A transient large flow soft measurement device and method based on pressure fluctuation
Patent Information
- Application Number
- CN202611048966.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-15
- Publication Date
- 2026-11-03
- Estimated Expiration
- 2046-07-15
AI Technical Summary
In existing technologies, when measuring the transient high flow rate of hydraulic valves, traditional flow meters have a slow response and are easily affected by fluid inertia and mechanical inertia, resulting in distorted measurement signals and high equipment costs.
A transient high-flow soft measurement device based on pressure fluctuations is adopted, including a main measurement pipeline, a pre-boost pump, a pressure sensor, a temperature sensor, and a transient flow solver. The flow rate is calculated by measuring the pressure and temperature values, the flow simulation measurement algorithm is optimized, and the pressure-flow characteristic curve is plotted.
It enables rapid and accurate measurement of transient large flow rates under highly dynamic flow conditions, reducing equipment size and power consumption, and lowering measurement costs.
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Figure CN122544878B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of hydraulic valve flow measurement technology, specifically to a transient high-flow soft measurement device and method based on pressure fluctuations. Background Technology
[0002] Measuring the pressure-flow characteristic curve of a hydraulic valve is fundamental to the design and analysis of fluid dynamic systems. With advancements in testing technology, the accuracy of flow measurement has significantly improved. ISO 4411 provides a standardized procedure for measuring pressure-flow characteristics. However, when this method is applied to the direct measurement of the pressure-flow characteristics of high-flow hydraulic valves, the testing equipment needs to stably provide a constant high flow rate, resulting in high costs and implementation difficulties in practical engineering.
[0003] Currently, to avoid the need for a large steady-state flow rate, the dynamic process of the fluid system itself can often be used to indirectly provide the required large flow rate. However, traditional flow meters are mostly suitable for steady-state or quasi-steady-state flow conditions. Their working principle determines that they have a hysteresis defect in response to rapid changes in the fluid state. Furthermore, in highly dynamic, short-term flow processes, they are easily affected by fluid inertia and mechanical inertia, resulting in distorted measurement signals and the inability to measure true transient flow signals. Summary of the Invention
[0004] To address the aforementioned technical problems, this invention provides a transient high-flow soft measurement device and method based on pressure fluctuations, which can solve the technical problems of expensive measurement equipment and low measurement accuracy under high dynamic conditions in the prior art.
[0005] The purpose of this invention is to address the shortcomings of existing technologies by proposing a transient high-flow-rate soft measurement device based on pressure fluctuations. This device includes:
[0006] The main measuring pipeline is equipped with a pre-pressurization pump, a valve under test, a first pressure sensor, a second pressure sensor, and a temperature sensor. The first and second pressure sensors are respectively installed at the inlet and outlet of the valve under test.
[0007] Install a quick-on / off valve on the outlet pipeline;
[0008] The branch pipe is connected to the test valve of the main measuring pipe and the quick-opening valve of the outlet pipe. The branch pipe is equipped with a shut-off valve and a flow meter to measure the steady-state flow of the system.
[0009] The transient flow solver is connected to the first pressure sensor, the second pressure sensor, and the temperature sensor respectively, and is used to obtain the flow value of the main measuring pipeline based on the measured values of the pressure sensor and the temperature sensor.
[0010] Furthermore, the main pipe and the outlet pipe are of equal length and are arranged in a spiral curling pattern.
[0011] Furthermore, the temperature sensor is used to measure the temperature of the fluid in the main measuring pipeline, and an accumulator is installed in the main measuring pipeline to assist in providing the required transient high flow rate.
[0012] Furthermore, an outlet oil filter is installed between the shut-off valve and the oil tank in the branch pipeline. The outlet oil filter is used to filter the oil flowing back to the oil tank. The steady-state flow measurement value is used to verify the accuracy of the flow simulation measurement algorithm based on pressure measurement value and temperature value.
[0013] Furthermore, the pressure sensor uses a non-invasive method to measure the fluid pressure changes in the main measuring pipe; the transient flow solver is configured to obtain the flow rate of the fluid in the pipe based on the pressure and temperature values and the flow simulation measurement algorithm that has been verified for accuracy.
[0014] Furthermore, under slightly transient flow conditions, the transient flow solver verifies the accuracy of the flow simulation measurement algorithm based on the calculated flow value and the flow meter measurement value. This verifies the accuracy of the flow simulation measurement algorithm and guides its optimization, ensuring that the calculated value continuously approaches the actual measured value, i.e., the error between the calculated value and the measured value meets the set actual accuracy requirements. Under significantly transient flow conditions, the optimized flow simulation measurement algorithm takes the measurements from the first pressure sensor and temperature sensor as input to simulate and measure the transient large flow value through the valve under test. Combined with the fluid pressure measurement value from the second pressure sensor, the pressure drop of the valve under test is determined, and the pressure-flow characteristic curve of the valve under test is plotted.
[0015] On the other hand, the present invention provides a transient high-flow soft measurement method based on pressure fluctuations, the method comprising the following steps:
[0016] The flow measurement data of the liquid in the branch pipe under steady-state flow and constant flow state of the flow meter are obtained, as well as the pressure and temperature of the fluid in the main measuring pipe, and the accurate pressure-flow characteristic curve of the valve under test is obtained.
[0017] Acquire transient pressure and temperature values of fluid under slight transient flow conditions, and use a transient flow solver to calculate the fluid flow rate in the main measuring pipe based on the fluid pressure and temperature.
[0018] The accuracy of the main measuring pipeline flow simulation measurement algorithm is verified based on the calculated fluid flow rate and the flow meter's measured flow rate. Errors are analyzed, the flow simulation measurement algorithm is optimized, and the error of the calculated flow rate is continuously reduced until the accuracy requirements are met.
[0019] The transient pressure and temperature values of the fluid under significant transient flow conditions are obtained. Based on the measured pressure and temperature and the optimized flow simulation measurement algorithm, the transient high flow rate value of the fluid in the main measuring pipe is obtained.
[0020] The pressure-flow characteristic curve of the valve under test was plotted based on the transient high flow rate value and the transient pressure value under the significant transient flow state.
[0021] Furthermore, taking the main measuring pipe and branch pipes as the research objects, the flow rate and pressure drop of the tested valve were measured under steady-state flow, and the pressure-flow characteristic curve of the tested valve was plotted to obtain accurate data of the curve.
[0022] Furthermore, a temperature sensor is used to measure the temperature of the fluid in the main measuring pipeline, and an accumulator is used to assist in providing the required transient high flow rate when the fast-switching valve is opened.
[0023] Furthermore, the pipe diameter D of the main measuring pipe is used to determine the upper limit of the flow calculation value, and the length L of the main measuring pipe is used to determine the pressure measurement window time. The outlet pipeline is used to reduce interference, and its relationship is as follows:
[0024]
[0025] in, Let be the speed of sound of the fluid at temperature T.
[0026] Furthermore, taking the main measuring pipe (1) and the outlet pipe (2) as the research objects, flow simulation measurement was performed. The branch pipe shut-off valve was closed, the outlet pipe quick-switch valve was closed, and the main measuring pipe was pressurized to a certain pressure using a pre-boost pump. The quick-opening valve is activated, and the first pressure sensor measures the transient fluid pressure value. The relationship between the instantaneous flow rate of the main measuring pipe (1) and the instantaneous pressure and temperature of the fluid is established as follows:
[0027]
[0028] In the formula To simulate and calculate the main measured flow rate value of the pipeline, This represents the initial pressure of the fluid in the pipe. Let be the instantaneous pressure value of the fluid in the pipe at time t. The density of the fluid in the main measuring pipe at the current temperature. The speed of sound in the fluid at the current temperature. The main measurement is of the inner radius of the pipe.
[0029] The beneficial effects of this invention are:
[0030] The transient high-flow soft measurement device based on pressure fluctuation provided by this invention pre-pressurizes the oil in the oil pipeline and then quickly opens the switching valve to generate a transient high flow rate, avoiding the need to provide a continuous constant high flow rate. Moreover, by spirally arranging the oil pipeline, this device is significantly smaller in size and consumes less power compared to traditional flow measurement devices, and has strong industrial application value.
[0031] The provided high-flow-rate measurement method based on pressure fluctuations measures the fluid pressure and temperature values, as well as the steady-state flow rate of the fluid, at the installation point using pressure sensors, temperature sensors, and flow meters installed in the pipeline. Then, the accuracy of the flow simulation measurement algorithm is verified using actual flow measurement values, the sources of error are analyzed, and the flow simulation measurement algorithm is optimized. Compared with traditional flow meters, this soft measurement method has a fast response speed and high measurement accuracy. Attached Figure Description
[0032] To more clearly illustrate the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0033] Figure 1 A schematic diagram of a transient high-flow soft measurement device based on pressure fluctuations according to a specific embodiment of the present invention is shown.
[0034] Figure 2 A schematic flowchart of a transient high-flow soft measurement method based on pressure fluctuations according to a specific embodiment of the present invention is shown. Detailed Implementation
[0035] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. It is understood that the specific embodiments described herein are intended to explain the technical solutions of the present invention, and not to limit it.
[0036] It should be noted that, without conflict, different embodiments of the present invention and their technical features can be combined with each other. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.
[0037] The following description will illustrate embodiments of the present invention with reference to the accompanying drawings. The dimensions and proportions shown in the drawings are merely illustrative and not intended to limit the actual structure. The step numbers or order mentioned herein are for convenience of explanation of specific embodiments and are not intended to limit the order of execution of steps. Furthermore, unless the context clearly indicates otherwise, the singular forms "a," "the," etc., used in this invention are intended to include the plural forms as well. The terms "comprising" or "including" indicate the presence of the stated feature, step, or component, but do not exclude the presence or addition of one or more other features, steps, components, or combinations thereof.
[0038] In one aspect of this invention, a transient high-flow soft measurement device based on pressure fluctuations is provided, see [link to relevant documentation]. Figure 1 As shown, it includes a main measuring pipe 1, an outlet pipe 2, a first pressure sensor 3, a second pressure sensor 4, a flow meter 8, an accumulator 6, a pre-boost pump 5, a shut-off valve 7, a test valve 9, a quick-switching valve 10, a temperature sensor 12, a branch pipe 11, and an outlet oil filter 13.
[0039] The main measuring pipe 1 is a fixed-length steel pipe with a uniform cross-section, providing a passage for fluid flow and also serving as mounting points for several components. The main measuring pipe 1 houses a pre-boost pump 5, an accumulator 6, a test valve 9, a first pressure sensor 3, a second pressure sensor 4, and a temperature sensor 12. The test valve 9 is installed at the edge of the main measuring pipe 1. The first pressure sensor 3 and the second pressure sensor 4 are installed at the inlet and outlet of the test valve 9, respectively. The temperature sensor 12 is also installed at the outlet of the test valve 9. At the edge of the main measuring pipe 1, it connects to the outlet pipe 2 and a branch pipe 11. The outlet pipe 2 is equipped with a quick-connect valve 10, and its outlet leads to an oil tank. The outlet pipe 2 is a steel pipe of approximately the same length and diameter as the main measuring pipe 1. The branch pipe 11 is equipped with a shut-off valve 7, a flow meter 8, and an outlet oil filter 13. The end of the branch pipe 11 also leads to an oil tank, and its diameter is the same as that of the main measuring pipe 1.
[0040] The transient flow rate calculator is connected to the first pressure sensor 3, the second pressure sensor 4, and the temperature sensor 12, respectively, and is used to obtain the flow rate value of the main measuring pipe 1 based on the measured values of the pressure and temperature sensors. The transient flow rate calculator uses the pressure measurement value of the first pressure sensor 3 as the input value, and uses the fluid temperature measurement value of the temperature sensor 12 to correct the fluid characteristic parameters. The measurement value of the second pressure sensor 4 is used to determine the pressure drop at the valve port under test.
[0041] In this invention, in order to improve measurement accuracy and ensure that the flow state of the fluid is not disturbed, the pressure sensor is installed in the pipeline in a non-invasive manner. In the case of high dynamic and short-term flow, non-invasive pressure measurement helps to accurately measure transient pressure.
[0042] Under slightly transient flow conditions, the transient flow solver optimizes the flow simulation measurement algorithm based on the calculated flow value and the flow meter measurement value, ensuring that the calculated value continuously approaches the actual measured value, i.e., the error between the calculated value and the measured value meets the set actual accuracy requirements. Under significantly transient flow conditions, the optimized flow simulation measurement algorithm uses the measurements from the first pressure sensor and temperature sensor as input to simulate and measure the transient large flow value through the valve under test. Combined with the fluid pressure measurement value from the second pressure sensor, the pressure drop of the valve under test is determined, and the pressure-flow characteristic curve of the valve under test is plotted.
[0043] In this invention, in order to improve space utilization, as a specific embodiment of the invention, the main measuring pipe and the outlet pipe are arranged in a spiral curling shape.
[0044] Another aspect of this invention provides a transient high-flow-rate soft measurement method based on pressure fluctuations, see [link to relevant documentation]. Figure 2 As shown, this method is applied to the aforementioned transient high-flow soft measurement device based on pressure fluctuations. The method includes: studying the main measuring pipe and branch pipes, and measuring the steady-state flow rate of the valve under test using a flow meter; studying the main measuring pipe and outlet pipe, measuring the transient pressure fluctuation before the valve under test using a first pressure sensor, measuring the fluid temperature in the main measuring pipe using a temperature sensor, and measuring the transient pressure fluctuation after the valve under test using a second pressure sensor; and obtaining the pipe flow rate based on the measurement value of the first pressure sensor and the temperature value.
[0045] To gain a further understanding of the present invention, the following is based on... Figure 2 This invention provides a detailed description of a transient high-flow soft measurement method based on pressure fluctuations.
[0046] like Figure 2 As shown, by setting the initial boundary conditions of the system, a pre-boost pump is used to pressurize the fluid in the pipeline, creating a pressure difference before and after the fast-opening valve. The fast-opening valve is then opened, generating a transient flow based on the high driving pressure difference. This transient flow propagates along the pipeline, and pressure and temperature sensors accurately measure the transient flow pressure and temperature values. Based on the transient pressure and temperature measurements, the fluid flow rate in the main measuring pipeline is obtained. This step is executed by a transient flow rate solver. The accuracy of the calculated flow rate is analyzed based on the steady-state flow rate of the valve under test measured by the branch pipeline flow meter. Error sources are analyzed, and the flow simulation measurement algorithm is optimized to ensure the accuracy of the calculated value meets preset requirements. Based on the optimized flow simulation measurement algorithm, different initial boundary conditions are set for the system, and the transient pressure and temperature of each transient flow are measured. These are input into the transient flow rate solver to obtain the flow rate of the valve under test under different pressure drops. A complete pressure-flow characteristic curve of the valve under test is plotted. This demonstrates a soft measurement method for large flow rates of the valve under test that can be achieved without the need for a pump station to supply a stable, large flow rate, based on the generated pressure fluctuations.
[0047] The measurement principle of the transient high-flow soft measurement method based on pressure fluctuations is as follows:
[0048] When a valve in a pipeline suddenly opens or closes, the fluid velocity changes drastically, generating a transient flow. The driving pressure difference causes the transient flow velocity to be extremely high, propagating along the pipeline and providing the large flow rate required for the flow measurement of the valve under test. Based on the transient pressure and fluid temperature values measured by the sensor, the transient large flow rate of the fluid in the pipeline is calculated.
[0049] The relationship between the instantaneous flow rate of the pipeline and the instantaneous pressure and temperature of the fluid is as follows:
[0050]
[0051] in, Preset the pressure for the pre-boost pump. Let be the instantaneous pressure value of the fluid in the pipe at time t. The main measurement is of the inner radius of the pipe. For fluid density, Let be the propagation speed of the wave in the fluid.
[0052] When a valve in a pipeline suddenly opens or closes, the relationship between the water hammer pressure and the fluid velocity is as follows:
[0053]
[0054] in, For preset pressure difference, This represents the fluid velocity.
[0055] The speed of wave propagation in the pipe is:
[0056]
[0057] in, The speed of sound in oil. For bulk modulus, The elastic modulus of the pipe wall material. The main measurement is the inner diameter of the pipe. This refers to the pipe wall thickness.
[0058] Optionally, the main measuring pipe length L is used to determine the pressure measurement window time. The length of the outlet pipe can be set to be equal to the length of the main measuring pipe to reduce interference caused by wave reflection due to boundary conditions and improve measurement accuracy. The relationship is as follows:
[0059]
[0060] As can be seen from the above disclosure, the principle of the transient high-flow soft measurement device and method based on pressure fluctuations in this embodiment specifically includes:
[0061] 1) Under steady-state low-flow conditions, collect the flow rate of the valve under test measured by the flow meter and the pressure difference measured by the pressure sensor, and plot the pressure-flow characteristic curve of the valve under test;
[0062] 2) Set the initial conditions of the system to keep the driving pressure differential at a low level, open the switching valve to generate transient flow, the sensor measures the transient flow pressure and temperature, calculate the transient flow rate, analyze the error, and optimize the flow simulation measurement algorithm;
[0063] 3) Set the initial conditions of the system to make the driving pressure difference a high level. Based on the optimized flow simulation measurement algorithm, with the sensor measurement value as the input value, calculate the transient large flow rate through the valve under test.
[0064] 4) Using the calculated transient high flow rate and the measured transient pressure difference of the valve under test, plot the complete pressure-flow characteristic curve of the valve under test to realize soft measurement of transient high flow rate based on pressure fluctuation.
[0065] In this specification, for ease of description, terms such as "an embodiment / method," "example," or "specific example" may be used to indicate that the described features, structures, materials, or characteristics may be included in at least one embodiment or example of this application. These illustrative references to terms do not necessarily refer to the same embodiment or example. The specific features, structures, materials, or characteristics may be combined in a suitable manner in any one or more embodiments or examples, and those skilled in the art can combine and modify different embodiments, examples, and their features without contradiction.
[0066] Furthermore, the terms "first," "second," etc., are used only to distinguish descriptions and do not imply relative importance or quantity limitations. "Multiple" refers to two or more. The terms "connected" and "linked" should be interpreted broadly, encompassing fixed, detachable, mechanical, electrical, direct, or indirect methods. When describing positional relationships, spatially relative terms such as "above" or "upper surface" may be used. These terms aim to cover situations where the device is used in different orientations (e.g., flipped, rotated); for example, "above" can include the opposite orientation, such as "below." It should be noted that the words "first," "second," etc., are only used to distinguish different components and, unless otherwise stated, have no special meaning and should not be construed as limiting the scope of protection of this application.
[0067] The above embodiments are only for illustrating the technical concept and features of the present invention. Their purpose is to enable those skilled in the art to understand the content of the present invention and implement it. They should not be used to limit the scope of protection of the present invention. All equivalent changes or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.
Claims
1. A transient high-flow soft measurement device based on pressure fluctuations, characterized in that, The device includes: The main measuring pipeline (1) is equipped with a pre-pressurization pump (5), a test valve (9), a first pressure sensor (3), a second pressure sensor (4), and a temperature sensor (12). The first pressure sensor and the second pressure sensor are respectively installed at the inlet and outlet of the test valve (9). The outlet pipe (2) is equipped with a quick-on / off valve (10). The branch pipe (11) is connected to the test valve (9) of the main measuring pipe (1) and the quick-switching valve (10) of the outlet pipe (2). The branch pipe (11) is equipped with a shut-off valve (7) and a flow meter (8) to measure the steady-state flow of the system. The transient flow solver is connected to the first pressure sensor (3), the second pressure sensor (4), and the temperature sensor (12) respectively. It is used to obtain the flow value of the main measuring pipe (1) based on the measured values of the first pressure sensor and the temperature sensor. Under significant transient flow conditions, the transient flow solver takes the measured values of the first pressure sensor and the temperature sensor as input, simulates and measures the transient large flow value through the valve under test, and determines the pressure drop of the valve under test by combining the fluid pressure measurement value of the second pressure sensor, and plots the pressure-flow characteristic curve of the valve under test.
2. The transient high-flow soft measurement device based on pressure fluctuations according to claim 1, characterized in that, The main measuring pipe (1) and the outlet pipe (2) are of equal length and are arranged in a spiral curling pattern.
3. The transient high-flow soft measurement device based on pressure fluctuations according to claim 1, characterized in that, The temperature sensor is used to measure the temperature of the fluid in the main measuring pipeline. An accumulator is installed in the main measuring pipeline (1) to assist in providing the required transient high flow rate.
4. The transient high-flow soft measurement device based on pressure fluctuation according to claim 1, characterized in that, The branch pipe (11) has an outlet oil filter (13) installed between the shut-off valve and the oil tank. The outlet oil filter (13) is used to filter the oil flowing back to the oil tank. The steady-state flow measurement value is used to verify the accuracy of the flow simulation measurement algorithm based on the measurement values of the first pressure sensor and temperature sensor.
5. The transient high-flow soft measurement device based on pressure fluctuation according to claim 3, characterized in that, The first pressure sensor and the second pressure sensor use a non-invasive method to measure the fluid pressure change in the main measuring pipe (1); the transient flow solver is configured to obtain the flow rate of the fluid in the main measuring pipe (1) based on the pressure value measured by the first pressure sensor, the temperature value measured by the temperature sensor, and the flow simulation measurement algorithm.
6. The transient high-flow soft measurement device based on pressure fluctuation according to claim 3, characterized in that, Under slightly transient flow conditions, the transient flow solver verifies the accuracy of the flow simulation measurement algorithm based on the calculated flow value and the flow meter measurement value. This verifies the accuracy of the flow simulation measurement algorithm and guides its optimization, ensuring that the calculated value continuously approaches the actual measurement value. In other words, the error between the calculated value and the measured value meets the set accuracy requirements.
7. A transient high-flow rate soft measurement method based on pressure fluctuation using the measuring device according to any one of claims 1-6, characterized in that, The method includes the following steps: The flow measurement data of the liquid in the branch pipe under steady-state flow conditions and the pressure and temperature of the fluid in the main measuring pipe are obtained to obtain the accurate pressure-flow characteristic curve of the valve under test. The transient pressure and temperature values of the first pressure sensor are obtained when the fluid is in a slightly transient flow state. The transient flow rate calculator is used to obtain the fluid flow rate calculation value in the main measuring pipe based on the fluid pressure and temperature. The accuracy of the main measuring pipeline flow simulation measurement algorithm is verified based on the calculated fluid flow rate and the flow meter's measured flow rate. Errors are analyzed, the flow simulation measurement algorithm is optimized, and the error of the calculated flow rate is continuously reduced until the accuracy requirements are met. The transient pressure and temperature values of the fluid under significant transient flow conditions are obtained from the first pressure sensor. Based on the measured pressure and temperature of the first pressure sensor and the optimized flow simulation measurement algorithm, the transient high flow rate value of the fluid in the main measuring pipe is obtained. The pressure-flow characteristic curve of the valve under test was plotted based on the transient high flow rate value and the transient pressure value under the significant transient flow state.
8. The transient high-flow-rate soft measurement method based on pressure fluctuations according to claim 7, characterized in that, The upper limit of the flow calculation value is determined based on the pipe diameter D of the main measuring pipe, and the pressure measurement window time at temperature T is determined based on the length L of the main measuring pipe and the sound velocity of the fluid at temperature T. The export pipeline is used to reduce interference.
9. The transient high-flow soft measurement method based on pressure fluctuations according to claim 7, characterized in that, Taking the main measuring pipe (1) and the outlet pipe (2) as the research objects, flow simulation measurement was performed. The branch pipe shut-off valve was closed, the outlet pipe quick-switch valve was closed, and the main measuring pipe was pressurized to a certain pressure using a pre-boost pump. The quick-opening valve is activated, and the first pressure sensor measures the transient fluid pressure value. The relationship between the instantaneous flow rate of the main measuring pipe (1) and the instantaneous pressure and temperature of the fluid is established as follows: In the formula To simulate and calculate the flow rate of the main measuring pipe, This represents the initial pressure of the fluid in the pipe. Let be the instantaneous pressure value of the fluid in the pipe at time t. The density of the fluid in the main measuring pipe at the current temperature. The speed of sound in the fluid at the current temperature. The main measurement is of the inner radius of the pipe.
Citation Information
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