JP2000180230A - Flowmeter and method for measuring flow rate - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a flowmeter and a flow rate measuring method capable of accurately measuring a flow rate without using a correction factor. SOLUTION: At the level H of fluid and at a plurality of water depths zk, the width W(zk) of a flow passage at each water depth zk is standardized to range from -1 to 1 in the cross direction of the flow passage, so as to establish coordinates in the cross direction of the flow passage; flow velocities (v) at a plurality of points 44 such that for a Legendre spherical function Pn(x), the roots (x1,...xn) of Pn(x)=0 are given are measured and the width W(zk) of the flow passage at each water depth is calculated. From the widths W(zk) of the flow passage and the flow velocities at the plurality of points 44, Gauss' numerical integration is performed to calculate the area of a flow velocity distribution at each water depth. The areas of the flow velocity distributions are integrated for all of the water depths so as to calculate flow rate.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a flow meter for measuring a flow rate of a fluid flowing through a flow path and a flow rate measuring method.

[0002]

2. Description of the Related Art Conventionally, as a flow meter of this type, a water level measuring section for measuring a water level of a fluid, and a flow rate measuring section for measuring a flow rate at a certain fixed point on a vertical line passing through the center of a flow path. ,
The average velocity of the cross section is obtained by multiplying the flow velocity value obtained by the flow velocity measurement unit by the correction coefficient (a function of the water level), the cross sectional area is calculated from the water level, and the flow velocity is obtained by multiplying the cross sectional area by the average flow velocity. Things are known. As the flow velocity measuring unit, a Doppler ultrasonic velocity meter is used.

[0003]

However, in such a conventional flow meter, the accuracy of the correction coefficient becomes a problem because the flow velocity measuring section multiplies the correction velocity by the correction coefficient from the flow velocity at one point. This correction coefficient is set assuming a symmetric flow velocity distribution, and the installation conditions of the flow meter are strictly determined. For example, as installation conditions, a straight section needs to be 10D or more (D is a pipe diameter) on the upstream side and 5D or more on the downstream side. However, even if the installation conditions are satisfied, there is a problem that an error occurs in the obtained flow meter if the symmetry of the flow velocity distribution is broken due to some influence on the upstream side. Further, since the correction coefficient must be obtained in advance, there is a problem that it takes time to determine the correction coefficient.
If the position of the measurement point of the flow velocity measurement unit is changed, the correction coefficient must be obtained again.

[0004] Another problem is that the measurement point of the flow velocity measuring unit cannot be easily changed for the above-mentioned reason, so that measurement cannot be performed when the water level is lower than the measurement point of the flow velocity measuring unit. In order to avoid such a problem, when the water level is lower than the measurement point, the flow velocity value is generated in a pseudo manner corresponding to the water level, and the flow rate is calculated in the same manner as described above. Since the flow velocity value to be generated is different from the actual state, there is a problem that an error occurs even when multiplied by the correction coefficient, which is different from the average flow velocity.

SUMMARY OF THE INVENTION The present invention has been made in view of such a conventional problem, and the invention according to claims 1 to 7 has a flow meter and a flow measuring method capable of accurately obtaining a flow rate without using a correction coefficient. Its purpose is to provide.

[0006]

In order to achieve the above object, a flow meter according to the present invention comprises a water level measuring unit for measuring the water level of a fluid, and a flow path width at each of a plurality of water depths. When the coordinates are taken in the width direction of the flow channel, normalized as a range from -1 to 1, the spherical function P of Legendre
For n (x), the root of Pn (x) = 0 (x1,... xn)
A flow velocity measurement unit that measures the flow velocity of a plurality of points, and calculates the flow channel width at each of the water depths, performs a Gaussian numerical integration from the flow widths and the flow velocities of the plurality of points measured by the flow velocity measurement unit. A flow rate calculation unit that calculates a flow rate by calculating an area of the flow velocity distribution at the water depth and integrating the area of the flow velocity distribution over the entire water depth.

In the flow rate measuring method of the present invention, the flow path width at each water depth and the water level at a plurality of water depths is standardized as extending from -1 to 1 in the flow path width direction. When the coordinates are taken, the root (x1,... X) of Pn (x) = 0 with respect to the Legendre's spherical function Pn (x)
n), the flow velocity at a plurality of points is measured, the flow path width at each water depth is calculated, and from the flow path width and the flow velocity at the plurality of points, Gaussian numerical integration is performed to calculate the flow velocity distribution at each water depth. The flow rate is calculated by calculating the area and integrating the area of the flow velocity distribution over the entire water depth.

A Gaussian numerical integration is an arbitrary function f
When (x) is a polynomial of degree 2n-1 or less,

[0009]

(Equation 1) And the integral of f (x) can be represented by the sum of the root of Pn (x) = 0 and the weighting factor wi derived from the root with respect to the Legendre spherical function Pn (x). is there. Here, the Legendre's spherical function is
For all polynomials Q (x) of degree n-1 or less,

[0010]

(Equation 2) Means an n-order polynomial Pn (x) that satisfies
Is

[0011]

(Equation 3) It is expressed as The roots of Pn (x) = 0 are x1, x2,.
xn, all the roots are real and single roots, -1 and 1
Between.

The weighting coefficient wi in the equation (1) is

[0013]

(Equation 4) It is represented by

Equation (1) is obtained as follows. That is, f (x), which is a polynomial of degree 2n-1 or less, is expressed as Pn
Divide by (x) and f (x) = Pn (x) Q (x) + φ
(X), both the quotient Q (x) and the remainder φ (x) are n−
Because it is less than primary

[0015]

(Equation 5) Becomes Furthermore, φ (x) is

[0016]

(Equation 6) Since φ (xi) = f (xi), (1)
An expression is obtained.

The above Legend when n = 2, 3, 4
The roots of the spherical function Pn (x) = 0 of re and the real values of the weighting coefficients are as shown in the following table.

[0018]

[Table 1] For the Legendre's spherical functions and Gauss's numerical integration, see "Analysis Overview" (Sadaharu Takagi, Third Edition, Light Edition, September 27, 1983, published by Iwanami Shoten Co., Ltd.,
Pp. 119-129).

Since the flow velocity distribution at a certain water depth is considered to be a 2n-1 order function of the position x in the flow channel width direction,
The area of the flow velocity distribution can be easily obtained by using the Gaussian numerical integration of the equation (1).

At a certain water depth zk, the flow path width W
When (zk) is normalized as extending from -1 to 1 in the flow channel width direction and coordinates are taken in the flow channel width direction, Legend
The root x of Pn (x) = 0 for the spherical function Pn (x) of re
The flow velocity at a plurality of points of 1, x2,.
(X1), vzk (x2),... Vzk (xn). By performing the Gaussian numerical integration of the equation (1), the area Azk of the flow velocity distribution becomes

[0021]

(Equation 7) Is calculated. Normally, it is considered that the flow velocity distribution is represented by a low-order function unless the flow is turbulent. Then, when it is estimated that the flow velocity distribution is a function of the third order or less (2n-1 = 3, n = 2), the area of the flow velocity distribution becomes n = 2 in the table.
Refer to the column of

[0022]

(Equation 8) Thus, the area of the flow velocity distribution can be obtained very easily and accurately. However, since the formula of the area of the flow velocity distribution is a case where the flow path width is standardized as 2 (x = −1 to 1), the actual flow velocity distribution is calculated using the flow path width W (zk). Needs to be converted to the area A ′ (zk). That is,

[0023]

(Equation 9) In this way, the flow rate can be calculated by calculating the area A ′ (zk) of the flow velocity distribution at a plurality of water depths and integrating the area of the flow velocity distribution over the entire water depth.
That is,

[0024]

(Equation 10) By integrating the area of the flow velocity distribution over the entire water depth, the flow rate Q can be calculated.

Optionally, the arithmetic processing can be simplified by integrating the area of the flow velocity distribution over the entire water depth with a Gaussian numerical integration. That is, the area A ′ (z) of the flow velocity distribution is also 2n−
Since it is considered to be a first-order function, when the water depth of the flow path is normalized in the vertical direction as ranging from −1 to 1 and coordinates are taken in the vertical direction, the Legendre's spherical function Pn
Using the area of the flow velocity distribution at the water depth at a plurality of points that are roots (z1,..., Zn) of Pn (z) = 0 with respect to (z),
The flow rate can be determined. The flow rate Q is

[0026]

[Equation 11] Is calculated. If the area of the flow velocity distribution is also considered to be a function of water depth, it is considered to be a lower-order function.

[0027]

(Equation 12) The flow rate can be obtained very easily and accurately.

At a plurality of water depths, an arbitrary means is used as a flow velocity measuring unit for measuring the flow velocity at a plurality of points at the root of the Legendre spherical function Pn (x) = 0 with respect to the flow path width at each water depth. But preferably,
A plurality of pulse Doppler ultrasonic velocimeters can be used that transmit pulsed ultrasonic waves in a direction at an angle to the flow of the fluid and receive reflected waves reflected by particles flowing in the fluid. By setting the transmission direction of the pulsed ultrasonic wave to a predetermined direction and receiving a reception signal from a predetermined direction after a lapse of a predetermined time from the transmission, it is possible to measure the flow velocity at an arbitrary measurement point. Therefore, Le
It is possible to measure the flow velocity at an arbitrary point that is the root of the gendre spherical function Pn (x) = 0.

Further, by transmitting the plurality of pulse Doppler ultrasonic waves upward from the bottom of the flow path, even if the water level becomes low, the predetermined measurement points can be reliably measured. The flow rate can be measured. Or
By providing a throttle mechanism detachably provided in the flow path downstream of each measurement point of the water level measurement unit and the flow velocity measurement unit, even when the water level is low, the sensor that transmits and receives pulsed ultrasonic waves submerges, ensuring The flow velocity at a predetermined measurement point can be measured. When the flow rate is large and the water level is constantly high, the restriction of the original flow can be prevented by removing the throttle mechanism.

The Legendre's spherical function Pn
The plurality of points that are roots of Pn (x) = 0 with respect to (x) include not only points that exactly match the roots of Pn (x) = 0 with respect to the Legendre spherical function Pn (x). , And points in the vicinity thereof.

[0031]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a block diagram illustrating a configuration of a flow meter according to the present invention.

In the figure, a flow meter 10 mainly includes a water level measurement unit 12 for measuring the water level of a fluid 42 flowing through an open channel (flow channel) 40, a flow velocity measurement unit 14 for measuring the flow velocity at a plurality of measurement points, A control unit 16 for controlling the measurement unit 12 and the flow velocity measurement unit 14, a flow calculation unit 18 for measuring the flow rate from the outputs from the water level measurement unit 12 and the flow velocity measurement unit 14, and a flow rate calculation unit 18 for displaying the flow rate. An input / output unit 20 connected to the display unit 22, the control unit 16 and the flow rate calculation unit 18 for inputting / outputting data from / to the outside; It has.

As the water level measuring unit 12, a known level meter such as a microwave type, an underwater type ultrasonic type, and a pressure type can be used. In this embodiment, an ultrasonic sensor is provided above the liquid level. An ultrasonic level meter to be arranged is used, and a transmission circuit 24 that outputs a transmission signal in response to a trigger signal from the control unit 16 and receives the transmission signal from the transmission circuit 24 and directs an ultrasonic pulse to the liquid surface Level sensor 26, which is composed of an ultrasonic transmitter for transmitting and receiving the reflected wave from the liquid level, and amplifying the reception signal from the ultrasonic receiver of the water level sensor 26, from the transmission signal to the reception signal. And a counter 29 for counting the time width of the gate signal. The output from the counter 29 indicates the distance from the water level sensor 26 to the liquid level. From the distance between the water level sensor 26 and the bottom surface of the open channel 40 which is known in advance, the water level sensor 2
By subtracting the distance from 6 to the liquid level, the water level H
(See FIG. 2).

The flow velocity measuring unit 14 outputs a transmission signal in response to a trigger signal from the control unit 16 at predetermined time intervals T, and receives a transmission signal from the transmission circuit 30 and receives an ultrasonic signal at predetermined intervals T. A flow rate sensor 32 including a transceiver that transmits and receives a pulse toward a fluid and is connected to a reception circuit 34 after transmission to receive a reflected wave, a reception circuit 34 that amplifies a reception signal from the flow rate sensor 32, By applying a gate to the received signal, sampling the received signal after a predetermined time has elapsed, and a Doppler shift detection circuit 36 that detects a Doppler shift frequency by performing a Fourier transform, comprising: a pulse Doppler ultrasonic current meter. is there.

As shown in FIG. 2, the flow rate sensor 32
It consists of two transceivers arranged at the bottom of the open channel 40, and is set so that the ultrasonic pulses transmitted from the transceivers 32, 32 face a predetermined direction. The predetermined direction, as shown in FIG. 2 (a), means that when viewed in a cross section of the open channel 40, the channel width at any water depth ranges from -1 to 1 at any water depth. Is set so as to pass through a point of about ± 0.577. Further, as shown in FIG. 2B, when viewed in a longitudinal section of the open channel 40, the ultrasonic pulse is set to be transmitted in a direction forming a predetermined angle θ with respect to the flow of the fluid. You.

The ultrasonic pulses transmitted from the transceivers 32, 32 are scattered and reflected by the particles in the fluid, and the reflected waves are received by the same transceivers 32, 32 again. Since the received reflected wave undergoes a Doppler shift, the Doppler shift detection circuit 36 performs a Fourier transform on the received signal, obtains the Doppler shift Δf, and performs A / D conversion.

The Doppler shift Δf is represented by v representing the flow velocity of the fluid, c representing the velocity of the ultrasonic wave in the fluid, and f representing the transmission frequency.
Assuming 0,

[0038]

Δf = (v / c) · cos θ · f0 (8)

The receiving circuit 34 can receive reflected waves from measurement points at a plurality of water depths. That is, a plurality of water depths z1, z2,..., Zk,.
The distance to the measurement point 44 where m ≦ H is L1, L2,.
··· Lk, ··· Lm, the time from transmission is almost 2L
1 / c, 2L2 / c,..., Lk / 2,.
A plurality of gate signals can be generated based on the water level signal from the flow rate calculator 18 so that the received signal after two lapses can be captured. In a predetermined cycle, the plurality of gate signals are sequentially switched to take in the received signals in the gates, so that the plurality of water depths z1, z2,
... Doppler shift Δf of measurement point 44 at zm
1, Δf2,..., Δfm can be obtained. 2
By performing the same processing on the received signals of the two transceivers 32, 32, the Doppler shift Δf1 (−f1) of the two measurement points 44 for each water depth z1, z2,.
0.577), Δf1 (0.577), Δf2 (−0.
577), Δf2 (0.577),..., Δfm (−
0.577) and Δfm (0.577).

The flow rate calculating section 18 has a water level H from the water level measuring section 12 and a Doppler shift Δ
f1 (−0.577), Δf1 (0.577), Δf2
(−0.577), Δf2 (0.577),..., Δ
fm (−0.577), Δfm (0.577), and temperature data from the temperature sensor 38 are fetched. The flow rate calculating section 18 can be constituted by a microprocessor including a CPU and a memory, and stores these data and calculates the flow rate using these data.

The calculation procedure in the flow rate calculation section 18 will be described below.

First, using the equation (8), the flow rate measuring unit 14
Shift Δf1 (−0.577), Δf
1 (0.577), Δf2 (−0.577), Δf2
(0.577),..., Δfm (−0.577), Δ
fm (0.577), the flow velocity v1 (−0.577), v
1 (0.577), v2 (-0.577), v2 (0.
577),..., Vm (−0.577), vm (0.
577). However, in equation (8), since the speed c of the ultrasonic wave in the fluid varies depending on the temperature, the speed c obtained by taking in the temperature from the temperature sensor 38 and correcting the temperature is used.

Next, using the above equation (3), each water depth z
The area of the flow velocity distribution at k is determined.

[0044]

A (z1) = v1 (−0.577) + v1 (0.577) A (z2) = v2 (−0.577) + v2 (0.577) A (zm) = vm (−) 0.577) + vm (0.577) In this manner, the area of the flow velocity distribution obtained is obtained by calculating the actual flow velocity distribution based on the equation (4) using the flow path width W (zk) at each water depth. Convert to area. Channel width W (z
k) can be obtained from the shape of the open channel 40 if zk is known. Then, the flow rate Q can be obtained by integrating the area of the converted flow velocity distribution using the equation (5) (FIG. 3).
reference).

[0045]

Q = A ′ (z1) · Δz + A ′ (z2) · Δ
z +... A ′ (zm) · Δz As described above, according to this embodiment, 1
In order to measure the flow velocity at a plurality of measurement points instead of just measurement points, even if the flow velocity distribution is not symmetrical, it is possible to respond, and by using Gaussian numerical integration, It is not necessary to measure the flow velocities at a large number of measurement points in all cross sections, and the flow rate can be accurately and easily obtained by measuring the flow velocities at limited measurement points.

Further, even when the water level is low, the flow velocity sensor 32 is attached to the bottom of the open channel 40, and the flow velocity can be measured by transmitting an ultrasonic pulse upward. Therefore, even at a low water level, the flow rate can be accurately measured.

Next, FIG. 4 is an explanatory diagram of a second embodiment of the present invention, and corresponds to FIG. Since the configuration block diagram of FIG. 1 is common, detailed description thereof is omitted.

In the first embodiment, the flow velocity is measured at many water depths, whereas in the present embodiment, only the flow velocity is measured at two water depths. . These two water depths are
When the water depth in the vertical direction ranges from -1 to 1,
The water depth is about ± 0.577. By appropriately setting the gate signal in the receiving circuit 34, the flow velocity at this water depth can be measured. Above (3) each depth _z = _{z 0.577 with,} obtains the area of the flow velocity distribution in the _{z -0.577.}

[0049]

A (0.577) = v _0.577 (−0.57)
7) + v _0.577 (0.577) A (−0.577) = v _−0.577 (−0.577) + v
_-0.577 (0.577) In this way, the areas of the two flow velocity distributions obtained are the flow path widths W (0.577) and W (-
0.577) is converted to the area of the actual flow velocity distribution based on the equation (4), and the converted flow area is added using the equation (7) to obtain the flow rate Q. be able to.

According to the second embodiment, the operation can be further simplified as compared with the first embodiment.

In the above embodiment, the inverted trapezoidal open channel 40
As described above, the flow rate of a circular open channel can be obtained by the same method.

As shown in FIG. 5, in the case of a circular waterway 50, two transceivers 32,
Regardless of the setting of the ultrasonic pulse transmitted from No. 32, when the width of the flow path ranges from -1 to 1 at each water depth, the ultrasonic pulse completely passes through a point of about ± 0.577. Cannot be set. However, for example, in the example shown in FIG. 5, the height D / 10 from the lowest point of the bottom.
(D is the pipe diameter), it is set so as to pass through a point near ± 0.577, and when the water level is smaller than the radius D / 2 of the circular waterway 50, a height other than the height D / 10 is used. The height can also be set so as to pass through a point which is approximately ± 0.577, and the error can be small. FIG. 6 shows the flow velocity and the position in the flow channel width direction (the distance from the center line of the flow channel width when half of the flow channel width is 1).
5 is a graph of a horizontal flow velocity distribution showing the relationship with the following. About ± 0.
In the vicinity of 577, since the flow velocity is almost constant, the error is small without any correction. However, when the accuracy is further improved, about ± 0.57 based on the relationship of FIG.
The correction may be performed so that the flow velocity at point 7 is obtained.

In the case of the circular channel 50, when the water level is sometimes larger than the radius D / 2 of the circular channel 50, as shown in FIG.
In addition, the transceivers 32 ′, 32 ′ may be arranged. The transmitter / receiver 3 is arranged such that the center line of the transmitter / receiver 32, 32 at the bottom in the transmission direction of the ultrasonic pulse and the center line of the transmitter / receiver 32 ′, 32 ′ in the transmission direction of the ultrasonic pulse are vertically symmetrical.
2 'and 32' are arranged. The flow rate is measured by the transceivers 32 ′ and 32 ′ for the portion higher than the radius D / 2, and the flow rate is measured by the transceivers 32 and 32 for the portion lower than the radius D / 2. At any depth, the flow velocity measurement at a point near about ± 0.577 can be performed.

The flow rate can be measured not only for the inverted trapezoidal open channel and the circular open channel but also for the water channel having an arbitrary shape such as a rectangular shape or an oval shape.

FIG. 8 shows an embodiment of a flow meter provided with a throttle mechanism 60 as a further measure against a low water level.

The throttle mechanism 60 is detachably provided in the circular water passage 50 downstream of the flow rate sensor 32 of the water level measuring section 12 and the water level sensor 26 of the flow rate measuring section 14. By reducing the flowing water area by the throttle mechanism 60 and raising the water level to, for example, about 1/10 of the pipe diameter, the flow velocity sensors 32, 32 of the flow velocity measuring unit 14 are surely submerged in the flow. Can be

When the flow rate is steadily increased and the water level constantly becomes, for example, 1/10 or more of the pipe diameter, the throttle mechanism 60
Can be removed to prevent restricting the original flow.

In the above-described embodiment, the flow velocity distribution at two points at each water depth is obtained assuming that the flow velocity distribution is a function of the third order or less of the position x in the flow channel width direction. Without limitation, it is of course possible to measure the flow velocity at three or more points to further improve the accuracy.

[0059]

As described above, according to the first aspect of the present invention,
According to the inventions described in (7), since the flow velocity at a plurality of points is measured at each water depth, it is possible to accurately cope with the case where the flow is asymmetric. Further, since the area of the flow velocity distribution at each water depth is calculated by performing the Gaussian numerical integration, the area of the flow velocity distribution and the flow rate can be accurately calculated even if the number of measurement points is small. Since the number of measurement points may be limited, measurement and calculation can be simplified.

According to the second and seventh aspects of the present invention, it is not necessary to measure the flow velocity at a large number of water depths, so that the measurement and the calculation can be further simplified.

According to the third aspect of the present invention, the flow velocity at an arbitrary measurement point can be measured by using the pulse Doppler type ultrasonic flow meter, so that Leg
Pn (x) = 0 for the spherical function Pn (x) of the endre
Can be measured at any point that is the root of the flow rate.

According to the fourth and fifth aspects of the present invention, even when the water level becomes low, the flow velocity at a predetermined measurement point can be measured reliably, and the flow rate can be accurately calculated. Furthermore, according to the fifth aspect of the invention, when the flow rate increases steadily, the restriction mechanism can be removed to prevent the original flow from being restricted.

[Brief description of the drawings]

FIG. 1 is a block diagram illustrating a configuration of a flow meter according to the present invention.

FIG. 2A is an explanatory diagram showing flow velocity measuring points as viewed from a horizontal cross section of a water channel, and FIG. 2B is an explanatory diagram showing flow velocity measuring points as viewed from a vertical cross section of the water channel.

FIG. 3 is an explanatory diagram showing a flow velocity distribution.

FIGS. 4A and 4B are explanatory diagrams illustrating flow velocity measurement points as viewed from a horizontal cross section of a water channel, and FIG. 4B is an explanatory diagram illustrating flow velocity measurement points as viewed from a vertical cross section of a water channel in the second embodiment. .

FIG. 5 is an explanatory diagram showing flow velocity measurement points as viewed from a cross section of a water channel in the case of a circular water channel.

FIG. 6 is a graph showing a relationship between a flow velocity and a position in a flow path width direction (a distance from a center line of the flow path width when a half of the flow path width is 1).

FIG. 7 is an explanatory diagram showing a flow velocity measurement point as viewed from a cross section of a circular channel in a case of a circular channel, showing a case where a water level is higher than a radius of the channel.

8A is a cross-sectional view of a flow meter provided with a throttle mechanism, illustrating a throttle mechanism as viewed from a transverse cross section of a water channel, and FIG. 8B is a cross-sectional view of the flow meter as viewed from a vertical cross section of the water channel.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 10 Flow meter 12 Water level measurement part 14 Flow velocity measurement part (pulse Doppler type ultrasonic velocity meter) 18 Flow rate calculation part 40 Open water path (flow path) 42 Fluid 50 Circular water path (flow path) 60 Throttling mechanism

Claims (7)

[Claims] 1. A flow meter for measuring a flow rate of a fluid flowing through a flow path, comprising: a water level measuring unit for measuring a water level of the fluid; When the coordinates are normalized in the range of 1 to 1 and the coordinates are taken in the channel width direction, the Legendre spherical function Pn
A flow velocity measuring unit that measures the flow velocity at a plurality of points that are the roots (x1,... Xn) of Pn (x) = 0 with respect to (x); Flow rate calculation unit that calculates the flow rate by calculating the area of the flow velocity distribution at each water depth by performing Gaussian numerical integration from the flow velocity at multiple points measured by the flow velocity measurement unit, and integrating the area of the flow velocity distribution over the entire water depth And a flow meter comprising: 2. A plurality of water depths measured by the flow velocity measuring unit are defined by standardizing the water depth of the flow path in the vertical direction as ranging from −1 to 1 and taking coordinates in the vertical direction, Legen.
The water depth of a plurality of points that are roots (z1,... zn) of Pn (z) = 0 with respect to the spherical function Pn (z) of dre, and the integral of the area of the flow velocity distribution performed by the flow rate calculator over the entire water depth is , The area of the velocity distribution at each water depth calculated by performing Gaussian numerical integration, and by performing Gaussian numerical integration,
The flow meter according to claim 1, wherein the flow rate is calculated. 3. The flow velocity measuring unit transmits the pulsed ultrasonic waves in a direction at an angle to the flow of the fluid and receives a reflected wave reflected by particles flowing in the fluid.
3. The flowmeter according to claim 1, wherein the flowmeter is a pulse Doppler ultrasonic flowmeter. 4. The flowmeter according to claim 3, wherein the pulse Doppler ultrasonic flowmeter transmits pulsed ultrasonic waves upward from the bottom of the flow path. 5. The apparatus according to claim 3, further comprising a throttle mechanism detachably provided in a flow path downstream of each of the measurement points of the water level measurement unit and the flow velocity measurement unit.
Flowmeter as described. 6. A flow rate measuring method for measuring a flow rate of a fluid flowing through a flow path, wherein, at a water level of the fluid and a plurality of water depths, a flow path width at each water depth ranges from -1 to 1 in the flow path width direction. When the coordinates are taken in the width direction of the flow channel standardized as
For the spherical function Pn (x) of Pn (x) = 0 (x
, Xn) are measured, the flow channel width at each of the water depths is calculated, and the Gaussian numerical integration is performed from the flow channel width and the flow speeds at the plurality of points at each of the water depths. A flow rate measurement method that calculates the flow rate by calculating the area of the flow velocity distribution and integrating the area of the flow velocity distribution over the entire water depth. 7. The plurality of water depths at which the measurement is performed are standardized by defining the water depth of the flow path in the vertical direction as ranging from −1 to 1, and taking coordinates in the vertical direction, the Legendre's spherical function Pn (z) , The root of Pn (z) = 0 (z1,... Z
n) The integral of the area of the flow velocity distribution over the entire water depth, which is the water depth of a plurality of points as described in (n), is obtained by performing the numerical integration of Gauss and calculating the area of the flow velocity distribution at each water depth and further performing the numerical integration of Gauss 7. The flow rate measuring method according to claim 6, wherein the calculation is performed.