KR20010069397A - A Method and a Device for the Measurement of Flow Rate in a Pipe using a Microphone Array - Google Patents

Abstract

PURPOSE: A method and a device for measuring the inside flow rate of a pipe using microphones arranged in equal intervals are provided to exactly and simply measure flow rate using a general formula of sound field arranged in equal intervals inside the pipe when there is a flow rate. CONSTITUTION: A method for measuring the inside flow rate of a pipe using microphones arranged in equal intervals includes the steps of obtaining the number of waves related with flow rate using correlation between sound pressures inside the pipes arranged in regular intervals since sound wave transferred in the pipe has the number of waves changed according to the flow rate, and measuring an average flow rate inside the pipe using a value of the wave number.

Description

A method and a device for the measurement of flow rate in a pipe using a microphone array}

The present invention relates to a flow rate measuring method and a measuring device in the tube using a microphone arranged at equal intervals.

In general, when measuring the flow rate inside the tube, a method of measuring the flow rate using a pitot tube or an orifice meter is generally used.

These methods have to be measured by inserting the flow measuring devices directly into the tube, so that the flow measuring devices are limited in that the flow of the fluid is deformed or disturbed.

In addition, there is another method of measuring the flow rate using ultrasonic waves that are non-contact with the fluid, but this device also has the nonuniform thickness of the tube, the contact state between the detector and the tube in the ultrasonic transmitter and receiver, the turbidity and the temperature of the fluid. Since the refraction angle and the transmission path of the ultrasonic waves are different, there is a limit that is very sensitive to changes in the environmental conditions.

The conventional measuring method has a limitation in that the average flow rate in the space inside the pipe cannot be measured because it only measures the flow rate at one position where the measuring device is placed.

The present invention proposes a method that can measure the average flow rate in space without disturbing the flow of the fluid using wave propagation characteristics as a method different from the conventional measuring method.

The propagation characteristics of the waves in the tube have the characteristic that the wave number changes according to the velocity of the fluid in the tube. "Measurement of in-tube sound field and average flow rate using a microphone array", Journal of the Korean Society of Mechanical Engineers, Vol. 22, No. 9, pp 1761 ~ 1768. The use of the auto spectrum term inevitably leads to measurement noise implications, as well as to a flow measurement method using three sensors (1996, "A three accelerometer method for the measurement of flow rate in pipe," J The flow measurement method using three sensors disclosed in Acoust.Soc.Am., Vol. 100, No. 2, pp. 717 ~ 726.) Shows a wave field signal that is symmetric about the sensor located among the three sensors. There has been a problem that the occurrence of singular values is inevitable when measured.

The present invention has been made to solve the above problems, a method for measuring the flow rate using the general relationship to the sound field formed inside the tube in the presence of the flow rate, the method of calculating the wave change amount, correction of the measurement error It is a technical object of the present invention to provide a method and a measuring apparatus for in-flow flow using microphones arranged at equal intervals verified through methods, application conditions, and simulations and experiments.

1 is a plane wave propagating through a fluid having a flow rate of U in a tube

Fig. 2 Measurement error and transfer function of microphone array system

Figure 3 contains the error caused by the difference in the size of the transfer function between the sensors

Simulation results for flow rate (10m / sec)

Figure 4 contains the error caused by the difference in the transfer function phase only between the sensors

Simulation results for flow rate (10m / sec)

Figure 5 corrects the error caused by the transfer function magnitude and phase difference between the sensors

Simulation results for flow rate (10m / sec)

Figure 6 Experimental apparatus for measuring the flow in the tube using a microphone

Figure 4 shows four microphones when the air flow rate in the tube is Q = 0, 8, 10, 12 l / sec.

Flow measurement results obtained without error correction between sensors

8 Four microphones are used when the air flow in the tube is Q = 0, 8, 10, 12 l / sec.

Flow measurement result obtained by using error correction between sensors

Fig. 9 Frequency distribution of measured flow rates obtained by frequency and Gaussian distribution

Fit curve

Fig. 10 shows the whole Youngdu method when the air flow in the pipe is Q = 0, 8, 10, 12 l / sec.

Flow measurement result obtained using

Figure 11 Kim's method when the air flow rate in the pipe is Q = 0, 8, 10, 12 l / sec.

Flow measurement result obtained using

<Description of the symbols in the drawing>

Tube (1), sonic measuring instrument (2)

In order to achieve the above object, the present invention can consider the tube as a rigid duct when the fluid flow in the tube having a uniform cross-sectional area as shown in Figure 1 is relatively very large compared to the acoustic impedance of the fluid in the tube. If possible, the sound field in the tube is expressed as Eq. (1), considering only one-dimensional sound wave propagation in the longitudinal direction in the tube. ⁽⁶⁾

(One)

here, Wow Represents the sound pressure in the fluid and the propagation velocity of the sound wave in the stationary fluid, respectively. Is the average flow velocity of the fluid inside the tube.

Since sound waves satisfying Equation (1) are plane waves that are one-dimensional waves, the general solution of Equation (1) can be expressed as Equation (2).

(2)

Where denotes a complex constant and denotes the frequency and frequency of sound waves respectively. Substituting Eq. (2) into Eq. (1) to obtain the propagation characteristics of the wave gives Eq. (3), which is the relationship between the frequency and the frequency of the wave.

(3)

here, Is a dimensionless value divided by the velocity of a sound wave, that is, Mach number.

Given that the kinematic viscosity of the media in the tube is so small that the effects of thermal viscous damping can be neglected, Is applied to equation (2) to obtain an expression representing the sound field inside the tube as shown in equation (4). ⁽⁷⁾

(4)

here,

(5a)

(5b)

In equation (5), the superscript (+) indicates the case where the flow direction of the fluid and the propagation direction of sound waves are the same, and the superscript (-) indicates the case where the flow direction of the fluid and the propagation direction of the sound waves are opposite to each other.

Looking at equation (5), the fluid is at rest, i.e. In this case, it can be seen that two sound waves having the same magnitude wave propagate in opposite directions. And when the flow velocity of the fluid increases, the sound wave propagating in the positive direction, which is the same direction as the flow direction of the fluid, decreases in magnitude, whereas the sound wave propagating in the negative direction increases the wave number. It can be seen that the Doppler effect appears.

In order to obtain a quantitative relationship between the flow rate and the wave change amount, the wave change amount is defined as shown in Eq. (6). From Eq. (5), the quantitative relationship between the flow rate and the wave change amount is shown in Eq. (7).

(6)

(7)

Therefore, the correlation between the flow rate and the wave number change amount is obtained from equation (7) as shown in equation (8).

(8)

here, Represents the inner diameter of the tube. It can be seen from Equation (8) that the flow rate in the pipe can be obtained only by knowing information such as the wave number change, the frequency and propagation speed of the sound wave, and the inner diameter of the pipe.

The actual sound field characteristics in the pipe must be known in order to determine the wave change associated with the flow in the pipe. In the case where standing waves are formed in the tube, the sound field at any position can be expressed as the sum of the waves traveling in the positive and negative directions as shown in Eq. (4). You need to know the magnitude and number of waves going on. Therefore, in order to obtain sound field characteristics, it is necessary to know the correlation between the sound pressure information of at least four points and the sound pressure information.

At equal intervals as shown in FIG. In the case of measuring sound pressures at four points, Fourier transform the sound pressures at three consecutive points (n, n + 1, n + 2) using Equation (4) to find a correlation between these sound pressures. In this case, the equation (9) is obtained.

(9)

here, ego, Is the distance between the sensors. On the left side in (9) And so on are the variables that we know from measurement Is an unknown complex.

Looking at Equation (9), since the unknown number of complex constants is four and the number of equations is three, it can be seen from Equation (9) that the solution of the complex constant cannot be obtained, but the correlation between the complex constants can be obtained. Among complex constants, the term related to the flow rate is Wow So only these are left, indicating the magnitude of the sound pressure Wow Will be deleted. In equation (9) Construct an arbitrary two-row equation in (9) to eliminate and Wow Obtaining this Wow Substituting into an expression with the rest of the row Wow Is erased. As an example, using the formula consisting of the first and second rows of Eq. (9) Wow Is given by Eq. (10).

10

Substituting equation (10) into the equation consisting of the third row of equation (9), Wow We get a recursive relation between the three points of sound pressure. In addition, even if any two other rows are selected in Equation (9) and the equation is arranged in the same manner as described above, the result is the same as in Equation (11).

(11)

Equation (11) becomes a general relation without special limitations between the sound pressures of three adjacent points at equal intervals when a plane wave propagates inside a tube having a uniform cross-sectional area. Equation (11) shows that the sound pressure at three adjacent points at equal intervals Is the value that can be obtained from the measurement Wow Is an unknown, so theoretically if you have two adjacent pairs of sound pressure information of at least four points Wow It can be seen that can be obtained.

Measurement signal information of four adjacent points at equal intervals In the case of the position, the relation between the measured signals is expressed by Equation (12) using Equation (11).

(12)

here,

(13a)

(13b)

Watchtower from equation (12) Wow However, cross-spectrum should be used to find a solution that minimizes the measurement noise error. In order to use the mutual spectrum, the first line of equation (12) Multiply by the second row Multiply by to get the result of Eq. (14).

(14)

In equation (14) Denotes a power spectrum defined by equation (15).

(15)

here, [.] Represents the expected value, and * represents the conjugate complex number. Using Cramer's Theorem to sum up Eq. (14) and Is expressed as shown in equation (16).

(16a)

(16b)

If you measure sound pressure signals at N points at equal intervals and Is obtained every four points as shown in equation (17). and It can be expressed as the spatial mean value of the values.

(17a)

(17b)

wave number Wow And wave change

Is represented by equations (18) and (19) from equations (13) and (17).

(18a)

(18b)

(19)

here, silver Indicates the phase angle of. If the negative pressure signals are obtained at the same intervals from Eqs. (18) and (19), the wave number and the wave number change can be obtained. Using this result and Eq. (8), the flow rate in the pipe can be obtained.

When measuring the flow rate using microphone signals arranged at equal intervals, there may be errors due to measurement noise in the form of white noise and characteristic differences between the sensors during the signal acquisition process. .

In general, measurement noise may exist at both the input and output terminals of the sensor as shown in FIG. 2, and the measurement noise may be assumed to be white noise. Output signal with mixed measurement noise in Fig. Fourier transform of Can be expressed as Eq. (20).

(20a)

(20b)

here, Denotes the transfer function by the input signal, the noise on the input signal side, the noise on the output signal side, and the sensor characteristics, respectively. Since the cross spectrum between the measured signals for each channel can be assumed to be white noise, the cross spectrum between the measured noise and the signal that is not mixed with the measured noise becomes 0 as shown in Equation (21a). It is expressed as (21b).

(21a)

(21b)

Looking at the cross-spectrum between the measured signals of each channel represented by Equation (21b), it can be seen that the terms related to the measured noise are excluded, and only the transfer function of the measurement system can be used to find the cross-spectrum of the original signal. have.

Errors due to characteristic differences between sensors exist structurally regardless of whether the fluid is stopped or not. Therefore, if the error correction coefficient due to the characteristic difference between the sensors can be obtained when the fluid is stopped, the flow rate can be more accurately obtained by applying the value of the correction coefficient to the flow of the fluid. In order to calculate the error correction coefficient, a transfer function representing the characteristics of each sensor will be defined as shown in Equation (22).

(22)

If errors due to characteristic differences between sensors are included, the relational expression of the mutual spectrum is expressed as Equation (23) using Equations (14), (21) and (22).

(23)

here,

If you look at equation (23) for the fluid at rest Is obtained from the measured value by the sensor Is unknown since equations (5) and (13) The value can be obtained by converting equation (23).

Unknown To get the value Wow The real part and the imaginary part of are defined as Eq. (24).

(24a)

(24b)

Substituting equation (24) into equation (23) to separate the real part and the imaginary part separately, the real part is expressed by equation (25) and the imaginary part is expressed by equation (26).

(25)

here,

,

And

(26)

here,

,

Looking at equations (25) and (26), the unknown coefficient, the correction factor, Wow Are five each, two each, and an unknown. Wow Since both are functions of frequency, strictly speaking, the unknowns cannot be obtained using equations (25) and (26).

However Wow Assuming that it is constant near the frequency to be estimated, six or more equations can be obtained for three or more frequencies including adjacent frequencies as shown in equations (27) and (28).

(27)

(28)

here, Is the frequency band, Is Wow It represents the arbitrary frequency in the frequency band between. If the number of equations (6 or more) becomes larger than the number of unknowns (5), as in equations (27) and (28), the unknowns are determined using the least-squares method. Wow Can be obtained.

Generally Matrix with the formula If the number of rows in is greater than the number of columns, the solution can be found using the least-squares method, in which case Is expressed as ⁽⁸⁾

(H: Hermitian operator)

Therefore, using the least-square method from the matrix obtained when there are three or more frequencies from equations (27) and (28) Wow The equations are expressed as equations (29) and (30).

(29)

(30)

Obtained from equations (29) and (30) for the fluid at rest Wow Since the value is represented by the difference in characteristics between the sensors, this value can be considered to have the same value even when the fluid is flowing. Therefore, when the fluid is at rest, it is obtained from equations (29) and (30). Wow The value and the measurement When fluid flows using and When the equation is obtained, equation (23) is expressed as equation (31).

(31)

Using Eqs. (31) and (18), it is possible to obtain the wave value excluding the characteristic difference between the sensors.

In the case of measuring the flow rate in the pipe, the flow measurement method is derived from the equation considering only the one-dimensional wave, so the flow measurement method proposed in this paper is effective in the condition that only one-dimensional wave propagates in the pipe. The upper limit of the frequency range in which only one-dimensional wave propagates in the pipe is expressed as in Eq. (32). ⁽⁹⁾

(32)

Therefore, if the frequency of the tube wave is greater than the upper limit frequency as shown in Eq. (32), an error may occur when measuring the flow rate using the method proposed in this paper.

Equation (11), which is used as a basic formula for measuring the flow rate in the present invention, is derived based on the assumption that the sensors are arranged at equal intervals as a space recirculation formula. The singularity that occurs is inevitable. This specific condition can be obtained by looking at the derivation process of Eq. (11).

As shown in equation (10) Wow In the process of finding Wow Matrix If the inverse is not available according to the sensor interval, that is, the matrix Can be a singular matrix. Matrix In the case of a singular condition in which the inverse of the equation cannot be obtained, Eq. (11) does not hold, so the wavenumber value obtained from Eq. (11) has an inaccurate result. procession Matrix if inverse does not exist The determinant of Therefore, this determinant can be used to derive a conditional expression when a singular condition occurs. In other words, In sum, Eq. (33) is obtained.

(33)

In order for Eq. (33) to hold, the wavenumber must be equal to Eq. (34).

(34)

Using the relation of, the conditional expression representing the singular frequency from Eq. (34) is obtained as Eq. (35).

(35)

The conditional expression in equation (35) is an ideal condition in the assumption that the sensor is located at one point, and in actual cases the diameter of the sensor ( In this case, the singular frequency range is expressed as Eq. (36).

(36)

In order to check whether the method proposed in the present invention is suitable, the flow field was simulated and the flow rate was obtained through simulation. The effects of the error in the simulation can be eliminated by using the spectral error among the error types, so this error is excluded and only the effect of the error due to the characteristic difference between the sensors is examined.

In order to simulate the sound field in the tube, Eq. (4) and Eq. (37), which represent the velocity of the fluid particles, are obtained.

(37)

(38)

here, Is the density of the fluid. In order to construct the simulated sound field in the hall, the conditions in the hall were arbitrarily assumed as follows. That is, in equation (38) It is assumed that the fluid type is air, the temperature is 20 ° C, and the fluid velocity is 10 m / sec. The simulated sound field was obtained by applying these conditions to equation (38). The sensor assumes that four sensors are arranged at 10 cm intervals.

In order to examine the effect of error due to the difference in characteristics between sensors, the transfer function ( ) Is expressed in the form that the error is included in the magnitude and phase of the transfer function.

(39)

here, Represents the magnitude of the error, Is an error, which is defined as a random number uniformly distributed between 0 and 1, and the subscripts n, m, and p represent the channel number, the magnitude and phase of the transfer function, respectively.

First, if an error exists only in the magnitude of the transfer function of the sensor among the characteristics of the sensor, that is, , ego In each case, When the values are shown in Table 1, the flow rate is calculated using the method presented in this paper without compensating for the error.

In addition, when an error exists only in the phase of the transfer function of the sensor among the sensor characteristics, that is, ego ego In each case, When the value is shown in Table 1, if the flow velocity is obtained without compensating for the error, the result shown in FIG. 4 is obtained.

Table 1 . Random number distribution of on each channel

Ch. One Ch. 2 Ch. 3 Ch. 4 0.0258 0.9210 0.7008 0.1901 0.5387 0.3815 0.0512 0.2851

Referring to Figures 3 and 4, the flow rate value has a large error in common at a frequency of around 1700 Hz, and this error is related to the error of the specific condition according to the sensor interval predicted using Equation (35) when the sensor interval is 10 cm. Matches.

Referring to FIG. 3, in the case where there is a difference only in the magnitude of the transfer function of the sensor for each channel, the flow rate is almost unaffected by the difference in the magnitude of the transfer function of the sensor for each channel in the frequency domain except for the frequency in which an error related to the sensor interval appears. It appears to be insensitive to changes in the properties.

Meanwhile, referring to FIG. 4, in the case where there is a difference only in the phase of the transfer function of the sensor for each channel, the flow rate represents a value that varies in a relatively wide frequency region centered on a frequency at which an error related to the sensor interval occurs. It is highly influenced by the phase difference of the transfer function and appears to be very sensitive to the change of phase size.

If both the magnitude and phase of the transfer function of the sensor are different, ie ego Where is the error per channel and When the flow rate is as shown in Table 1, the flow rate is similar to that of FIG. 4. When the error correction method presented in this paper is applied to the result, the flow rate is as shown in FIG. 5.

When the error correction method is applied from FIG. 5, a slight error occurs only in the frequency part of the specific condition related to the sensor interval, and the error due to the sensor characteristic is well corrected in the other frequency domains.

Experimental Example

In order to confirm the validity of the method proposed in the present invention was carried out an experiment to measure the flow rate in the pipe, the experimental apparatus was configured as shown in FIG. The inner diameter and length of the tube were 40 cm and 3 m, respectively, and the microphones were mounted with four 1/4 inch diameter B & K type 4938 microphones flush mounted at intervals of 10 cm. The flow field was formed using an air compressor, an air storage tank, and an automatic flow control valve to allow a certain amount of flow. A commercial flow measuring device was installed inside the pipe for comparison with the actual flow rate. The sound field inside the tube was made white noise by using the speaker installed at the front end of the tube. The experiments were carried out with varying flow rates of 0, 8, 10 and 12 liters / sec, and sound pressure signals were measured and analyzed using a microphone and B & K Type 3560 PULSE analyzer.

Considering the application conditions of the above-mentioned measuring method in relation to the experimental apparatus, considering the inner diameter of the tube from Eq. (32), the upper limit frequency of the frequency range where only one-dimensional sound wave propagates is 5 kHz, and Eq. (36) Considering the sensor spacing and the diameter of the sensor, the frequency range where the singular condition occurs is 1610 ~ 1830 Hz.

Figure 7 shows the results obtained by calculating the flow rate in the 600 ~ 3000 Hz frequency range by the method proposed in this paper without correcting the error. From the flow rate of Figure 7 can be seen that the singular value by the sensor interval in the frequency range of 1600 ~ 1900 Hz as expected, the simulation results when there is a difference in phase characteristics between the sensors in the entire frequency range It can be seen that the same type of flow rate is obtained.

FIG. 8 shows the results obtained by applying the error correction method to the flow rate obtained as shown in FIG. 7. It can be seen from FIG. 8 that the flow rate is obtained relatively close to the actual flow rate in the frequency domain except for the 1600-1900 Hz frequency range where the singular value appears.

When calculating the statistical average flow rate of the flow rate values in all frequency ranges, if the arithmetic average of the flow rate values for each frequency is obtained, the average value is shifted due to the singular value represented by the sensor interval, resulting in inaccurate results. Therefore, in order to avoid this, the frequency of the flow rate values for each frequency was drawn as a histogram, and then a Gaussian distribution fitting equation was obtained, and the mean value of the fit equation was determined as the flow measurement value.

Figure 9 shows a histogram showing the frequency of the flow rate value for each frequency and curves of Gauss distribution fit equation for it. In Figure 9 it can be seen that the average value of the Gauss distribution fit equation is in good agreement with the actual flow rate, and the relative error percentage of the measured value with respect to the actual value and the standard deviation value of the Gauss distribution curve are shown in Table 2. From Table 2, it can be seen that the maximum error and maximum standard deviation of the flow measurement values are 4.8% and 0.45, respectively.

Table 2 . The flow rate and theirs estimated from the Gaussian distribution curve fit

True flow rate (liter / s) Estimated flow rate (liter / s) % error in flow rate × 100 Standard deviation of (liter / s) 0 -0.0003 - 0.03 8.0 8.38 4.8 0.34 10.0 10.2 2 0.39 12.0 12.47 3.9 0.45

To compare the flow measurement method and the flow measurement method using wave propagation characteristics mentioned in the introduction, Jeon Young Doo method ⁽⁴⁾ and Kim's method ⁽⁵⁾ , the flow rate to the error correction by Jeon Young Doo method and Kim's method The results are shown in FIGS. 10 and 11, respectively. From the results of FIG. 10, it can be seen that the Jeon Young Do method exhibits a result in which error correction is not performed well in a frequency band higher than the frequency at which the singular value appears due to the sensor interval. In addition, in the result of FIG. 11, Kim's method shows not only the singular value due to the sensor interval but also the singular values due to the wave signals symmetrical around the sensor located among the three sensors. . Comparing the results of FIG. 8, FIG. 10 and FIG. 11, the present flow measurement method has a frequency band in which the dispersion of the flow rate data is smaller and the singular value due to the sensor interval is relatively smaller than that of the Jeon Young Doo method and the Kim method. It appears to be closer to the actual value in the excluded frequency band.

The present invention proposes a method for measuring the flow rate in a pipe by using the characteristic that the sound wave propagated in the pipe changes in the axial wave number according to the flow rate. The wave change amount correlated with the flow rate in the pipe can be obtained by using the correlation between the sound pressure inside the pipe at equal intervals, and the pipe flow rate is finally obtained from the correlation between the wave change amount and the flow rate. In this flow measurement method, there are application conditions due to the assumption of sound waves as plane waves and sensor intervals, and the frequency ranges of these application conditions are presented. The types of errors that can occur during flow measurement and their correction methods are also presented. Through the simulation, we confirmed the applicability of the flow measurement method, and through the actual experiment, we measured the flow rate when there was flow inside the pipe, and the measured flow value was well within the 5% error range compared to the actual value. A matching result was obtained.

Hereinafter, the drawings of the present invention will be briefly described.

Figure 1 includes a plane wave propagating through a fluid having a flow rate of U in a pipe, a measurement error of FIG. 2 and a transfer function of a microphone array system, and an error caused by a difference only in the size of the transfer function between the sensors of FIG. Simulation results for 10 m / sec), simulation results for flow rate (10 m / sec) when the error generated due to the difference in the phases of the transfer functions between the sensors in FIG. 4 is included, transfer function magnitudes between the sensors in FIG. Simulation results for the flow rate (10m / sec) when the error caused by the phase difference is corrected, the experimental apparatus for measuring the flow rate in the tube by using the microphone of Figure 6, the air flow rate of the tube in Figure 7 Q = 0, 8, As a result of the flow measurement obtained without error correction between the sensors using four microphones at 10 and 12 l / sec, four microphones were used when the air flow in the pipe was Q = 0, 8, 10 and 12 l / sec. Flow rate calculated by using error correction between sensors As a result of the measurement, the frequency distribution of the measured flow rate obtained by the frequency of FIG. 9, the Gaussian distribution curve, and the flow rate obtained by using the front zero method when the air flow rate in FIG. 10 is Q = 0, 8, 10, 12 l / sec As a result of the measurement, FIG. 11 shows the flow measurement results obtained by using Kim's method when the air flow rate in the tube is Q = 0, 8, 10, 12 l / sec. It is understood that it is shown

In the flow rate measuring method of the present invention, the surface of the sensor must be installed so that the surface of the sensor coincides with the inner surface of the tube in order to measure the sound pressure. The flow rate must be measured, and the sensor should select an appropriate sensor that can withstand the pressure and temperature of the fluid in the tube.

The present invention manufactured as described above has the effect of accurately and simply measuring the flow rate with a simple device using a general relationship to the sound field arranged at equal intervals formed inside the tube in the presence of the flow rate.

Claims (5)

In the pipe flow measurement method using microphones arranged at equal intervals, the sound wave propagated in the pipe has the characteristic that the wave number changes according to the flow rate. A method for measuring the flow rate in a pipe using microphones arranged at equal intervals, wherein the average flow rate in the pipe is measured from the wave number value. (8) (17a) (17b) (18a) (18b) (19) here, silver Indicates the phase angle of. If you get a sound pressure signal at equally spaced positions, The sound pressure signal interspectral of the form can be obtained, and using Equation (17) and Values can be obtained, and the wave number and wave change amount can be obtained from equations (18) and (19). From this, it can be seen that the flow rate in the pipe can be obtained using equation (8). In-flow flow measurement method using a microphone arranged at equal intervals by correcting the noise error when measuring the flow rate measured in claim 1. (21a) (21b) (20a) (20b) Where denotes the transfer function by the input signal, the noise on the input signal side, the noise on the output signal side, and the sensor characteristics, respectively. In-flow flow measurement method using a microphone arranged at equal intervals by correcting the wave number value according to the following equation in the error due to the characteristic difference between the sensors when measuring the flow rate measured in claim 1. (31) (29) (30) here, , And , here , , , Are each Wow The real and imaginary parts of are defined as (24a) (24b) Since the flow measuring method measured in claim 1 is derived under the condition that only one-dimensional wave propagates in the pipe, the upper limit of the preferable effective frequency range is expressed as shown in Eq. The singular frequency range is as shown in Equation (36), and the flow rate measurement method using the microphones arranged at equal intervals, characterized in that the flow rate is measured in the frequency range except the singular frequency range. (32) (36) In the pipe flow rate measuring apparatus using the microphones arranged at equal intervals, arranged at equal intervals, characterized in that the top of the pipe (1) having a uniform cross-sectional area is composed of four or more sound wave meters (2) in the longitudinal direction in the tube Flow measurement device using a conventional microphone.