Apparatus and method for measuring friction factor of non-full pipe fluid in hydraulic smooth region

Abstract

The application discloses a device and method for measuring the friction coefficient of non-full pipe fluid in a hydraulic smooth area, which comprises a plastic ball feeding system, a fluid circulating system, a liquid level monitoring device and a data processing and display device. The fluid circulating system comprises a circulating pump, an inclined pipe, a liquid storage tank and a return pipe, and the fluid is circulated in the pipes and the liquid storage tank through the circulating pump suction. The plastic ball feeding system comprises plastic balls, a ball storage box and a timing feeder, and can feed the plastic balls at the same interval. The liquid level monitoring device can measure the volume flow rate of the non-full pipe fluid flowing through the inclined pipe by monitoring the plastic balls and the hydraulic radius of the fluid flowing through the section where the device is located. The data processing and display device can calculate the Reynolds number of the fluid and the friction coefficient of the fluid in the hydraulic smooth area. The method improves the calculation precision of the friction coefficient of the non-full pipe fluid in the hydraulic smooth area, and provides accurate basic parameters for a fluid flow calculation model based on the friction coefficient.

Description

Technical Field

[0001] This invention relates to the field of flow measurement in industry, and more particularly to an apparatus and method for measuring the friction coefficient of a fluid in a hydraulically smooth region. Background Technology

[0002] In open channels or pipelines, when using formulas to calculate flow rate, the friction coefficient is a fixed value when the fluid is in steady flow. However, when the fluid flow is turbulent, the friction coefficient is the only parameter that cannot be directly measured. The friction coefficient in the smooth and transitional regions of turbulent flow is highly dependent on the Reynolds number of the fluid or the roughness of the pipe material. Pipelines offer high transportation efficiency and minimal environmental impact, and are widely used in urban water supply, agricultural irrigation, and inter-regional water transfer in water conservancy and industry. The appropriate selection of hydraulic calculation formulas and friction coefficients for pipelines is crucial for fluid transport engineering design. Commonly used hydraulic calculation formulas and corresponding friction coefficients in existing standards and engineering designs include: the Darcy-Weissbar formula and the Darcy friction coefficient λ, and the Heisenberg-Williams formula and the Heisenberg-Williams coefficient C. h The Chezy-Manning formula and the Manning roughness coefficient n are crucial factors. Therefore, when using mathematical models for hydraulic calculations, the friction coefficient is one of the three important calculation parameters. If the friction coefficient is an estimated value or obtained by looking up a table, it will differ significantly from the actual flow state, leading to a significant reduction in the accuracy of the calculated flow rate. If the flow rate prediction error is large, applying this predicted flow rate in practical engineering applications will result in serious safety accidents or huge economic losses. However, existing domestic standards provide a wide range of friction coefficient values ​​and do not comprehensively consider the factors affecting the friction coefficient, making it difficult to accurately determine the friction coefficient in engineering design, especially for large-diameter water pipelines, resulting in significant errors in the hydraulic calculations of some projects.

[0003] In the hydraulically smooth region, the friction coefficient is only related to the Reynolds number of the fluid, which is influenced by velocity. Changes in velocity will lead to changes in the Reynolds number, resulting in significant errors when calculating fluid flow rate using a fixed Reynolds number. Flow rate, like temperature and pressure, is a crucial parameter in industrial production. These parameters are used to monitor and control production processes, which is a vital standard for ensuring production safety. In China, most calculations of the friction coefficient are based on Nikolai's 1933 experiment with artificially roughened tubes. The influencing factors of the friction coefficient vary in different hydraulic resistance regions. While current Chinese design codes provide formulas for calculating pipeline pressure drop, they do not specify the selection of the friction coefficient λ, requiring designers to choose it based on measured data or practical experience. Currently, there are over 100 formulas for calculating the friction coefficient, with significant differences in their applicable conditions and acquisition methods. Based on the above, this invention provides an apparatus and method for measuring the friction coefficient of fluid in a hydraulically smooth region in a non-full pipe. This apparatus and method can effectively solve the problem of not being able to accurately obtain the friction coefficient in a hydraulically smooth region, and provide accurate basic parameters for fluid flow calculation models based on the friction coefficient.

[0004] The present invention provides a device and method for measuring the friction coefficient of a non-full pipe fluid in a hydraulically smooth region, which can be applied to fields such as petroleum engineering, water conservancy engineering, and urban heating. Summary of the Invention

[0005] The purpose of this invention is to solve the problem that the friction coefficient required for calculating the flow rate of a non-full pipe fluid using the Manning formula cannot be accurately determined. To this end, an apparatus for measuring the friction coefficient of a non-full pipe fluid in a hydraulically smooth region has been invented, and based on this apparatus, a method for measuring the friction coefficient of a non-full pipe fluid in a hydraulically smooth region is proposed.

[0006] The present invention provides a device for measuring the friction coefficient of a non-full pipe fluid in a hydraulically smooth region, the structure of which mainly includes: a fluid circulation system (1, 5, 6, 7, 8), a plastic ball delivery system (2), a liquid level monitoring device (3), and a data processing and display device (9).

[0007] The fluid circulation system consists of a circulation pump (1), an inclined pipe (5), a water storage tank (7), and a return pipe (6). The fluid to be tested (8) is circulated in the inclined pipe (5), the water storage tank (7), and the return pipe (6) by the circulation pump (1).

[0008] The plastic ball delivery system (2) includes plastic balls (4), a ball storage box (12) and a timed delivery device (13). The timed delivery device (13) delivers the plastic balls (4) in the ball storage box (12) into the inclined tube (5) at the same interval.

[0009] The liquid surface flow section monitoring device (3) obtains the time it takes for the plastic ball (4) to travel from the section where the timed dispenser (13) is located to the section where the liquid surface flow section monitoring device (3) is located by monitoring the non-full pipe flow liquid surface state of the section. It calculates the flow velocity of the fluid particles in the inclined pipe (5) by combining the distance between the two sections, and then combines the monitored fluid hydraulic radius to realize the measurement of the volume flow velocity of the fluid flowing through the inclined pipe (5).

[0010] The data processing and display device (9) processes the signals transmitted from the plastic ball delivery system (2) and the liquid surface flow section monitoring device (3), and combines the input fluid density ρ and viscosity μ to calculate the flow velocity v of the fluid particles in the non-full pipe, the height h of the non-full pipe flow liquid surface to the highest pipe wall in the inclined pipe, the Reynolds number Re of the fluid to be measured, and the friction coefficient λ of the non-full pipe fluid in the hydraulically smooth region, and displays the above input parameters and calculation results on the digital display.

[0011] Furthermore, the fluid circulation system includes a circulation pump (1), an inclined pipe (5), a storage tank (8), and a return pipe (6); the circulation pump (1) is connected to the inclined pipe (5), the inclined pipe (5) is connected to the storage tank (8), the bottom opening of the storage tank (8) is connected to the return pipe (6), and the return pipe is then connected to the circulation pump (1). The fluid to be tested (8) is circulated in the inclined pipe (5), the storage tank (8), and the return pipe (6) by the circulation pump (1).

[0012] Furthermore, the plastic ball dispensing system (2) includes a plastic ball (4), a ball storage box (12), and a timed dispenser (13); the plastic ball (4) is stored in the ball storage box (12), the ball storage box (12) is connected to the timed dispenser (13), and the timed dispenser (13) is connected to the slot at the top of the inclined tube (5) by a plastic ball dispenser fixing screw (14) to realize the dispensing of plastic balls (4) to the inclined tube (5) at the same interval time. The signal of the timed dispenser (13) dispensing plastic balls is transmitted to the data processing and display device (9) through the plastic ball dispensing signal data line (10).

[0013] Furthermore, the liquid level monitoring device (3) is an ultrasonic sensor (16) capable of monitoring fluid interface characteristics, an ultrasonic sensor protective shell (15), a liquid level monitoring signal data line (11), and a liquid level monitoring device fixing screw (17). The liquid level monitoring device (3) is installed on the inclined tube (5) by the liquid level monitoring device fixing screw (17). The ultrasonic sensor (16) monitors the plastic ball (4) flowing through the grooved section of the inclined tube (5) and the hydraulic radius of the fluid, and transmits the monitoring signal to the data processing and display device (9) through the liquid level monitoring signal data line (11). The movement time of the plastic ball (4) from the section where the timed dispenser (13) is located to the section of the ultrasonic sensor (16) is determined by combining the plastic ball release time.

[0014] Furthermore, this device, combined with this method, can constitute a method for measuring the friction coefficient of a non-full pipe fluid in a hydraulically smooth region, including the following steps:

[0015] S1: Measure the density ρ of the fluid to be tested (8), the viscosity μ of the fluid to be tested (8), and the inner diameter d of the inclined tube (5).

[0016] S2: Inject the fluid to be tested (8) into the storage tank (7), and use the circulation pump (1) to draw the fluid to be tested (8) into the fluid circulation system at a certain flow rate for more than 5 minutes. Start the plastic ball delivery system (2) to deliver plastic balls (4) at the same interval. When the liquid level monitoring device (3) monitors the plastic balls (4) and the time interval is the same, it is determined that the liquid flow rate is stable. After stopping the delivery of plastic balls (4), the liquid level monitoring device (3) measures the height of the non-full pipe liquid level to the highest pipe wall of the inclined pipe (5) and records it as h. Calculate the cross-sectional area A of the inclined pipe (5) using formula (1).

[0017]

[0018] In the formula, A is the cross-sectional area of ​​the inclined pipe (5) where the water flows through a non-full pipe, in m². 2 ;d is the inner diameter of the inclined tube (5), m;h is the height of the non-full flow liquid surface of the inclined tube to the highest point of the tube wall, m.

[0019] S3: Calculate the wetted perimeter C of the non-full pipe flow section of the inclined pipe (5) using formula (2).

[0020]

[0021] In the formula, C is the wetted perimeter length, in meters (m).

[0022] S4: Calculate the hydraulic radius r of the non-full pipe flow section of the inclined pipe (5) using formula (3).

[0023]

[0024] In the formula, r is the hydraulic radius of the non-full pipe cross section of the inclined pipe (5), in meters.

[0025] S5: Plastic ball (4) is launched through plastic ball launching system (2). The time of launching plastic ball (4) is recorded as t1. Liquid level monitoring device (3) monitors the plastic ball (4) flowing through the section monitored by ultrasonic sensor (16). The time is recorded as t2. The length from the section where timed launcher (13) is located to the section monitored by ultrasonic sensor (16) is recorded as l. Plastic ball (4) flows with the fluid to be tested (8) in inclined tube (5). The moving speed of plastic ball (4) is the flow speed of fluid particles in non-full tube, v. v is calculated by formula (4).

[0026]

[0027] In the formula, v is the flow velocity of fluid particles in a non-full pipe, m / s; l is the length from the section where the timed dispenser (13) is located to the section monitored by the ultrasonic sensor (16), m; t2-t1 is the movement time of the plastic ball (4) from the section where the timed dispenser (13) is located to the section monitored by the ultrasonic sensor (16), s.

[0028] S6: The Reynolds number of the fluid (8) to be tested in the inclined tube (5) is calculated by formula (5).

[0029]

[0030] In the formula, Re is the Reynolds number of the fluid to be measured, which is dimensionless; ρ is the density of the fluid to be measured (8), in kg / m³. 3 μ is the viscosity of the fluid to be tested (8), in Pa·s.

[0031] S7: The friction coefficient λ of non-full pipe fluid in the hydraulically smooth region is calculated using formula (6).

[0032]

[0033] In the formula, λ is the friction coefficient of a non-full pipe fluid in the hydraulically smooth region, which is dimensionless.

[0034] In summary, by adopting the above technical solution, the beneficial effects of this invention are as follows: This invention utilizes the actual fluid being measured to simulate the flow state of a non-full pipe, directly measuring the friction coefficient calculation parameters of the non-full pipe fluid in the hydraulically smooth region, thereby obtaining an accurate friction coefficient of the non-full pipe fluid in the hydraulically smooth region. This invention effectively solves the problem of the inability to accurately obtain the friction coefficient in the hydraulically smooth region, providing accurate basic parameters for fluid flow calculation models based on the friction coefficient. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of a device for measuring the friction coefficient of a fluid in a hydraulically smooth region when the pipe is not fully filled.

[0036] Figure 2A schematic diagram of a plastic ball launching system (2) for measuring the friction coefficient of a non-full pipe fluid in a hydraulically smooth region.

[0037] Figure 3 A schematic diagram of a liquid level monitoring system (3) for measuring the friction coefficient of a non-full pipe fluid in a hydraulically smooth region.

[0038] Figure 4 This is a schematic diagram of the cross-section of the inclined tube (5) of the liquid level monitoring system (3) of the device for measuring the friction coefficient of a non-full pipe fluid in the hydraulically smooth region according to the present invention.

[0039] Figure 5 This is a schematic diagram of a method for measuring the friction coefficient of a non-full pipe fluid in a hydraulically smooth region, involving the dropping of a plastic ball.

[0040] Figure 6 This is a physical diagram of a device for measuring the friction coefficient of a fluid in a hydraulically smooth region when the pipe is not fully filled.

[0041] Figure 7 To compare the flow rate calculated using Manning's formula with the actual flow rate measured by the flow meter.

[0042] In the diagram: 1. Circulating pump; 2. Plastic ball dispensing system; 3. Liquid level monitoring device; 4. Plastic ball; 5. Inclined tube; 6. Return tube; 7. Storage tank; 8. Liquid to be tested; 9. Data processing and display device; 10. Plastic ball dispensing signal data cable; 11. Liquid level monitoring signal data cable; 12. Ball storage tank; 13. Timed dispenser; 14. Plastic ball dispenser fixing screw; 15. Ultrasonic sensor protective shell; 16. Ultrasonic sensor; 17. Liquid level monitoring device fixing screw. Detailed Implementation

[0043] 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. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0044] In the accompanying drawings, the dimensions and thicknesses of each component shown are arbitrary, and the invention does not limit the dimensions and thickness of each component. For clarity, the dimensions of some parts are appropriately exaggerated in the drawings; for distinction, the areas filled with dashed lines represent fluids.

[0045] like Figure 1As shown, this invention provides a device and method for measuring the friction coefficient of a non-full pipe fluid in a hydraulically smooth region. A circulating pump (1) adjusts the fluid discharge during circulation and is tightly connected to an inclined pipe (5), a storage tank (7), and a return pipe (6) to form a complete fluid circulation system. A plastic ball dispensing system (2) is tightly connected to the slotted top section of the inclined pipe (5) to store and control the release of only one ball at a time. The plastic ball (4) is released by the plastic ball dispensing system (2), and the time of dispensing the plastic ball (4) is recorded as t1. When the plastic ball (4) flows through the cross-section monitored by the ultrasonic sensor (16), the time measured by the liquid level monitoring device (3) is recorded as t2. The distance from the plastic ball dispensing system (2) to the liquid level monitoring device (3) is recorded as l. The velocity v of the plastic ball (4) is calculated using l, t1, and t2. Treating v as the velocity of a non-full pipe fluid particle, the Reynolds number of the fluid can be obtained, and the friction coefficient of the fluid in the smooth region of water can be calculated. A physical diagram of the device is shown below. Figure 6 .

[0046] This example also discloses a method for measuring and calculating the coefficient of friction of a fluid. Taking pure water as an example, the method includes the following steps:

[0047] 1. Measure the density of the liquid to be tested as 1000 kg / m³. 3 Viscosity 0.00298 Pa·s, pipe inner diameter 0.2 m.

[0048] 2. After circulating the fluid for 5 minutes at a fixed displacement using the circulating pump (1) to stabilize the fluid flow, the liquid level height h is measured using the ultrasonic sensor (16) and recorded as 0.07m. The cross-sectional area A of the guide channel is calculated as 0.0266m² using formula (1). 2 .

[0049] 3. The wetted perimeter length C on the flow cross section is calculated to be 0.396m using formula (2).

[0050] 4. The hydraulic radius r of the flowing fluid is calculated to be 0.0672m using formula (3).

[0051] 5. Plastic ball (4) is launched through plastic ball launching system (2). The time of launching plastic ball (4) is recorded as t1 = 13.43s. The liquid level monitoring device (3) detects the rise of the liquid level. It is then determined that the plastic ball (4) has passed the monitoring section of the liquid level monitoring system. The time is recorded as t2 = 15.01s. The length from the section of the timed launcher (13) to the monitoring section of the ultrasonic sensor (16) is recorded as l = 1.45m. The plastic ball (4) flows with the fluid to be tested (8) in the inclined tube (5). The moving speed v of the plastic ball (4) is the flow speed v of the non-full tube fluid particles. v is calculated by formula (4) and v = 0.918m / s.

[0052] 6. The Reynolds number of the fluid (8) to be tested in the inclined tube (5) is calculated by formula (5), Re = 41406.553.

[0053] 7. The friction coefficient λ of non-full pipe fluid in the hydraulically smooth region is calculated using formula (6), λ=0.0218.

[0054] 8. The above calculation process is automatically processed and calculated by the data processing and display device (9). In the data processing and display device, the inner diameter d of the inclined tube (5) and the length l from the section where the timed dispenser (13) is located to the section monitored by the ultrasonic sensor (16) are inherent parameters of the device. The height h of the liquid surface of the non-full pipe to the highest pipe wall, the release time t1 of the plastic ball (4) and the monitoring time t2 of the plastic ball by the ultrasonic sensor (16) are the equipment monitoring data. The density ρ and viscosity μ of the fluid to be tested (8) are the input data. The flow velocity v of the non-full pipe fluid particles, the Reynolds number Re of the fluid to be tested, and the friction coefficient λ of the non-full pipe fluid in the hydraulically smooth region are the calculated data.

[0055] After measuring the friction coefficient of the fluid in a partially filled pipe according to the above steps, substitute the friction coefficient into the Manning formula to calculate the flow rate, and compare it with the flow rate measured by the flow meter. Figure 7 .from Figure 7 As can be seen, the flow rate of the non-full pipe fluid measured by the flow meter and the flow rate of the non-full pipe fluid calculated using the friction coefficient measured by this method have a high degree of consistency, with an average error of 2.16%. This demonstrates that the device and method proposed in this invention for measuring the friction coefficient of a non-full pipe fluid in a hydraulically smooth region are reliable in measuring the friction coefficient of the non-full pipe fluid in a hydraulically smooth region and can be applied to calculate flow rate using the Manning formula.

[0056] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A device for measuring the friction coefficient of a non-full pipe fluid in a hydraulically smooth region, characterized in that, Includes a fluid circulation system (1, 5, 6, 7, 8), a plastic ball delivery system (2), a liquid level monitoring device (3), and a data processing and display device (9); The fluid circulation system consists of a circulation pump (1), an inclined pipe (5), a storage tank (7), and a return pipe (6). The fluid to be tested (8) is circulated in the inclined pipe (5), the storage tank (7), and the return pipe (6) by the circulation pump (1). The fluid circulation system includes a circulation pump (1), an inclined pipe (5), a storage tank (7), and a return pipe (6); the circulation pump (1) is connected to the inclined pipe (5), the inclined pipe (5) is connected to the storage tank (7), the bottom opening of the storage tank (7) is connected to the return pipe (6), and the return pipe is then connected to the circulation pump (1). The fluid to be tested (8) is circulated in the inclined pipe (5), the storage tank (7), and the return pipe (6) by the circulation pump (1). The plastic ball delivery system (2) includes plastic balls (4), a ball storage box (12) and a timed delivery device (13). The timed delivery device (13) delivers the plastic balls (4) in the ball storage box (12) into the inclined tube (5) at the same interval. The liquid level monitoring device (3) obtains the time it takes for the plastic ball (4) to travel from the section where the timed dispenser (13) is located to the section where the liquid level monitoring device (3) is located by monitoring the non-full pipe flow liquid level state of the section where it is located. It calculates the flow velocity of the fluid particles in the inclined pipe (5) by combining the distance between the two sections. Then, it combines the monitored fluid hydraulic radius to realize the measurement of the volume flow velocity of the fluid flowing through the inclined pipe (5). The liquid level monitoring device (3) is an ultrasonic sensor (16) that can monitor the characteristics of the fluid interface, an ultrasonic sensor protective shell (15), a liquid level monitoring signal data line (11), and a liquid level monitoring device fixing screw (17). The liquid level monitoring device (3) is installed on the inclined tube (5) by the liquid level monitoring device fixing screw (17). The ultrasonic sensor (16) monitors the plastic ball (4) flowing through the grooved section of the inclined tube (5) and the hydraulic radius of the fluid, and transmits the monitoring signal to the data processing and display device (9) through the liquid level monitoring signal data line (11). The movement time of the plastic ball (4) from the section where the timed dispenser (13) is located to the section of the ultrasonic sensor (16) is determined by combining the plastic ball release time. The data processing and display device (9) processes the signals transmitted from the plastic ball delivery system (2) and the liquid level monitoring device (3), and combines them with the input density of the fluid to be measured. ρ and viscosity μ It can calculate the velocity of fluid particles flowing through a non-full pipe. v、 The height of the liquid level from the highest point of the pipe wall in a non-full-flow inclined pipe h , where Re is the Reynolds number of the fluid under test and the friction coefficient of the non-full pipe fluid in the hydraulically smooth region. λ The input parameters and calculation results are then displayed on a digital monitor.

2. A method for calculating the friction coefficient of a non-full pipe fluid in a hydraulically smooth region using the apparatus described in claim 1 for measuring the friction coefficient of a non-full pipe fluid in a hydraulically smooth region, characterized in that, The following steps are required: S1: Measure the density of the fluid to be tested (8). ρ Viscosity of the fluid to be tested (8) μ , Inclined tube (5) inner diameter d ; S2: Inject the fluid to be tested (8) into the storage tank (7), and use the circulation pump (1) to draw the fluid to be tested (8) into the fluid circulation system at a certain flow rate for more than 5 minutes. Then start the plastic ball delivery system (2) to deliver plastic balls (4) at the same interval. When the liquid level monitoring device (3) monitors that the time interval of the plastic balls (4) is the same, it is determined that the liquid flow rate is stable. After stopping the delivery of plastic balls (4), the liquid level monitoring device (3) measures the height of the non-full pipe liquid level to the highest pipe wall of the inclined pipe (5) and records it as follows. h The cross-sectional area of ​​the inclined tube (5) is calculated using formula (1). A ; （1）； In the formula, A The cross-sectional area of ​​the inclined pipe (5) for non-full pipe flow is m². 2 ; d The inner diameter of the inclined tube (5) is in meters (m). h The height (m) from the liquid level at the highest point of the pipe wall during non-full flow in the inclined pipe. S3: Calculate the wetted perimeter of the non-full-pipe flow section of the inclined pipe (5) using formula (2). C ; （2）； In the formula, C The wetted perimeter is in meters. S4: Calculate the hydraulic radius of the non-full-pipe flow section of the inclined pipe (5) using formula (3). r ; （3）； In the formula, r The hydraulic radius of the non-full pipe cross section of the inclined pipe (5) is in meters; S5: Start dropping plastic balls (4) through the plastic ball dropping system (2), and record the time of dropping plastic balls (4) as follows. t 1. The liquid level monitoring device (3) monitors the plastic ball (4) flowing through the cross section monitored by the ultrasonic sensor (16), and the time is recorded as follows: t 2. The length from the section where the timed delivery device (13) is located to the section monitored by the ultrasonic sensor (16) is recorded as follows: l If the plastic ball (4) flows with the fluid to be measured (8) in the inclined tube (5), then the moving speed of the plastic ball (4) is the flow speed of the fluid particles in the non-full tube. v , v It is calculated using formula (4); （4）； In the formula, v The velocity of fluid particles in a non-full pipe is m / s; l The length from the section where the timed delivery device (13) is located to the section monitored by the ultrasonic sensor (16) is, in meters; t 2- t 1 represents the time (s) it takes for the plastic ball (4) to move from the section where the timed dispenser (13) is located to the section monitored by the ultrasonic sensor (16); S6: The Reynolds number of the fluid (8) to be measured in the inclined tube (5) is calculated by formula (5); （5）； In the formula, Re is the Reynolds number of the fluid to be measured, which is dimensionless; ρ The density of the fluid to be tested (8) is kg / m³. 3 ; μ Let be the viscosity of the fluid to be tested (8), in Pa·s; S7: Friction coefficient of fluid in a non-full pipe in the hydraulically smooth region λ Calculated using formula (6); （6）； In the formula, λ is the friction coefficient of a non-full pipe fluid in the hydraulically smooth region, and is dimensionless.

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