Steam pipe loss abnormity positioning method combining simulation and machine learning

Abstract

The invention relates to the technical field of smart city operation, and discloses a steam pipe loss abnormity positioning method combining simulation and machine learning, and the method comprises the following steps: S1, collecting the pressure, temperature and flow data of a steam pipe network in real time, and carrying out the preprocessing; s2, constructing a multi-physical field coupling simulation model based on the pipe network topological parameters, and generating simulation predicted values of pressure, temperature and condensate water distribution; s3, fusing real-time data and a simulation prediction value to train a machine learning model, and outputting a fault probability and a fault type; s4, according to the simulation prediction deviation and a machine learning result, determining an abnormal type and positioning a fault pipe section; and S5, dynamically optimizing the model and detecting a threshold value based on feedback data. Through a multi-node real-time data acquisition and dynamic simulation calibration technology, second-level anomaly perception and alarm of pressure and temperature of a pipe network are realized, and potential safety hazards caused by fault information lag in the traditional technology are dealt with.

Description

Technical Field

[0001] The present invention relates to the technical field of smart city operation, and specifically to a method for abnormal positioning of steam pipe loss combining simulation and machine learning. Background Art

[0002] As a key energy supply infrastructure for modern cities and industries, the safe and efficient operation of the steam pipe network directly affects the energy consumption and economic benefits of enterprises. The current mainstream pipe loss detection technologies are mainly based on the principles of fluid mechanics and Internet of Things sensing means: the flow balance method determines leakage through the difference between the head and end flow meters, with low implementation cost and easy deployment; the pressure gradient method estimates the leakage location using the propagation characteristics of pressure waves and has certain applicability in simple pipe networks; the real-time transmission model method combines fluid dynamics equations with real-time data to construct a digital mapping of the pipe network state. In addition, auxiliary means such as acoustic detection and infrared thermal imaging are also applied in specific scenarios.

[0003] With the expansion of the scale of the steam pipe network and the complexity of the operating environment, the above methods are gradually facing new challenges in engineering practice. The flow balance method is limited by data acquisition delay and lack of positioning ability, making it difficult to block the expansion of pipe loss in a timely manner; the pressure gradient method has a significant decrease in positioning accuracy due to pressure wave attenuation and reflection interference in complex branched pipe networks; and existing real-time models mostly use fixed parameter settings and are difficult to adapt to gradual working conditions such as pipe aging and degradation of insulation performance. In addition, due to sparse monitoring nodes in the middle section (network side) of the pipe network, the sensitivity of fault perception is insufficient, resulting in early signals of leakage and corrosion being easily missed. How to achieve real-time monitoring, dynamic optimization and multi-fault collaborative diagnosis of the entire pipe network has become a technical bottleneck that the industrial community urgently needs to break through. Summary of the Invention

[0004] Aiming at the deficiencies of the prior art, the present invention provides a method for abnormal positioning of steam pipe loss combining simulation and machine learning, which solves the problems of low pipe loss positioning accuracy and response lag caused by insufficient real-time performance, monitoring blind spots on the network side and lack of insulation corrosion diagnosis in the existing steam pipe loss detection technology.

[0005] To achieve the above objectives, the present invention is realized through the following technical solutions: A method for abnormal positioning of steam pipe loss combining simulation and machine learning, comprising the following steps: S1. Real-time collect the pressure, temperature and flow data of the steam pipe network and perform preprocessing; S2. Based on the pipe network topology parameters, construct a multi-physical field coupling simulation model to generate simulation prediction values of pressure, temperature and condensate distribution; S3. Integrate real-time data and simulation prediction values to train a machine learning model and output the fault probability and type; S4. Determine the abnormal type and locate the faulty pipe section according to the simulation prediction deviation and the machine learning result; S5. Dynamically optimize the model and detection threshold based on the feedback data.

[0006] Preferably, in the S1 step, the preprocessing includes outlier removal and missing value filling. The outlier removal adopts principle, and the missing value filling adopts linear interpolation method or manual intervention alarm.

[0007] Preferably, in the S2 step, the multi-physical field coupling simulation model includes: The hydrodynamic model calculates the pressure, velocity distribution and pipeline pressure drop by solving the Navier-Stokes equation; The thermodynamic model calculates the specific enthalpy of superheated steam and the condensate water distribution, including the simulation of the sensible heat - latent heat conversion process.

[0008] Preferably, in the S3 step, the input features of the machine learning model include the combined time series data of real-time data and simulation prediction values, which are cut into time series segments of fixed length by a sliding window; The machine learning model is an LSTM network, whose hidden layer contains double-layer LSTM units, and the output layer generates the fault probability and type through the Sigmoid function and the Softmax function respectively.

[0009] Preferably, in the S4 step, the abnormal type determination includes: Leakage detection: The real-time pressure is lower than 90% of the simulation prediction value and the leakage probability output by the machine learning exceeds 85%; Thermal insulation corrosion detection: The temperature gradient exceeds 2 °C / m and the corrosion probability output by the machine learning exceeds 75%.

[0010] Preferably, in the S4 step, the fault pipe section location is realized by the spatial interpolation method, and the pipe network topology structure is reversely fitted based on the abnormal node coordinates, and the suspicious pipe section ID and priority are output.

[0011] Preferably, in the S5 step, the dynamic optimization includes: Incremental learning: The daily new data triggers the model fine-tuning, retains the historical weights and updates the parameters of the fully connected layer; Full-scale retraining: When the predicted mean absolute error exceeds 15% for three consecutive days, the model training is automatically restarted.

[0012] Preferably, in the thermodynamic model, the saturation temperature and the saturation pressure are calculated by the following formula: ; where, is the saturation pressure; is the saturation temperature; is the empirical constant.

[0013] Preferably, the specific enthalpy of the superheated steam is calculated by the following formula: ; wherein, is the specific enthalpy of saturated steam; is the function of the specific heat capacity at constant pressure varying with temperature.

[0014] Preferably, in the hydrodynamic model, the pipeline pressure drop is calculated by the following formula: ; wherein, is the friction coefficient; is the pipeline length; is the inner diameter of the pipeline; is the fluid density; is the fluid velocity.

[0015] The present invention provides a method for abnormally locating steam pipe loss by combining simulation and machine learning. It has the following beneficial effects: 1. Through the multi-node real-time data acquisition and dynamic simulation calibration technology, the present invention realizes the second-level abnormal perception and alarm of the pipe network pressure and temperature. Compared with the traditional flow balance method that relies on the head and end flow meters, it breaks through the problem of lag in fault perception in the middle section of the pipe network and addresses the safety hazards caused by the lag of fault information in traditional technologies.

[0016] 2. By deploying multi-type sensors at key nodes of the pipeline and establishing a fault propagation model, the present invention, aiming at the shortcoming of the existing technology that only focuses on the monitoring of the source side and the load side, realizes the synchronous diagnosis of network side leakage and heat preservation corrosion for the first time, fills the blank of monitoring in the middle section of complex pipe networks, and effectively curbs the deterioration of pipe loss caused by network side aging.

[0017] 3. By cross-verifying the simulation prediction deviation and the output of fault probability, the present invention can still maintain high reliability under complex working conditions compared with the traditional single-threshold determination method, greatly reducing the false alarm rate and avoiding the waste of energy and the virtual consumption of maintenance resources caused by incorrect shutdown.

[0018] 4. By accurately extracting fault features in a strong interference environment and real-time updating the corrosion determination rules, the present invention significantly improves the detection ability of network side corrosion and micro-leakage compared with the problem of missed detection caused by noise interference in the traditional pressure gradient method, and provides a targeted solution for the problem of the unique decline in heat preservation performance of thermal pipe networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 is the flow chart of the steps of the location method of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0020] Next, in combination with the accompanying drawings of the present invention specification, the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0021] Please refer to the attached Figure 1 , the embodiment of the present invention provides a method for abnormally locating steam pipe losses combining simulation and machine learning, including the following steps: S1. Real-time collect the pressure, temperature and flow data of the steam pipe network and perform preprocessing; In step S1, the preprocessing includes outlier removal and missing value filling. The outlier removal adopts principle, and the missing value filling adopts linear interpolation method or manual intervention alarm; Specifically, in this embodiment, step S1 is used to obtain the original data of the steam pipe network operation and perform normalization processing, providing high-quality input for subsequent simulation modeling and machine learning. The preprocessing process needs to ensure data integrity, effectiveness and compatibility with the physical model, and at the same time form a technical closed loop with the simulation model construction in step S2 and the feature engineering in step S3.

[0022] Generally, the physical connection sensing devices deployed at the key nodes of the pipe network (such as the gas source inlet, user outlet, elbow and valve) are used to collect pressure , temperature , mass flow and other parameters in real time. Specifically, the sensing data is transmitted to the central processor via the SCADA system at a frequency of 10 seconds / time, forming an original time series data set.

[0023] As an option, principle is adopted to identify abnormal data. Define the abnormal determination condition of the data point as: ; Among them, is the mean value of the data within the sliding window; is the standard deviation. For example, in the pressure data sequence, if the collected value at a certain moment exceeds the historical mean by range, it is determined as an outlier and removed.

[0024] Specifically, for short-term data loss (such as a single acquisition failure), linear interpolation is used to complete the data at adjacent times. For the case where the continuous data loss exceeds 5 minutes, an alarm is triggered and it is marked as an invalid section, and manual intervention is required to check the device status.

[0025] In a possible implementation, the original data is mapped to a unified dimension. The normalization formula is defined as: ; where and are the statistical values of historical data under the reference working conditions. For example, for the pressure parameter , , to ensure that the magnitudes of different sensors are consistent.

[0026] The preprocessed data will be directly used as the input parameters of the simulation model in step S2 and affect the construction of the sliding window time series features in step S3. For example, the cleaned flow rate data will participate in the solution of the hydrodynamic equation and be combined with the simulation prediction value to form a five-dimensional feature vector as the input to the LSTM model.

[0027] S2. Construct a multi-physics field coupling simulation model based on the pipe network topology parameters to generate simulation prediction values of pressure, temperature, and condensate water distribution; In step S2, the multi-physics field coupling simulation model includes: A hydrodynamic model that calculates the pressure, velocity distribution, and pipe pressure drop by solving the Navier-Stokes equation; A thermodynamic model that calculates the specific enthalpy of superheated steam and the condensate water distribution, including the simulation of the sensible heat-latent heat conversion process; In the thermodynamic model, the relationship between the saturation temperature and the saturation pressure is calculated by the following formula: ; where is the saturation pressure; is the saturation temperature; is an empirical constant; The specific enthalpy of superheated steam is calculated by the following formula: ; where is the specific enthalpy of saturated steam; is the function of the specific heat capacity at constant pressure varying with temperature; In the hydrodynamic model, the pipe pressure drop is calculated by the following formula: ; where is the friction coefficient; is the pipe length; is the inner diameter of the pipe; is the fluid density; is the fluid velocity; Specifically, in this embodiment, step S2 is used to construct a numerical simulation model of the steam pipe network, simulate the operating state under the thermo-fluid coupling effect, provide a physical constraint benchmark for the machine learning model in step S3, and support the anomaly determination and location in step S4. The model needs to dynamically adjust the boundary conditions based on the preprocessed data in step S1 to ensure that the simulation results are consistent with the actual working conditions.

[0028] Generally, a three-dimensional geometric model is generated according to the pipe network topology structure. Specifically, a parametric modeling tool (such as ANSYS-DesignModeler) is used to import the pipe CAD drawings and extract the key geometric features. For example, for a DN200 pipe, the inner diameter is defined as 200 mm, and the elbow curvature radius is taken as 1.5D.

[0029] As an option, unstructured grids are used to locally refine complex regions (such as valves and elbows). The grid size is defined as 0.1mm ≤ Δx ≤ 5mm, and the grid quality threshold is set as Skewness < 0.8. In a possible implementation, hexahedral grids are used for the straight pipe sections, and tetrahedral grids are used for transition in the elbow regions to reduce the computational amount and ensure the accuracy.

[0030] Multi-physics control equations: Specifically, the simulation model includes the following core equations: Hydrodynamics equation: ; where is the fluid density; is the velocity vector; is the pressure; is the dynamic viscosity; is the acceleration due to gravity; And in the hydrodynamics equation, the pipe pressure drop is calculated by the following formula: ; where is the friction coefficient; is the pipe length; is the inner diameter of the pipe; is the fluid density; is the fluid velocity.

[0031] Thermodynamics equation: ; Among them, is the specific enthalpy, is the thermal conductivity, is the temperature, is the latent heat source term for phase change; And regarding The calculation formula for specific enthalpy is as follows: ; Among them, is the specific enthalpy of saturated steam; is the function of the specific heat capacity at constant pressure varying with temperature.

[0032] Humidity transfer equation: ; Among them, is the humidity mass fraction; is the diffusion coefficient.

[0033] In a possible implementation, set the boundary conditions dynamically based on the preprocessed data in step S1: Inlet boundary: Pressure , Temperature , where , is the real-time data from step S1; Outlet boundary: Mass flow rate (user demand curve), and the demand curve is generated by fitting historical data; Wall condition: No-slip boundary, heat flux density , where is the thermal conductivity of the insulation layer.

[0034] Specifically, compare the simulation prediction value with the real-time data in step S1, and calculate the relative error: ; If the error exceeds the threshold, automatically calibrate the model parameters, such as the pipe roughness and the heat loss coefficient of the insulation layer.

[0035] The prediction value output by the simulation will be used as the feature input for step S3 and combined with the real-time data to form a five-dimensional time series feature. For example, in the LSTM model The difference between and will be used to calculate the pressure deviation feature

[0036] S3. Train a machine learning model by fusing real-time data and simulation prediction values, and output the failure probability and type; In step S3, the input features of the machine learning model include the combined time-series data of real-time data and simulation prediction values, which are cut into time-series segments of a fixed length through a sliding window. The machine learning model is an LSTM network, whose hidden layer contains two layers of LSTM cells, and the output layer generates the fault probability and type through the Sigmoid function and the Softmax function respectively. Specifically, in this embodiment, step S3 is used to construct a machine learning model that fuses physical simulation and real-time data, realizes the intelligent identification of fault probability and type, and provides a probabilistic decision-making basis for the anomaly determination in step S4. The model needs to be dynamically aligned with the simulation prediction values in step S2 and adapted to the characteristics of the preprocessed data in step S1 to form a cross-domain feature fusion mechanism.

[0037] Generally, the real-time data in step S1 and the simulation prediction values in step S2 are combined into a five-dimensional feature vector: ; Specifically, a sliding window mechanism is used to slice the time-series data. The window length is set to 60 minutes (360 sampling points), and the step size is set to 5 minutes to generate the input sample set.

[0038] As an option, a long short-term memory network (LSTM) is used as the core model. In a possible implementation, the network structure is defined as follows: Input layer: Receives a 360×5 time-series feature matrix, corresponding to the time step and the feature dimension; Hidden layer: Contains two layers of LSTM cells, with 128 neurons in each layer, and the inter-layer Dropout rate is 0.2; Output layer: Fault probability output: Generates the leakage probability Pleak∈[0,1] through the Sigmoid function; Fault type classification: Outputs three types of labels (leakage, thermal insulation corrosion, normal) through the Softmax function.

[0039] Specifically, a weighted cross-entropy loss function is used to solve the problem of class imbalance. The loss function is defined as: ; Among them, 、 correspond to the weight coefficients of the leakage and corrosion categories respectively, is the true label, is the predicted probability. The Adam algorithm is selected as the optimizer, the initial learning rate is set to α = 10−4, and the batch size is set to 64.

[0040] In a possible implementation, the simulation prediction deviation in step S2 , As an additional supervision signal. Define the joint training objective as: ; where is the balance coefficient, which constrains the model to optimize both the classification accuracy and physical consistency.

[0041] The fault probability output by the model will be input to the decision-making logic in step S4 for joint decision-making with the simulation deviation. For example, when , a leakage alarm is triggered and the localization process in step S4 is started.

[0042] S4. Determine the abnormal type and locate the faulty pipe section based on the simulation prediction deviation and the machine learning result; In step S4, the determination of the abnormal type includes: Leakage detection: The real-time pressure is lower than 90% of the simulation prediction value and the leakage probability output by machine learning exceeds 85%; Thermal insulation corrosion detection: The temperature gradient exceeds 2 °C / m and the corrosion probability output by machine learning exceeds 75%; In step S4, the location of the faulty pipe section is achieved by the spatial interpolation method. Based on the abnormal node coordinates, the pipe network topology is inversely fitted to output the suspicious pipe section ID and priority; Specifically, in this embodiment, step S4 is used to comprehensively determine the abnormal type and locate the faulty pipe section based on the simulation prediction deviation in step S2 and the machine learning output result in step S3, providing accurate decision-making support for operation and maintenance response. The decision-making logic needs to integrate physical laws and data-driven results to ensure that the false alarm rate is controllable and the location accuracy meets the engineering requirements.

[0043] Generally, multi-level decision-making conditions are defined to distinguish fault types such as leakage and thermal insulation corrosion: Leakage decision-making condition: The real-time pressure is lower than 90% of the simulation prediction value; The leakage probability output by machine learning exceeds 85%; When the above conditions are met simultaneously, it is determined as a leakage event.

[0044] Thermal insulation corrosion decision-making condition: The temperature gradient exceeds the threshold (such as 2 °C / m): ; where is the adjacent sensor spacing, is the measured temperature difference between the actual and adjacent node simulations; The corrosion probability output by machine learning exceeds 75%; When the above conditions are met simultaneously, it is determined as thermal insulation layer corrosion.

[0045] Specifically, based on the coordinates of abnormal nodes and the pipe network topology, the spatial interpolation method is used to inversely fit the suspicious area. The interpolation weight function is defined as: ; where is the coordinate of the center point of the th pipe segment, is the coordinate of the abnormal node, and is the smoothing coefficient to prevent the denominator from being zero. The suspicious probability of the pipe segment is calculated by weighted summation: ; where is the indicator function (taking 1 if the pipe segment j is connected to the node i, otherwise taking 0). Finally, the list of suspicious pipe segment IDs is output and sorted in descending order of priority according to .

[0046] In some embodiments, the determination threshold is dynamically optimized according to historical fault data. The update formula for the leakage probability threshold is defined as: ; where is the threshold for the th iteration, is the learning rate, is the current false alarm rate, and is the target false alarm rate.

[0047] In a possible implementation, the acoustic emission sensor data and the temperature gradient information are combined to improve the positioning accuracy. The fused suspiciousness score is defined as: ; where is the energy intensity of the acoustic signal, is the temperature anomaly score, and is the fusion weight coefficient.

[0048] S5. Dynamically optimize the model and detection threshold based on the feedback data; In step S5, the dynamic optimization includes: Incremental learning: Newly added data every day triggers model fine-tuning, retaining the historical weights and updating the parameters of the fully connected layer; Full-scale retraining: When the predicted mean absolute error exceeds 15% for three consecutive days, the model training is automatically restarted.

[0049] Specifically, in this embodiment, step S5 is used to dynamically optimize the machine learning model parameters in step S3 and the detection threshold in step S4 according to the abnormal determination result in step S4 and the historical operation data, so as to achieve self-adaptive improvement of the system. The optimization process needs to ensure that the model continuously adapts to the changes in the pipe network working conditions, and at the same time avoid performance degradation caused by data distribution shift.

[0050] Generally, the LSTM model is updated online based on the daily newly added real-time - simulation data pairs (from steps S1 and S2). Specifically, the incremental learning objective is defined as minimizing the weighted sum of the newly added data loss and the historical model parameter deviation: ; where, is the cross - entropy loss of the new batch of data, are the model parameters before and after the update respectively, is the regularization coefficient. During optimization, the weights of the bottom layer of the LSTM are frozen, and only the parameters of the fully connected layer are fine - tuned to balance stability and adaptability.

[0051] As an option, full - scale training is initiated when the cumulative data distribution deviation exceeds a threshold. The distribution deviation index is defined as: ; where, and are the feature distributions of the new data and the historical data respectively. If , the model is retrained using all historical data, and the optimizer state is reset.

[0052] Specifically, according to the simulation - measured deviation under historical normal operating conditions, the decision threshold in step S4 is dynamically adjusted. The pressure deviation threshold update formula is defined as: ; where, and are the mean and standard deviation of the pressure deviation within the rolling window (default 30 days). Similarly, the temperature gradient threshold is updated as: ; where, and are the mean and standard deviation of the temperature gradient within the rolling window.

[0053] In a possible implementation, historical fault events (time, location, type, repair records) are stored as a structured knowledge base. The fault feature vector is defined as: ; where, is the feature vector of the historical case and the current query; is the cosine similarity value.

[0054] Cases with a similarity exceeding 0.8 will be recommended to the operation and maintenance personnel to assist in making quick decisions.

[0055] Although embodiments of the present invention have been shown and described, those of ordinary skill in the art will appreciate that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for locating abnormal steam pipe damage by combining simulation and machine learning, characterized in that: The following steps are involved: S1, real-time collection of pressure, temperature and flow data of the steam network and pre-processing; S2. Construct a multi-physics field coupling simulation model based on the pipe network topology parameters to generate simulation prediction values ​​of pressure, temperature and condensate distribution; S3, integrate real-time data and simulation prediction values ​​to train machine learning models and output fault probability and type; S4. Determine the abnormality type and locate the faulty pipe section based on the simulation prediction deviation and machine learning results; S5. Dynamically optimize the model and detection threshold based on feedback data.

2. According to claim 1, a method for locating abnormal steam pipe damage by combining simulation and machine learning is characterized in that: In the step S1, the preprocessing includes outlier removal and missing value filling. In principle, missing values ​​are filled using linear interpolation or manual intervention alarms.

3. The method for locating abnormal steam pipe damage by combining simulation and machine learning according to claim 1, characterized in that: In the step S2, the multi-physics field coupling simulation model includes: Fluid dynamics model, calculating pressure, velocity distribution and pipeline pressure drop by solving Navier-Stokes equations; Thermodynamic model, calculation of superheated steam specific enthalpy and condensate distribution, including simulation of sensible heat-latent heat conversion process.

4. The method for locating abnormal steam pipe damage by combining simulation and machine learning according to claim 1, characterized in that: In the step S3, the input features of the machine learning model include the combined time series data of the real-time data and the simulation prediction value, which are cut into time series segments of fixed length by a sliding window; The machine learning model is an LSTM network, whose hidden layer includes a double-layer LSTM unit, and the output layer generates the fault probability and type through the Sigmoid function and the Softmax function respectively.

5. The method for locating abnormal steam pipe damage by combining simulation and machine learning according to claim 4, characterized in that: In the step S4, the abnormality type determination includes: Leak detection: The real-time pressure is lower than 90% of the simulation prediction value and the machine learning output leakage probability exceeds 85%; Insulation corrosion detection: The temperature gradient exceeds 2°C / m and the corrosion probability output by machine learning exceeds 75%.

6. The method for locating abnormal steam pipe damage by combining simulation and machine learning according to claim 5, characterized in that: In the step S4, the faulty pipe section is located by a spatial interpolation method, and the pipe network topology is reversely fitted based on the coordinates of the abnormal nodes to output the suspicious pipe section ID and priority.

7. The method for locating abnormal steam pipe damage by combining simulation and machine learning according to claim 1, characterized in that: In the step S5, the dynamic optimization includes: Incremental learning: Daily new data triggers model fine-tuning, retains historical weights and updates fully connected layer parameters; Full retraining: When the forecast mean absolute error exceeds 15% for three consecutive days, model training will be automatically restarted.

8. The method for locating abnormal steam pipe damage by combining simulation and machine learning according to claim 3, characterized in that: In the thermodynamic model, the saturation temperature With saturation pressure The relationship is calculated by the following formula: ； in, is the saturation pressure; is the saturation temperature; is an empirical constant.

9. The method for locating abnormal steam pipe damage by combining simulation and machine learning according to claim 3, characterized in that: The specific enthalpy of the superheated steam Calculated by the following formula: ； in, is the specific enthalpy of saturated steam; is the function of the constant pressure specific heat capacity changing with temperature.

10. The method for locating abnormal steam pipe damage by combining simulation and machine learning according to claim 3, characterized in that: In the fluid dynamics model, the pipeline pressure drop Calculated by the following formula: ； in, is the friction coefficient; is the length of the pipeline; is the inner diameter of the pipe; is the fluid density; is the fluid velocity.

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