment, the cooling system architecture differs among different vehicle models. The components of the electric drive cooling system for pure electric heavy-duty trucks generally include a water pump, motor controller, multi-function controller, motor water jacket, and radiator; while the battery thermal management system generally includes a water pump, battery water cooling plate, DC-DC converter, WPTC, etc.; the cooling system components for hydrogen fuel cell vehicles and hybrid vehicles are also different.
[0050] In this embodiment, the flow-pressure drop data of the cooling system components includes the head curve obtained based on the water pump as the power source and the flow-pressure drop curves of the radiator and each heat source obtained based on the resistance element. The purpose of obtaining this data is to fit the flow-pressure equation of each component, which is then used to formulate the pressure balance equation to obtain the flow rate. As vehicle development progresses, the flow-pressure drop data of the components can be obtained from the company's database.
[0051] In this embodiment, the quadratic equation fitted based on the flow-pressure drop data of the pipeline has an intercept of 0 because when the coolant flow rate is 0, there is no pressure difference across the resistance element, and the resistance is 0. The basis for choosing a quadratic equation is that the total pipeline resistance consists of frictional resistance and local resistance, both of which are linear equations without intercepts about the square of the flow rate, and their superposition still results in a quadratic equation without intercepts. The quadratic equation fitted based on the flow-pressure drop data of the components has an intercept because the pump's head curve (head is in meters, but the data used here is converted to Pa) is parabolic, and the smaller the flow rate, the greater the pressure rise it can provide. The equations for other resistance elements use directly the test data provided by the manufacturer.
[0052] In this embodiment, the pressure drop data in the flow-pressure drop data is obtained by importing the pipeline model into CFD software for calculation.
[0053] In this embodiment, the layout of the cooling system is analogous to an equivalent circuit network model; wherein, the water pump, resistance element, pipeline and coolant flow rate in the cooling system are respectively equivalent to the battery, resistor, wire and current of the circuit, and the flow resistance generated when the coolant flows through the resistance element and pipeline is equivalent to the resistance.
[0054] In this embodiment, when the cooling system is arranged in a series structure, the expression based on the principles of flow conservation and pressure balance is a quadratic equation in one variable concerning flow. After solving this equation to obtain the flow, it is substituted into the resistance equations of each component and pipeline to obtain the pressure drop of each component.
[0055] When the cooling system is arranged in a parallel structure, it is divided into a main pipeline and n parallel branches. We need to construct equations for each branch, so we need to sum the equations for the resistance elements within the same branch to obtain the equivalent flow resistance of the branch. The quadratic equation with an intercept represents the pump equation, while the other quadratic equations with zero intercepts are used to simulate the resistance elements in the pipeline and system. Assuming there are n branches, the equivalent equation for the resistance-flow rate of each branch is added to the equation of the main pipeline to form a new equation. Based on the principle of pressure balance, the result of the new equation is 0. Based on the principle of mass conservation, we can establish the flow rate relationship between the main pipeline and the n branches. Solving the (n+1) equations simultaneously yields the flow rate of the main pipeline and each branch. The expression based on the principles of flow rate conservation and pressure balance is:
[0056]
[0057] In the formula, To control the traffic flow on the main road, For the flow of n parallel branches, The equivalent flow resistance of the main pipeline is a quadratic equation in one variable. The equivalent flow resistance is a quadratic equation in one variable for n parallel branches.
[0058] When the cooling system is arranged in a hybrid configuration, the hybrid configuration is decomposed into a combined structure consisting of series sub-modules and several parallel sub-modules, and the calculations are performed separately according to the above method.
[0059] In this embodiment, the planning solution method is the nonlinear generalized irreducible gradient method.
[0060] In this embodiment, the flow rate of all branches is obtained based on the planning and solving method, which is achieved by calculation software developed by Python and PySide6. This software can freely assemble pipes and components according to the cooling system architecture and complete the flow rate calculation of all branches in one go.
[0061] In this embodiment, the components to be cooled in the cooling system include the battery water-cooled plate of the battery cooling system and the motor controller, drive motor, and multi-function controller of the electric drive cooling system. The minimum rated flow requirements of the above-mentioned components are given in their datasheets. This method only processes one cooling system loop in a single calculation. If there are multiple independent cooling systems in the vehicle, this method is executed on each system separately in sequence, and the obtained flow distribution results are summarized.
[0062] Example 2:
[0063] This embodiment expands upon the application of Embodiment 1, proposing a method for optimizing the flow distribution of a vehicle cooling system based on a planning and solving method, which can quickly complete the evaluation of the flow distribution of the cooling system.
[0064] The motor cooling system of a certain pure electric vehicle requires the flow rates of the multi-in-one controller, drive motor one, and drive motor two to reach 25L / min, 30L / min, and 30L / min, respectively. The evaluation and optimization process includes the following specific steps:
[0065] A. Obtain the coolant piping model, extract the inner surface, and cut and segment the piping at the tees and component connection points, resulting in a total of 9 pipe segments. The original architecture diagram after the cutting is shown below. Figure 2 As shown. Mesh generation and mesh independence verification were performed in CFD software, and pressure drop was calculated for five flow rates. A quadratic equation with a zero intercept was used to fit the pressure drop-flow rate equation.
[0066] B. Obtain the water pump performance curve and the flow-pressure drop data of the radiator, all-in-one controller and drive motor, and fit them using a quadratic equation.
[0067] C. According to the architecture, in software developed based on the problem-solving method, components and pipelines are correctly combined, such as... Figure 3 As shown, the calculated total flow rate is 77.53 L / min, and the flow rates of the multi-function controller, drive motor one, and drive motor two branches are 21.72 L / min, 29.25 L / min, and 26.56 L / min, respectively, which do not meet the design requirements.
[0068] D. In the existing design, the multi-function controller and two drive motors form three parallel branches, which is quite challenging to meet the required flow rate of 85 L / min. Analysis of the flow resistance equations for each component and pipeline revealed that the multi-function controller has a significantly higher flow resistance than the drive motors. Therefore, various solutions were explored, including placing the multi-function controller in the main pipeline and connecting the two drive motors in parallel. Ultimately, it was found that the solution of two parallel branches consisting of the multi-function controller and the two drive motors could meet the requirements. The solution is as follows: Figure 4 As shown, the calculation results are as follows Figure 5 As shown, the total flow rate calculated by this scheme is 67.14 L / min, and the flow rates of parallel branch one (multi-in-one controller branch) and parallel branch two (two drive motor branches) are 35.66 L / min and 31.48 L / min, respectively.
[0069] E. Complete the evaluation, provide optimization suggestions to the designers, and complete this analysis task.
[0070] The technical method of calculating flow resistance equations in pipeline segments, solving system flow planning, and combining optimization according to the present invention can quickly achieve the design scheme, greatly shorten the product development cycle, and improve the first-time design success rate of the product.
[0071] Example 3:
[0072] Based on Embodiment 1, this embodiment proposes a vehicle cooling system flow distribution optimization device, including a cooling system data acquisition module, a cooling pipe flow resistance analysis module, a flow-pressure function establishment module, and a branch flow optimization module;
[0073] The cooling system data acquisition module is used to acquire the coolant piping model and layout architecture of the cooling system, as well as the flow-pressure drop data of the components of the cooling system;
[0074] The cooling pipeline flow resistance analysis module is used to obtain the flow rate-pressure drop data of the pipeline;
[0075] The flow-pressure function establishment module is used to fit the flow-pressure drop data of components and the flow-pressure drop data of pipelines into quadratic equations, and fit multiple quadratic equations. Except for the equation corresponding to the water pump, the intercepts of the other equations are all 0.
[0076] The branch flow optimization module is used to solve for the flow of all branches based on the planning solution method. If the flow of any branch is less than the minimum rated flow of the corresponding component, the flow resistance coefficient of the pipeline is adjusted until the flow of all branches is greater than or equal to the minimum rated flow.
[0077] The branch flow optimization module is used to solve for the flow of all branches based on the planning solution method. If the flow of any branch is less than the minimum rated flow of the corresponding component, the flow resistance coefficient is adjusted by changing the pipeline design, adjusting the layout of the cooling system, or replacing the pump with a high-head pump, until the flow of all branches is greater than or equal to the minimum rated flow.
[0078] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.
Claims
1. A method for optimizing flow distribution in a vehicle cooling system, characterized in that, include: Obtain the coolant piping model of the target vehicle's cooling system and its layout, including the main pipeline and several branch pipelines; Acquire flow-pressure drop data for components of the cooling system, including a power source and a resistance element; Extract the inner surface of the coolant pipeline model, segment the pipeline at each connection point on the inner surface, and seal both ends of each segment to obtain the pipeline model. Based on the pipeline model, pressure drop data under different flow rates are obtained, and the relationship between pressure drop and flow rate is fitted into a quadratic equation with an intercept of 0. The flow-pressure drop data based on the aforementioned components are fitted into a quadratic equation, wherein the power source pressure drop equation includes an intercept, and the resistance element pressure drop equation has an intercept of 0. Based on the layout of the cooling system, for each branch, the equivalent flow resistance equation of the branch is obtained by summing the quadratic equation with zero intercept and the quadratic equation with intercept in the branch. Based on the principles of flow conservation and pressure balance, the equivalent flow resistance equation and flow relationship of the main pipeline and each branch are established simultaneously. The flow of the main pipeline and each branch is obtained by independently building a calculation software based on the planning and solving method. If the flow rate of any branch is less than the minimum rated flow rate of the component being cooled, calculate the relative error between the actual branch flow rate and the minimum rated flow rate, and set an error threshold. If the relative error is lower than the error threshold, adjust the pipeline design to change the flow resistance coefficient. If the relative error is higher than the error threshold, adjust the layout of the cooling system or replace it with a high-lift power source until the flow rate of all branches is greater than or equal to the minimum rated flow rate.
2. The vehicle cooling system flow distribution optimization method according to claim 1, characterized in that, The flow-pressure drop data of the components of the cooling system include head curves obtained based on the power source and flow-pressure drop curves of the radiator and each heat source obtained based on the resistance element.
3. The vehicle cooling system flow distribution optimization method according to claim 1, characterized in that, The pressure drop data in the flow-pressure drop data is obtained by importing the pipeline model into CFD software for calculation.
4. The vehicle cooling system flow distribution optimization method according to claim 1, characterized in that, The layout of the cooling system is analogous to an equivalent circuit network model; wherein, the power source, resistance element, pipeline and coolant flow rate in the cooling system are respectively equivalent to the battery, resistor, wire and current in the circuit, and the flow resistance generated when the coolant flows through the resistance element and pipeline is equivalent to the resistance.
5. The vehicle cooling system flow distribution optimization method according to claim 1, characterized in that, When the cooling system is arranged in a series structure, the expression based on the principle of flow conservation and pressure balance is a quadratic equation in one variable concerning the flow rate. After solving the equation to obtain the flow rate, it is substituted into the resistance equations of each component and pipeline to obtain the pressure drop of each component. When the cooling system is arranged in a parallel structure, it is divided into a main pipeline and n parallel branches. The expression based on the principles of flow conservation and pressure balance is: ; In the formula, To control the traffic flow on the main road, For the flow of n parallel branches, The equivalent flow resistance of the main pipeline is a quadratic equation in one variable. The equivalent flow resistance quadratic equation for n parallel branches; When the layout architecture is a hybrid structure, the hybrid structure is decomposed into a combined structure consisting of serial sub-modules and several parallel sub-modules, and the calculations are performed according to the above method.
6. The vehicle cooling system flow distribution optimization method according to claim 1, characterized in that, The planning solution method is the nonlinear generalized reduced gradient method.
7. The vehicle cooling system flow distribution optimization method according to claim 1, characterized in that, The adjustment methods for the flow resistance coefficient of the pipeline include adjusting the pipe diameter and the pipeline direction.
8. The vehicle cooling system flow distribution optimization method according to claim 1, characterized in that, The calculation software, which is independently built based on the planning and solving method, is used to solve for the flow of all branches. This is achieved through calculation software developed using Python and PySide6.
9. A vehicle cooling system flow distribution optimization device, characterized in that, It includes a cooling system data acquisition module, a cooling pipe flow resistance analysis module, a flow-pressure function establishment module, and a branch flow optimization module; The cooling system data acquisition module is used to acquire the coolant piping model and layout architecture of the cooling system, as well as the flow-pressure drop data of the components of the cooling system; The cooling pipeline flow resistance analysis module is used to obtain the flow rate-pressure drop data of the pipeline; The flow-pressure function establishment module is used to fit the flow-pressure drop data of the component and the flow-pressure drop data of the pipeline into quadratic equations, and fit multiple quadratic equations, wherein the intercept of the other equations is 0, except for the equation corresponding to the power source. The branch flow optimization module is used to solve for the flow of all branches based on the planning solution method. If the flow of any branch is less than the minimum rated flow of the corresponding component, the flow resistance coefficient is adjusted by changing the pipeline design, adjusting the layout of the cooling system, or replacing the high-head power source, until the flow of all branches is greater than or equal to the minimum rated flow.