JP2019020191A - Tube flow measuring device and tube downstream pressure prediction control device - Google Patents

Abstract

To provide a tube flow measurement device for measuring the flow rate of a tube when a liquid flows in a steady flow state, wherein a cross section of the tube is made uniform, and a downstream pressure prediction device for predicting a downstream pressure to a setting value under a setting flow rate by adjusting an upstream pressure.SOLUTION: A tube with a pressure gauge and a liquid temperature are measured at the upstream and downstream sides of a tube where the section is uniform, and the liquid thermometer is installed at the downstream and the pressure gauge and the liquid temperature are measured. A first tube friction coefficient and Reynolds number function based on the known Darcy Weissbach formula with the pressure difference, liquid density, liquid viscosity and tube size as a coefficient and a second tube friction coefficient and Reynolds number function dependent on the roughness of the inner wall of the tube and independent of the type of liquid are created; and the tube friction coefficient and the Reynolds number are obtained directly from the calculation by solving the functions as a simultaneous equation and the flow rate is measured. The flow rate of the curved tube and a large number of pipelines with a high height difference can easily be measured with high accuracy.SELECTED DRAWING: Figure 1

Description

The present invention provides a pipe flow measuring device that measures the flow rate of a pipe in which a liquid flows down in a steady flow state through a pipe having a uniform pipe cross section, and predicts by adjusting the upstream pressure to a set value based on the downstream pressure. The present invention relates to a downstream pressure prediction control device to be controlled.
In the present invention, “steady flow” is defined as a flow in which there is no change in the flow of the entire pipe over time.
“Uniform cross-section pipe” is defined as a pipe having the same cross-sectional dimensions and the same wall roughness.
"Steady flow with uniform cross-section pipe" is defined as a flow in which the flow in the uniform cross-section pipe does not change in time and has a uniform cross section, and the flow velocity and flow rate are spatially the same by the law of continuity. To do.

In the present invention, the flow rate of a pipe where a liquid flows down in a steady flow state through a pipe having a uniform pipe cross section is measured by electrical transmission of the measured value of the pressure gauge installed upstream and the pressure gauge installed downstream. Installed in the upstream to predict and control the pressure at the downstream pressure predictive control point to the set pressure under the set flow rate, with the pipe flow measuring device that obtains the pipe flow rate by the flow rate calculation device installed in the remote place by the head and the transmission line This is a pipe downstream pressure prediction control device that obtains and sets the pressure set point pressure by calculation by adjusting the pressure of the pressure setter.
The pipe downstream pressure prediction control device is installed in the vicinity of the upstream pressure setter or in a remote place by a signal transmission unit and a transmission line by electrical means.

Patent No. 4503830 JP-A-6-94490 JP 50-36163

First fluid mechanics Emura Tamura Scientific book publication P115-P156 2014 Mechanical Engineering Handbook Fundamentals α4 Fluid Engineering The Japan Society of Mechanical Engineers P69-P71 2006 Fluid resistance of pipelines and ducts Japan Society of Mechanical Engineers P22-P29 1979

Conventionally, as a pipe flow measuring device, an electromagnetic flow meter, an ultrasonic flow meter, and an orifice flow meter are used as typical methods.
Electromagnetic flowmeters are difficult to measure non-conductive liquid flow rates. In addition, the flow meter installation is a flange type, so the installation work is expensive. This is particularly expensive when the pipe diameter is large.
The ultrasonic flowmeter has an error in the flow velocity distribution in the pipe due to flow disturbance such as laminar flow and turbulent flow, and the accuracy is lower than that of the electromagnetic flowmeter. Compared to the electromagnetic type, the price is low for large diameters.
Since the orifice type measures the flow rate by creating friction loss in the pipe, the head loss of the pipe becomes a problem.
As the pipe flow rate measurement method, the predicted flow rate corresponding to the pressure difference between the upstream and downstream measured using the diagram showing the relationship between the Reynolds number and the coefficient of friction called the Moody diagram shown in FIG. 3 and the well-known Darcy-Weissbach equation However, there is no practicality for automatic flow rate measurement due to the complexity of reading the Moody diagram, the poor reading accuracy, and the complexity of the calculation process.
Another problem is the development of a flow meter that is less expensive than conventional electromagnetic and ultrasonic flow meters without the friction loss of pipes due to the installation of the flow meter.
In particular, the development and low development of pipe flow measuring devices that can be used universally for networks such as agricultural pipelines, oil transportation pipelines, chemical plant pipelines, and water supply pipelines that require the installation of many flow meters. Pricing is an issue.

管内を流れる液体の粘度 μ［Ｐａ・ｓ］
動粘度 ν＝μ／ρ［ｍ^２／ｓ］
とすれば、レイノルズ数Ｒｅは数式２で示される。

数式１と数式２から平均速度ｕを消去し、摩擦係数λについて整理した式を数式３
に示す。

数式３はダルシー・ワイスバッハの式をベースとした第一管摩擦係数、レイノルズ数関数と定義する。本関数の係数を演算する第一管摩擦係数、レイノルズ数関数係数演算部４において、数式３の管摩擦係数λ、レイノルズ数Ｒｅ以外の係数を決定する。
上流圧力計１、下流圧力計２で測定した上流圧力Ｐ１、下流圧力Ｐ２を電気信号により伝送する信号伝送部８および伝送路９により伝送して第一管摩擦係数、レイノルズ数関数係数演算部４において、
ΔＰ＝Ｐ１−Ｐ２の差圧演算をおこない係数を決定する。
液体温度計３で測定した液体温度Ｔを電気信号により伝送する信号伝送部８および伝送路９により伝送して第一管摩擦係数、レイノルズ数関数係数演算部４において、液体密度、粘度を設定する液体パラメータ設定部７により設定されている基準温度における液体密度、粘度を測定した液体温度Ｔにおける液体密度、粘度に換算する。換算はあらかじめ設定されている換算テーブルを参照して換算値を求めるか、または粘度の場合は公知のアンドレード粘度換算数式により換算する。
本発明においては、上流圧力計１と下流圧力計２の距離Ｌは管内面は平滑の場合の流量測定も行うことになるために、この間の管摩擦損失を大きくして、測定精度を向上させるために距離Ｌは１ｋｍ以上となることもあり、また、流量演算装置１４は広域に設置された多数の流量計測に対応することを想定して、上流圧力計１または下流圧力計２と流量演算装置１４との間は伝送回線で接続する。
この他に第一管摩擦係数、レイノルズ数関数係数演算部４に管の水力直径として円形管の場合は管内径ｄ、上流圧力計１と下流圧力計２間の距離Ｌを管寸法パラメータ設定部により設定する。
以上により、数式３の係数はすべて決定して、第一管摩擦係数、レイノルズ数関数の管摩擦係数λはレイノルズ数Ｒｅのみの関数となる。 The invention of "Claim 1" is made to solve the above-mentioned "problem to be solved by the invention". FIG. 1 is a basic configuration diagram of the invention of claim 1. An upstream pressure gauge 1 for measuring the upstream pressure of the pipe and a downstream pressure gauge 2 for measuring the downstream pressure are installed so that the liquid flows down in a steady flow state through the pipes arranged in the same horizontal plane with a uniform pipe cross section.
A liquid thermometer 3 for measuring the temperature of the liquid is installed at a position representing the liquid temperature of the pipe. The liquid thermometer 3 corrects the liquid viscosity and density accompanying the temperature change.
When the circular pipe shown in Fig. 1 is installed horizontally,
Pressure of upstream pressure gauge P1 [Pa]
Downstream pressure gauge pressure P2 [Pa]
Pressure loss ΔP = (P1−P2) [Pa]
Distance between upstream and downstream pressure gauges L [m]
Tube friction coefficient λ [Dimensionless number]
Liquid density ρ [kg / m ³ ]
Average flow velocity u [m / s]
Pipe inner diameter d [m]

Then, the well-known Darcy-Weissbach equation is expressed by Equation 1.

Viscosity of the liquid flowing in the pipe μ [Pa · s]
Kinematic viscosity ν = μ / ρ [m ² / s]
Then, the Reynolds number Re is expressed by Equation 2.

The average speed u is eliminated from Equation 1 and Equation 2, and the equation obtained by arranging the friction coefficient λ is represented by Equation 3
Shown in

Formula 3 is defined as the first pipe friction coefficient and the Reynolds number function based on the Darcy-Weissbach formula. In the first pipe friction coefficient / Reynolds number function coefficient calculation unit 4 for calculating the coefficient of this function, coefficients other than the pipe friction coefficient λ and Reynolds number Re in Expression 3 are determined.
The upstream pressure gauge 1 and the downstream pressure gauge P2 measured by the upstream pressure gauge 1 and the downstream pressure gauge 2 are transmitted by the signal transmission section 8 and the transmission path 9 that transmit the electrical signals, and the first pipe friction coefficient and Reynolds number function coefficient calculation section 4 are transmitted. In
A coefficient is calculated by performing a differential pressure calculation of ΔP = P1−P2.
The liquid temperature T measured by the liquid thermometer 3 is transmitted by a signal transmission unit 8 and a transmission path 9 that transmit electric signals, and the first pipe friction coefficient and Reynolds number function coefficient calculation unit 4 set the liquid density and viscosity. The liquid density and viscosity at the reference temperature set by the liquid parameter setting unit 7 are converted into the liquid density and viscosity at the measured liquid temperature T. For conversion, a conversion value is obtained with reference to a conversion table set in advance, or in the case of viscosity, conversion is performed using a well-known Andrade viscosity conversion formula.
In the present invention, since the distance L between the upstream pressure gauge 1 and the downstream pressure gauge 2 also measures the flow rate when the pipe inner surface is smooth, the pipe friction loss between them is increased to improve the measurement accuracy. Therefore, the distance L may be 1 km or more, and the flow rate calculation device 14 is assumed to support a large number of flow rate measurements installed in a wide area, and the upstream pressure gauge 1 or the downstream pressure gauge 2 and the flow rate calculation. The device 14 is connected by a transmission line.
In addition, the first pipe friction coefficient and Reynolds number function coefficient calculation unit 4 sets the pipe inner diameter d and the distance L between the upstream pressure gauge 1 and the downstream pressure gauge 2 in the case of a circular pipe as the hydraulic diameter of the pipe. Set by.
Thus, all the coefficients of Equation 3 are determined, and the tube friction coefficient λ of the first tube friction coefficient and the Reynolds number function is a function of only the Reynolds number Re.

乱流の場合の管摩擦係数、レイノルズ数の関数は公知の式として、複数の式があるが、レイノルズ数の適用範囲が広く、管内面の粗さにも対応できる式として、数式５に示す公知のコールブルックの式がある。従って、本発明ではコールブルックの式を例として説明する。
ここで、εは絶対粗さで、管内径との比ε／ｄは相対粗さと呼ばれている。
ε／ｄは管相対粗さ設定部１０により設定する。
図４に管内壁の絶対粗さと相対粗さの関係を示す。

数式５においてε／ｄ＝０とすれば、管内面の粗さが滑らかな管に相当し、数式６のように置き換えることができる。数式６は公知の式であり、プラントル・カルマンの式と呼ばれている。

また、数式５においてε／ｄが大きくなり、管内面が粗く摩擦係数がレイノルズ数の影響を無視できる場合は、数式７のように置き換えることができる。数式７は公知の式であり、カルマン・ニクラーゼの式と呼ばれている。

乱流の場合、ε／ｄの値により、数式６は滑らかな管の場合、数式７は粗い管の場合となるが、いずれもε／ｄの値を選べば数式５が適用可能なため、以下数式５により第二管摩擦係数、レイノルズ数関数係数を計算する。
第二管摩擦係数、レイノルズ数関数係数演算部５に管相対粗さを管相対粗さ設定部１０により設定し、臨界レイノルズ数を臨界レイノルズ数設定部１１により設定する。
層流から乱流に変化する遷移流の管摩擦係数に対するレイノルズ数の関数として、下記によるものとする。
（１）臨界レイノルズ数は下限、上限がある。
（２）下限、上限間のレイノルズ数と摩擦係数の関係は層流と乱流曲線を結ぶ直線近似とする。
これは下限、上限間のレイノルズ数と摩擦係数の関係は図５に示す実験データから下限、上限間のレイノルズ数と摩擦係数の関係は直線的に近似可能となるためである。
（３）遷移流となる上、下限のレイノルズ数は管と流体依存性が大きく確定できないために設定値とする。
（４）層流と遷移流、遷移流と乱流への変化時に摩擦係数対レイノルズ数曲線は不連続とならない。

層流と遷移流の境界の臨界レイノルズ数 Ｒｅ_Ｌ
遷移流と乱流の境界の臨界レイノルズ数 Ｒｅ_Ｈ
層流と遷移流の境界の摩擦係数 λ_Ｌ
遷移流と乱流の境界の摩擦係数 λ_Ｈ

とし、レイノルズ数Ｒｅを横軸、摩擦係数λを縦軸にとった時の遷移流の直線の方程式は数式８となる。
臨界レイノルズ数Ｒｅ_Ｌ およびＲｅ_Ｈは臨界レイノルズ数設定部１１により設定する。

ここで、λ_Ｌは数式４により、λ_Ｌ＝ ６４／ Ｒｅ_Ｌにより計算する。また、λ_Ｈは乱流曲線の数式５において、レイノルズ数Ｒｅ_Ｈを代入した数式９により計算される。
流量計測対象管のε／ｄの値は管の粗さに対応して設定する。

なお、実用管について直径ｄと相対粗さの例を図６に示す。
以上により数式９は乱流域と接続する摩擦係数λ_Ｈ以外の係数は与えられ、λ_Ｈ
について解くことが可能である。数式９は陰関数のためλ_Ｈの値はニュートン・
ラプソン法等を用いて数値的に解くか、Ｅｘｃｅｌ等の表計算ソフトであるゴールシーク、ソルバーなどを管流量計測装置１４に組込むことにより演算で求める。
λ_Ｈが求められたことにより、遷移流のλ、Ｒｅの直線の方程式の係数が求められた。
以上、第二管摩擦係数、レイノルズ数関数係数演算部５の係数と数式が求められた。図７に第二管摩擦係数、レイノルズ数関数の遷移域における直線近似の方法を示す。 In the first pipe friction coefficient and Reynolds number function coefficient calculation section 4, it depends on the type of liquid, pipe dimensions, distance L between the upstream pressure gauge and downstream pressure gauge, the measured upstream pressure P1, and the differential pressure ΔP between the downstream pressure P2. The first pipe friction coefficient and the Reynolds number function coefficient are obtained.
In the second pipe friction coefficient and Reynolds number function coefficient calculation unit 5, the mathematical formulas are different for each laminar flow, transitional flow from laminar flow to turbulent flow region, and turbulent flow. The pipe friction coefficient and Reynolds number function that depend only on the roughness of the wall are defined as the second pipe friction coefficient and Reynolds number function. The coefficient and mathematical expression of the coefficient calculation unit of this function are shown below.
The function of the tube friction coefficient and the Reynolds number in the case of a laminar flow is expressed by Equation 4 as a well-known equation.

There are a plurality of well-known expressions for the coefficient of tube friction coefficient and Reynolds number in the case of turbulent flow, but the expression range 5 is shown as an expression that has a wide range of application of the Reynolds number and can cope with the roughness of the tube inner surface. There is a well-known Colebrook equation. Therefore, in the present invention, the Colebrook equation will be described as an example.
Here, ε is the absolute roughness, and the ratio ε / d to the tube inner diameter is called the relative roughness.
ε / d is set by the tube relative roughness setting unit 10.
FIG. 4 shows the relationship between the absolute roughness and the relative roughness of the pipe inner wall.

If ε / d = 0 in Equation 5, it corresponds to a tube having a smooth inner surface, and can be replaced as Equation 6. Formula 6 is a known formula and is called the Prandtl Kalman formula.

Further, when ε / d becomes large in Equation 5 and the inner surface of the tube is rough and the friction coefficient can ignore the influence of the Reynolds number, it can be replaced as Equation 7. Formula 7 is a well-known formula and is called the Kalman-Niclase formula.

In the case of turbulent flow, depending on the value of ε / d, Equation 6 is a smooth tube, Equation 7 is a coarse tube, but in any case, Equation 5 can be applied if the value of ε / d is selected. Hereinafter, the second pipe friction coefficient and the Reynolds number function coefficient are calculated by Equation 5.
In the second pipe friction coefficient and Reynolds number function coefficient calculation unit 5, the pipe relative roughness is set by the pipe relative roughness setting unit 10, and the critical Reynolds number is set by the critical Reynolds number setting unit 11.
As a function of the Reynolds number for the tube friction coefficient of a transition flow changing from laminar to turbulent,
(1) The critical Reynolds number has a lower limit and an upper limit.
(2) The relationship between the Reynolds number and the friction coefficient between the lower limit and the upper limit is a linear approximation connecting the laminar flow and the turbulent flow curve.
This is because the relationship between the Reynolds number and the friction coefficient between the lower limit and the upper limit can be approximated linearly from the experimental data shown in FIG. 5.
(3) The upper limit of the Reynolds number for the transition flow is set to a set value because the dependence on the pipe and the fluid cannot be determined.
(4) The friction coefficient vs. Reynolds number curve does not become discontinuous when changing to laminar flow and transition flow, or transition flow and turbulence.

Critical Reynolds number at the boundary between laminar and transition flow Re _L
Critical Reynolds number at the boundary between transition and turbulent flow Re _H
Friction coefficient at the boundary between laminar flow and transition flow λ _L
Friction coefficient at the boundary between transitional flow and turbulent flow λ _H

The equation of the straight line of the transition flow when the Reynolds number Re is taken on the horizontal axis and the friction coefficient λ is taken on the vertical axis is given by Equation 8.
The critical Reynolds numbers Re _L and Re _H are set by the critical Reynolds number setting unit 11.

Here, λ _L is calculated by λ _L = 64 / Re _{L according} to Equation 4. Further, λ _H is calculated by Expression 9 in which the Reynolds number Re _H is substituted in Expression 5 of the turbulent flow curve.
The value of ε / d of the flow rate measurement target pipe is set corresponding to the roughness of the pipe.

An example of the diameter d and the relative roughness of the practical pipe is shown in FIG.
Equation 9 coefficients other than friction coefficient lambda _H connecting the turbulent is given the above, lambda _H
It is possible to solve for. Since Equation 9 is an implicit function, the value of λ _H is Newton ·
It is solved numerically using the Rapson method or the like, or is obtained by calculation by incorporating a goal seek, solver or the like, which is a spreadsheet software such as Excel, into the pipe flow measuring device 14.
By obtaining λ _H , coefficients of linear equations of λ and Re of the transition flow were obtained.
The second pipe friction coefficient and the Reynolds number function coefficient calculation unit 5 coefficients and mathematical formulas have been obtained. FIG. 7 shows a method of linear approximation in the transition region of the second pipe friction coefficient and the Reynolds number function.

表１の第一および第二管摩擦係数、レイノルズ数関数の係数は第一および第二管摩擦係数、レイノルズ数関数係数演算部で値が求められているために、いずれの数式も管摩擦係数λおよびレイノルズ数Ｒｅのみを変数とする関数である。 The simultaneous pipe friction coefficient / Reynolds number calculation unit 12 calculates the pipe friction coefficient and the Reynolds number by simultaneously using the first and second pipe friction coefficients and the Reynolds number function.
The first pipe friction coefficient and the Reynolds number function are expressed by Equation 3.
The second pipe friction coefficient and Reynolds number function are based on separate equations for laminar flow, transition flow, and turbulent flow.
For laminar flow, Equation 4,
For transition flow, Equation 8
For turbulence, Equation 5
It is.
Table 1 summarizes these mathematical expressions.

Since the coefficients of the first and second pipe friction coefficients and the Reynolds number function in Table 1 are determined by the first and second pipe friction coefficients and the Reynolds number function coefficient calculation unit, both formulas are used for the pipe friction coefficient. It is a function having only λ and Reynolds number Re as variables.

In the simultaneous pipe friction coefficient and Reynolds number calculation unit 12, the first pipe friction coefficient, the Reynolds number function and the second pipe friction coefficient and the Reynolds number function obtained for each laminar flow, transition flow, and turbulent flow are used as simultaneous equations, and the friction coefficient λ and Reynolds number Re are obtained.
The order of calculation is performed by automatically selecting the procedure shown in FIG.
First, the friction coefficient λ and the Reynolds number Re are obtained for turbulent flow.
When the Reynolds number Re is less than the critical Reynolds number Re _H upper determines that turbulence.
The critical Reynolds number Re _H at less than seek Reynolds number Re assuming transitional flow. When the Reynolds number Re determined on the assumption of a transition flow is smaller than the upper limit critical Reynolds number Re _H and equal to or higher than the lower limit critical Reynolds number Re _L , it is determined as a transition flow.
When the obtained Reynolds number Re is smaller than the lower limit critical Reynolds number Re _L , the friction coefficient λ and the Reynolds number Re are obtained for the laminar flow. When the Reynolds number Re is less than the critical Reynolds number Re _L of lower limit is determined to laminar flow.
In the case of turbulent flow, when solving the simultaneous equations of the first pipe friction coefficient, the Reynolds number function, the second pipe friction coefficient, and the Reynolds number function, the numerical formula becomes an implicit function numerically using the Newton-Raphson method, etc. Solved or obtained by calculation by incorporating a goal seek, solver or the like, which is a spreadsheet software such as Excel, into the pipe flow measuring device 14.

また、Ｒｅで表現した場合は管流量Ｑは数式２を用いて、数式１１の計算により求められる。

流量演算装置１４の流量表示部１３において、数式１０または数式１１により計算した流量Ｑを表示する。 In the flow rate calculation display unit 13 for calculating and displaying the pipe flow rate, calculation is performed using the simultaneous pipe friction coefficient, the friction coefficient λ obtained by the Reynolds number calculation unit 12, and the Reynolds number Re. The pipe flow rate Q when expressed by λ is obtained by Equation 10 using Equation 1.

Further, when expressed in Re, the pipe flow rate Q is obtained by the calculation of Expression 11 using Expression 2.

In the flow rate display unit 13 of the flow rate calculation device 14, the flow rate Q calculated by the formula 10 or the formula 11 is displayed.

As a method of measuring the flow rate using the pressure difference ΔP of the pressure gauge installed upstream and downstream of the pipe, regardless of the restriction mechanism such as an orifice, the Reynolds number with respect to this assumed flow rate value Q is assumed assuming the flow rate value to be measured. Re is obtained from Equation 11, the friction coefficient λ is read from a known chart called Moody diagram, ΔP measured in Equation 10 and the read λ are substituted to calculate the flow rate Q. Next, the assumed flow rate value is changed so that the calculated flow rate Q and the assumed flow rate value coincide with each other, and Re and λ are obtained again using the Moody diagram, and the flow rate Q is calculated by Equation (10). A method is conceivable in which this procedure is repeated until the flow rate value calculated by Equation 10 matches the assumed flow rate value, and the matched flow rate is used as the flow rate measurement value.
As a method of searching for the flow rate by repetition for this purpose, there is a method in which the Reynolds number Re and the friction coefficient λ of the Moody diagram are stored as a table in the memory of the data processing device, and the flow rate measurement value is automatically searched by data processing. Conceivable.
The present invention does not use a Moody diagram, and therefore does not require a table of the Moody diagram. The first Reynolds number Re obtained from the well-known Darcy-Weissbach equation, the functional equation of the friction coefficient λ, the liquid The Reynolds number Re and the friction coefficient λ are obtained by simultaneously combining two independent functional expressions of the second Reynolds number Re and the friction coefficient λ. For this reason, the second Reynolds number Re and the coefficient of friction coefficient λ in the turbulent region are represented by the function of the Reynolds number Re and the friction coefficient λ other than the well-known Colebrook empirical formula used in the Moody diagram. Known formulas such as formulas and nickase formulas can also be used depending on the application.
Further, in the Moody diagram, the diagram of the transition basin that changes from laminar flow to turbulent flow is not shown, but in the present invention, Formula 8 is newly created as a relational expression between the Reynolds number Re and the friction coefficient λ of the transition basin, The Reynolds number Re and the friction coefficient λ can be automatically calculated over the laminar flow region, transition flow region, and turbulent flow region.
In the present invention, the relationship between the Reynolds number Re and the friction coefficient λ becomes a continuous value by formulating, and no error is caused by the discrete values of the Reynolds number Re and the friction coefficient λ due to the table formation of the Moody diagram.
Major differences from Patent Document 1 Patent No. 4503830 are shown below.
Patent No. 4503830 shows the mass flow rate Qmass that seems to be derived from the orifice flow rate formula in equation (2), where Qmass is proportional to the coefficient of friction Cd and proportional to the square root of the specific gravity ρ of the fluid. It has become. "Q _i -Q _i-1 is converged below the convergence reference value by using the flow diagram shown in FIG. 6 and the Moody diagram based on the equation (2) in which Q mass is proportional to the friction coefficient Cd. This value is output as the mass flow rate value Qi ”, but this process cannot be understood.
In the present invention, the flow rate Q directly derived from the Darcy-Weissbach equation is shown in Equation 10. The flow rate Q is an equation that is inversely proportional to the square root of the friction coefficient λ and the density ρ of the liquid. Therefore, there is a fundamental difference in the flow rate calculation method from Patent No. 4503830.
In claim 2 of Japanese Patent No. 4503830, “a portion of the pipe between the first position and the second position is such that the coefficient of friction of the pipe portion is constant over a range of Reynolds numbers. The transmitter according to claim 1, wherein the transmitter has a roughness with respect to the inner diameter ratio. ”
This description means that the friction coefficient of the portion of the pipe between the first position and the second position is different from the friction coefficient of the pipe connected between the first position and the second position. Yes. In the present invention, the friction coefficient between the upstream pressure gauge and the downstream pressure gauge does not need to have a different friction coefficient in order to install the pressure gauge in the pipe to be measured. In the flow meter of Japanese Patent No. 4503830, similarly to the flow meter using the orifice, the friction loss of the pipe is generated by changing the friction coefficient of the measurement unit. On the other hand, in the flow rate measuring device of the present invention, there is no need to vary the friction coefficient of the measuring tube, so no friction loss occurs.
Claim 1 of Japanese Patent No. 4503830 describes that “the first and second ports are fluidly connected”. In the present invention, the connection between the upstream pressure gauge, the downstream pressure gauge, and the flow rate calculation device is described in claim 1 as “a signal transmission section and a transmission path for transmitting by an electrical signal”. In the present invention, it is assumed that the distance between the upstream pressure gauge and the downstream pressure gauge is 1 km or more by utilizing the friction loss of the pipe. The first and second ports are not fluidly connected but are transmitted by electrical signals.
Major differences from Japanese Patent Laid-Open No. 6-94490 are disclosed below.
Japanese Patent Application Laid-Open No. 6-94490 is a case where the pipe wall is considered to be heat insulation, and the steady flow of the compressible fluid intended for the gas considering the friction caused by the fluid is defined as the Fanno flow, and the pipe flow rate based on the well-known Fanno equation. Seeking.
In contrast, the present invention is intended for incompressible liquids, and the flow rate is obtained based on the well-known Darcy-Weissbach equation. Therefore, the present invention has a fundamental difference in the flow rate measurement method from JP-A-6-94490.
Major differences from Japanese Patent Laid-Open No. 50-36163 are described below.
As a first difference, Japanese Patent Laid-Open No. 50-36163 uses a very high frequency cavity as a method for measuring the pressure of a pipe through which liquid sodium for cooling a nuclear reactor flows, and which shows a resonance frequency response by the pressure of liquid sodium flowing through the pipe. To measure the pressure. In the present invention, it is assumed that the pressure is measured by a pressure gauge used for process control in which a diaphragm pressure sensor such as a semiconductor type or a capacitance type is inserted into a tube. In Japanese Patent Laid-Open No. 50-36163, the ultra high frequency wave is returned to the electrical signal corresponding to the pipe pressure in the processing electronics unit through the waveguide, and the differential pressure between the pressures in the pipes of the sensors installed at the first and second positions of the pipe. To obtain the flow rate. Although the pressure measurement method is different from that of the present invention, the present invention is the same as that disclosed in Japanese Patent Laid-Open No. 50-36163 in that the flow rate is converted from the differential pressure due to the electric signal.
The second difference is that Japanese Patent Application Laid-Open No. 50-36163 claims that “it has a first resonant hypersonic cavity that responds to a pressure change outside it and supplies an electrical output that indicates the pressure change. The first ultra-high frequency sensor to do;
A second ultra-high frequency sensor having a second resonant hypersonic cavity responsive to the external pressure change and providing an electrical output indicating the pressure change; and supplied from the first and second sensors It consists of a means for comparing each output and responding to each output. " This claim automatically calculates the Reynolds number from the flow velocity each time it is measured, reads the coefficient of friction from the Moody diagram, and calculates the Darcy-Weissbach formula described as the Δp formula in the specification. The processing to be performed is not described. In addition, FIG. No part 1 performs these processes.
These processes described in the specification are not performed every time the flow rate is measured, but the flow rate of liquid sodium necessary for cooling the reactor and the differential pressure between the first and second sensors are obtained. It can be interpreted that the flow rate required for cooling is estimated by comparing the measured differential pressure with the previously determined differential pressure. In the present invention, these processes are performed in the pipe flow rate measuring device every time the flow rate is measured. Therefore, Japanese Patent Laid-Open No. 50-36163 and the present invention are basically different as a flow rate measuring device.

また、数式２のレイノルズ数Ｒｅの管内平均流速ｕは数式１２を用いて管内流量Ｑで置換えると数式２は数式１４で表すことができる。

液体の温度を測定する前記温度計３を管の液体温度を代表する位置に設置する。液体温度計３は温度変化に伴う液体粘度と密度を補正するものである。
数式１３は、管摩擦係数λ、差圧ΔＰの関数としてλ、ΔＰ以外の値は係数とし設定または演算により求める。
数式１４のレイノルズ数は演算により求める。
液体温度計３で測定した液体温度Ｔを電気信号により伝送する信号伝送部８および伝送路９により伝送して管摩擦係数、差圧関数係数演算部およびレイノルズ数演算部１７において、液体密度、粘度を設定する液体パラメータ設定部７により設定されている基準温度における液体密度、粘度を測定した液体温度Ｔにおける液体密度、粘度に換算する。換算はあらかじめ設定されている換算テーブルを参照して換算値を求めるか、または粘度の場合は公知のアンドレード粘度換算数式により換算する。
管の水力直径として円形管の場合は管内径ｄ、上流圧力設定点２２と下流圧力予測制御点間の距離Ｌを管寸法パラメータ設定部６により設定する。
また、下流圧力予測制御点１７の圧力予測は設定した管流量Ｑのもとで行うため管流量設定部１８により管流量Ｑを設定する。以上により、数式１３の係数はすべて決定して、管摩擦係数、差圧関数の変数はλとΔＰのみの関数となっている。
数式１４のレイノルズ数の値もＱ、ｄは設定値で、ρ、μは設定値を液体温度計３で測定した液体温度に換算して求められるために値が決定している。管摩擦係数演算部１９においては、レイノルズ数演算部で数式１４により求めたレイノルズ数Ｒｅにより摩擦係数λを演算により求める。演算式はレイノルズ数Ｒｅの値により層流、層流から乱流域に遷移する遷移流、乱流毎に数式が異なる。
数式の選定はレイノルズ数の値により下記により選定する。
層流の場合（Ｒｅ＜Ｒｅ_Ｌ）は数式４
遷移流の場合（Ｒｅ_Ｈ＞Ｒｅ≧Ｒｅ_Ｌ）は数式８
乱流の場合（Ｒｅ≧Ｒｅ_Ｈ）は数式５
により演算する。
摩擦係数λの演算において数式が陰関数の場合は、請求項１の場合と同様に、
ニュートン・ラプソン法等を用いて数値的に解くか、Ｅｘｃｅｌ等の表計算ソフトであるゴールシーク、ソルバーなどを下流圧力予測制御装置２４に組込むことにより演算で求める。
管摩擦係数演算部１９に管相対粗さを管相対粗さ設定部１０により設定し、臨界レイノルズ数を臨界レイノルズ数設定部１１により設定する。
管摩擦係数演算部１９で求めた摩擦係数λは管摩擦係数、差圧関数演算部２０
において、数式１３に代入して差圧ΔＰを求める。
上流設定圧力演算表示部２１において、前記差圧ΔＰに下流設定圧力設定部２３で設定している下流設定圧力を加算する。この加算した圧力は上流圧力設定値であり、上流設定圧力演算表示部２１で表示する。
同時に前記上流圧力設定値は前記上流圧力設定器１６に対して電気信号により信号伝送部８および伝送路９により伝送して前記上流圧力設定器１６で圧力設定を行う。 表２に、これらの数式を整理して示す。

FIG. 2 is a basic configuration diagram of “claim 2”.
The upstream pressure and the downstream pressure prediction control point 17 are adjusted by adjusting the pressure of the upstream pressure set point 22 of the pipe 15 where the fluid flows down in a steady flow state through the pipe 15 arranged linearly on the same horizontal plane with a uniform pipe cross section. Is controlled by the upstream pressure setter 16 installed at the upstream pressure set point 22 under a set constant pipe flow rate Q.
In the pipe friction coefficient, the differential pressure function coefficient calculation unit, and the Reynolds number calculation unit 17, the coefficients of the Darcy-Weissbach equation of Equation 1 are calculated. If the relationship between the u in equation (12) and the in-pipe flow rate Q is used as the average flow velocity u in equation (1), equation (1) becomes equation (13).
Can be expressed as

Further, when the in-pipe average flow velocity u of the Reynolds number Re in Formula 2 is replaced with the pipe flow rate Q using Formula 12, Formula 2 can be expressed by Formula 14.

The thermometer 3 for measuring the temperature of the liquid is installed at a position representing the liquid temperature of the pipe. The liquid thermometer 3 corrects the liquid viscosity and density accompanying the temperature change.
Equation 13 is obtained by setting or calculating the values other than λ and ΔP as functions of the pipe friction coefficient λ and the differential pressure ΔP.
The Reynolds number of Expression 14 is obtained by calculation.
The liquid temperature T measured by the liquid thermometer 3 is transmitted by a signal transmission unit 8 and a transmission path 9 that transmit electrical signals, and the pipe friction coefficient, the differential pressure function coefficient calculation unit, and the Reynolds number calculation unit 17 perform liquid density and viscosity. The liquid density and viscosity at the reference temperature set by the liquid parameter setting unit 7 are converted into the liquid density and viscosity at the measured liquid temperature T. For conversion, a conversion value is obtained with reference to a conversion table set in advance, or in the case of viscosity, conversion is performed using a well-known Andrade viscosity conversion formula.
In the case of a circular pipe, the pipe diameter parameter setting unit 6 sets the pipe inner diameter d and the distance L between the upstream pressure setting point 22 and the downstream pressure prediction control point as the hydraulic diameter of the pipe.
Further, since the pressure prediction at the downstream pressure prediction control point 17 is performed under the set pipe flow rate Q, the pipe flow rate setting unit 18 sets the pipe flow rate Q. As described above, all the coefficients of Expression 13 are determined, and the variables of the pipe friction coefficient and the differential pressure function are functions of only λ and ΔP.
The values of Reynolds number in Expression 14 are also determined because Q and d are set values, and ρ and μ are determined by converting the set values to the liquid temperature measured by the liquid thermometer 3. In the pipe friction coefficient calculation unit 19, the friction coefficient λ is obtained by calculation using the Reynolds number Re obtained by Equation 14 in the Reynolds number calculation unit. The calculation formula varies depending on the value of the Reynolds number Re for each laminar flow, transition flow from laminar flow to turbulent flow region, and turbulent flow.
The formula is selected according to the Reynolds number as follows.
In the case of laminar flow (Re <Re _L ), Equation 4
In the case of a transition flow (Re _H > Re ≧ Re _L ), Equation 8
In the case of turbulent flow (Re ≧ Re _H ), Equation 5
Calculate by
In the calculation of the friction coefficient λ, when the mathematical expression is an implicit function, as in the case of claim 1,
It can be solved numerically using the Newton-Raphson method or the like, or can be calculated by incorporating a goal seek, solver, etc., which is a spreadsheet software such as Excel, into the downstream pressure prediction control device 24.
In the pipe friction coefficient calculation unit 19, the pipe relative roughness is set by the pipe relative roughness setting unit 10, and the critical Reynolds number is set by the critical Reynolds number setting unit 11.
The friction coefficient λ obtained by the pipe friction coefficient calculator 19 is the pipe friction coefficient, differential pressure function calculator 20.
In this case, the differential pressure ΔP is obtained by substituting it into the equation 13.
In the upstream set pressure calculation display unit 21, the downstream set pressure set by the downstream set pressure setting unit 23 is added to the differential pressure ΔP. This added pressure is an upstream pressure set value and is displayed on the upstream set pressure calculation display unit 21.
At the same time, the upstream pressure set value is transmitted to the upstream pressure setter 16 by an electric signal through the signal transmission unit 8 and the transmission path 9 and the upstream pressure setter 16 sets the pressure. Table 2 summarizes these mathematical expressions.

ただし、ζ_ｂはベンドの損失係数であり、数式１６による。

ただし、ζ_ｅはエルボの損失係数であり、数式１８による。

となる。
図１１は、上流圧力計１および下流圧力計２間の高さが基準点高さに対して、それぞれＨ１およびＨ２で上流圧力計１と下流圧力計２間に曲がりがある管を示している。
管は一様断面の管１５に定常流状態で液体が流れている場合、流速ｕは管路内で
一定である。また、上流圧力計１と下流圧力計２間の総損失Ｈ_Ｌは摩擦損失と曲がり損失の合計であり数式１９なる。

ただし、ζは曲がり損失係数であり、曲がりが複数個所の場合は損失係数ζはこれらの合計である。ｇは重力の加速度である。
速度水頭は上下流で同じであることを考慮して、上流圧力計１と下流圧力計２間にベルヌーイの定理を適用すれば数式２０が得られる。

Ｐ１−Ｐ２＝ΔＰ、Ｈ１−Ｈ２＝ΔＨとし、数式２０をΔＰについてまとめれば数式２１となる。

数式２１は上流圧力計１と下流圧力計２間に高低差ΔＨおよび曲り管がある場合の数式１に相当する式である。
数式２を用いて、数式２１からｕを消去してλについて整理すれば数式２２となる。

数式２２は上流圧力計１と下流圧力計２間に高低差ΔＨおよび曲り管がある場合の数式３に相当する式である。
上流圧力計１と下流圧力計２間に高低差ΔＨおよび曲り管がある場合の流量計算式は、第一管摩擦係数、レイノルズ数関数として、同一水平面の直管路の式として数式３の代わりに、数式２２を用いる。
すなわち、第一および第二管摩擦係数、レイノルズ数関数を連立方程式として管摩擦係数、レイノルズ数を演算する。
第一管摩擦係数、レイノルズ数関数は数式２２である。
第二管摩擦係数、レイノルズ数関数は層流、遷移流、乱流に対して別々の数式による。
層流については数式４、
遷移流については数式８
乱流については数式５
である。
表３ に、層流、遷移流、乱流の場合について、連立方程式として、摩擦係数、
レイノルズ数を求める第一管摩擦係数、レイノルズ数関数および第二管摩擦係数、レイノルズ数関数の一覧を示す。
乱流の場合において、第一管摩擦係数、レイノルズ数関数および第二管摩擦係数、レイノルズ数関数の連立方程式を解くにあたり数式が陰関数となる場合、ニュートン・ラプソン法等を用いて数値的に解くか、Ｅｘｃｅｌ等の表計算ソフトであるゴールシーク、ソルバーなどを管流量計測装置に組込むことにより演算で求める。

摩擦係数λを用いた流量計算式は数式２１より、流速ｕを求めることにより、数式２３により計算する。

なお、レイノルズ数Ｒｅを用いた流量計算式は高低差ΔＨおよび曲り管がある場合についても数式１１で計算される。 In a pipeline installed in a wide area, there may be a case where a straight pipe without height difference cannot be secured for flow measurement.
As a typical example of the bent pipe, there is a bend shown in FIG. 9 which is bent at an angle of θ degrees with a radius of curvature R and an elbow shown in FIG. 10 which is bent at an angle of θ degrees without drawing a curve.
Bend loss head Delta] h _b and known Head Loss Delta] h _e elbow official, respectively shown in Equation 15 and Equation 17.

Here, ζ _b is a bend loss coefficient and is given by Equation 16.

Where ζ _e is the loss factor of the elbow and is given by equation 18.

It becomes.
FIG. 11 shows a pipe in which the height between the upstream pressure gauge 1 and the downstream pressure gauge 2 is bent at the height between the upstream pressure gauge 1 and the downstream pressure gauge 2 with respect to the reference point height at H1 and H2, respectively. .
When the liquid is flowing in a steady flow state in the tube 15 having a uniform cross section, the flow velocity u is constant in the pipe line. The total loss H _L between the upstream pressure gauge 1 and the downstream pressure gauge 2 is the sum of the friction loss and the bending loss, and is given by Equation 19.

However, ζ is a bending loss coefficient, and when there are a plurality of bendings, the loss coefficient ζ is the sum of these. g is the acceleration of gravity.
Considering that the velocity head is the same in the upstream and downstream, Equation 20 is obtained by applying Bernoulli's theorem between the upstream pressure gauge 1 and the downstream pressure gauge 2.

When P1−P2 = ΔP and H1−H2 = ΔH, and formula 20 is summarized for ΔP, formula 21 is obtained.

Formula 21 is a formula corresponding to Formula 1 when there is a height difference ΔH and a curved pipe between the upstream pressure gauge 1 and the downstream pressure gauge 2.
Using Equation 2, when u is deleted from Equation 21 and arranged for λ, Equation 22 is obtained.

Formula 22 is a formula corresponding to Formula 3 when there is a height difference ΔH and a curved pipe between the upstream pressure gauge 1 and the downstream pressure gauge 2.
The flow rate calculation formula when there is a height difference ΔH and a curved pipe between the upstream pressure gauge 1 and the downstream pressure gauge 2 is expressed as a first pipe friction coefficient and a Reynolds number function, instead of formula 3 as a straight pipe expression on the same horizontal plane. For this, Equation 22 is used.
That is, the pipe friction coefficient and the Reynolds number are calculated using the first and second pipe friction coefficients and the Reynolds number function as simultaneous equations.
The first pipe friction coefficient and the Reynolds number function are represented by Formula 22.
The second pipe friction coefficient and Reynolds number function are based on separate equations for laminar flow, transition flow, and turbulent flow.
For laminar flow, Equation 4,
For transition flow, Equation 8
For turbulence, Equation 5
It is.
Table 3 shows the friction coefficient, the simultaneous equation for laminar flow, transition flow, and turbulent flow.
A list of the first pipe friction coefficient, the Reynolds number function, the second pipe friction coefficient, and the Reynolds number function for obtaining the Reynolds number is shown.
In the case of turbulent flow, when solving the simultaneous equations of the first pipe friction coefficient, the Reynolds number function, the second pipe friction coefficient, and the Reynolds number function, the numerical formula becomes an implicit function numerically using the Newton-Raphson method, etc. Solve or obtain by calculation by incorporating a goal seek, solver, etc., which is a spreadsheet software such as Excel, into the pipe flow measuring device.

The flow rate calculation formula using the friction coefficient λ is calculated by Formula 23 by obtaining the flow velocity u from Formula 21.

Note that the flow rate calculation formula using the Reynolds number Re is calculated by Formula 11 even when there is a height difference ΔH and a curved pipe.

In the first and second aspects, it is necessary to set the hydraulic diameter in the pipe dimension paralator setting section 6. The hydraulic diameter in the case of a circular tube is the tube inner diameter d. For the hydraulic diameter other than the circular pipe, it is necessary to select a parameter equivalent to the pipe inner diameter d of the circular pipe.
The cross-sectional area of the tube is A, and the length of the periphery of the cross-section (referred to as a wetting edge) is S. m = A / S is the ratio of the cross-sectional area A and the wetting edge S, and is called the hydraulic average depth.
The hydraulic diameter de of the arbitrary cross section is de = 4 m.
As an example,
In the case of a circle m = A / s = {π (d / 2) ² } / {2π (d / 2)} = d / 4 de = 4 m = d
In the case of a square, since one side is B, and m = A / s = B ² / 4B = B / 4, d = 4 m = B
It becomes.

In the pipe flow rate measuring apparatus according to claim 1 of the present invention, pressure gauges are installed upstream and downstream of a pipe having a uniform pipe cross section found in many liquid pipelines, and the differential pressure of the upstream and downstream pressure gauges, the pipe In addition, the flow rate is measured from the liquid data. Since the pressure gauge installed in the pipe does not have a throttling mechanism such as an orifice, there is no friction loss with respect to the fluid. According to the present invention, without using a Moody diagram, both the coefficient of friction, the Reynolds number function and the Reynolds number function derived from the Reynolds-Weissbach equation, which are common to liquids and depend only on the roughness of the inner wall of the pipe. It is now possible to directly calculate the pipe flow rate by solving the simultaneous equations and obtaining the friction coefficient and Reynolds number.
In addition to the functions used in the Moody diagram, other functional expressions can be applied as the friction coefficient and Reynolds number function common to liquids.
The present invention can automatically measure laminar flow, transition flow, and turbulent flow to measure the pipe flow rate, prevent flow measurement errors due to reading errors in the moody diagram, and improve the accuracy and simplification of the measurement. It is possible to measure the flow rate of pipelines for agricultural water, oil, liquefied natural gas, waterworks, various industrial plants, etc.
The pipe to be measured can be applied to a curved pipe and the measurement of pipe flow with different heights.
The pipe downstream pressure prediction control apparatus according to claim 2 of the present invention calculates the pipe friction coefficient corresponding to the set flow rate and performs pipe downstream pressure prediction control, so that the accuracy of the upstream pressure setting is improved, and an excessive pressure setting is achieved. Energy loss can be reduced because it is not necessary.
In addition, by measuring the change in pipe downstream pressure value due to the aging deterioration of the inner wall surface of the pipe and comparing it with the pipe downstream pressure prediction value before aging deterioration, by grasping the change in the absolute roughness value of the pipe inner wall surface Pipe deterioration diagnosis becomes possible.
In addition, the calibration of the pipe flow measuring device can be easily performed by flowing the calibration flow at the position of the upstream pressure gauge, measuring the flow from the differential pressure with the downstream pressure gauge, and comparing it with the calibration flow. .
In addition, the pipe flow rate measuring device is composed of a general-purpose pressure gauge installed upstream and downstream, a liquid thermometer installed at a representative point, a simple telemeter, and a flow rate calculation device. In particular, when the flow rate is measured by a common flow rate calculation device, the flow rate can be measured economically.

An example of pipe flow measurement according to claim 1 is shown.
The following values are set values.
(1) Liquid Water (2) Liquid density at 0 ° C. 999.8 Kg / m 3
(3) Liquid viscosity at 0 ° C. 0.001782 Pa · s
(4) Pipe type Carbon steel pipe for piping 20A Inner diameter 21.6mm
Tube wall absolute roughness ε = 0.045mm
(5) Distance between upstream and downstream pressure gauges 1,000m
(6) Pipe laying straight line without height difference (7) Critical Reynolds number lower limit critical 2,000
Upper criticality 4,000

The following values are obtained as measured values.
(1) Upstream pressure 200 KPa Downstream pressure 100 KPa
(2) Liquid temperature 20 ° C

The tube flow rate obtained under the above conditions is 0.000127 m3 / s.
Table 4 shows the measurement results.

Pipe downstream pressure prediction control according to claim 2 The following values are set values.
(1) Liquid Water (2) Liquid density at 0 ° C. 999.8 Kg / m 3
(3) Liquid viscosity at 0 ° C. 0.001782 Pa · s
(4) Pipe type Carbon steel pipe for piping 300A Inner diameter 304.7mm
Tube wall absolute roughness ε = 0.045mm
(5) Distance between upstream and downstream pressure gauges 10km
(6) Pipe laying straight line without height difference (7) Pipe set flow rate 0.0150m3 / s
(8) Downstream set pressure 5,000 Pa
(9) Critical Reynolds number lower limit criticality 2,000
Upper criticality 4,000

The following values are obtained as measured values.
(1) Liquid temperature 20 ° C

The following values are obtained as operation values.
(1) Differential pressure between upstream pressure set point and downstream pressure prediction control point 10,129 Pa

The value obtained for the set pressure of the upstream pressure set point under the above conditions is 15,129 Pa.
It is.
Table 5 shows the results of the downstream pressure prediction control.

FIG. 2 is a basic configuration diagram of the invention of claim 1. These are the basic block diagrams of invention of "Claim 2". Is a Moody diagram showing the relationship between the Reynolds number and the friction coefficient. These are explanatory drawings of the absolute roughness ε and the relative roughness ε / d of the pipe inner wall. Is experimental data showing that the relationship between the Reynolds number and the friction coefficient of the transition zone transitioning between the laminar and turbulent regions can be linearly approximated. FIG. 4 is a diagram showing the relationship between diameter d and relative roughness ε / d for a practical pipe. Is an explanatory diagram of a straight line approximation method in the transition region of the Reynolds number and the friction coefficient function. Fig. 5 is a flowchart for automatically determining laminar flow, transition flow, and turbulent flow in pipe flow measurement. FIG. 4 is an explanatory diagram of a bend pipe that bends in a circle having a radius of curvature R; These are explanatory drawings of an elbow pipe that bends at an angle θ. FIG. 5 is an explanatory diagram for applying Bernoulli's theorem to a pipe having a gradient and a bend. Shows a method for controlling the set value of the pipe flow rate using the pipe flow rate measuring device. FIG. 3 is a configuration diagram of an embodiment for collectively performing a plurality of pipe flow rate measurements with a flow rate calculation device of a management office. FIG. 5 is a configuration diagram of an embodiment for setting pressure management in a pressurized pump station by cascade-type pipe downstream pressure prediction control that distributes water to a plurality of pipe downstream reservoirs under a set flow rate and set pressure. FIG. 3 is a graph showing the principle of measuring the roughness of the pipe or calibrating the flow rate measurement value of the pipe flow rate measuring device.

The pipe flow rate measuring device according to claim 1 of the present invention has a uniform cross section existing in many liquid pipelines and can be applied to the flow rate measurement of a pipe line in a steady flow state. There are many such pipelines such as agricultural irrigation channels, water supply trunks, petroleum or liquefied natural gas pipelines, and chemical plant piping.
The pipe flow rate measuring device according to the present invention is capable of efficiently measuring the flow rate of a large number of flow rate measurement sections scattered in a wide area in addition to the flow rate measurement of one zone installed upstream and downstream, and centrally managing it at a management office. .
The pipe downstream pressure prediction control apparatus according to claim 2 of the present invention can reduce energy loss by optimizing the terminal pressure by calculating the pipe friction coefficient and predicting and controlling the pipe downstream pressure with respect to the set flow rate. It becomes.

FIG. 12 shows an example of pipe flow rate control using the flow rate measurement value of the pipe flow rate measuring device.
The pipe flow rate is output to the pump control device from the flow rate calculation device of the pipe flow rate measuring device.
The pump control device compares the pipe flow rate with the set flow rate Qs and automatically increases or decreases the pump pressurization signal so that the pipe flow rate becomes the set flow rate Qs.

FIG. 13 shows an example of an agricultural water management system that grasps and manages the flow rate of agricultural trunk lines dispersed in a wide area.
The upstream and downstream pressures in each flow rate measurement section are collected by a telemeter at a flow rate calculation device at a management office and processed by a common flow rate calculation device to perform flow rate measurement, so that economical flow rate measurement is possible.
In FIG. 13, a wireless line is shown as the transmission line, but the transmission line and the signal transmission unit are selected for wired or wireless, for business use, and for private use in consideration of economy and reliability. To do.

FIG. 14 is an example of pipeline downstream pressure predictive control by a pressurizing pump that distributes a prescribed flow rate to a distribution area where agricultural water taken from one water source pond is scattered.
For example, the pressurizing pump station 1 controls the set flow rate of Q1 using the No. 1 main line as the predicted pressure of the H1 water level of the water absorption tank of the water supply destination. That is, the pressure obtained by adding the loss of the No. 1 main line to the terminal water level H1 is controlled as the set pressure.
The pressurizing pump station 2 controls the set flow rate of Q2 using the No. 2 main line as the predicted pressure based on the H2 water level of the water discharge tank. That is, the pressure obtained by adding the loss of the No. 2 main line to the terminal water level H2 is controlled as the set pressure.

FIG. 15 is a graph showing the principle of measuring the roughness of the pipe or calibrating the flow rate measurement value of the pipe flow rate measuring device.
An upstream pressure gauge, a downstream pressure gauge, and a liquid thermometer are installed in the pipe, and a calibration flow rate and a calibration pressure are set as calibration values at the position of the upstream pressure gauge.
In the example graph,
The following values are set values.
(1) Liquid Water-liquid density 999.8Kg / m3 at 0 ° C
(2) Viscosity at 0 ° C. 0.001782 Pa · s
(3) Type of pipe Carbon steel pipe for piping 200A Inner diameter 204.7mm
(4) Distance between upstream and downstream pressure gauges 1,000m
(5) Pipe installation Straight installation without height difference (6) Set flow rate of upstream pressure gauge 0.05m3 / s
(7) Upstream pressure gauge set pressure 180Kps

The calculated value of the Reynolds number for the above setting is 3,098,310.
In FIG. 15, the calculated value of the downstream pressure with respect to the absolute roughness of the tube of 0.45 × 10 ⁻³ to 1 × 10 ⁻³ m is shown.
The calculated value of the downstream pressure with respect to the absolute roughness is 100 to 10 KPa.
The absolute roughness when the pipe is newly installed is 0.45 × 10 ⁻³ m, and the measured value of the downstream pressure is 100 KPa, which is the same as the calculated value. For example, when the downstream pressure measurement value decreases to 40 KPa due to secular change or the like, it is determined from the graph of FIG. 15 that the absolute roughness has deteriorated to 0.5 × 10 ⁻³ m.

管内を流れる液体の粘度 μ［Ｐａ・ｓ］
動粘度 ν＝μ／ρ［ｍ^２／ｓ］


とすれば、レイノルズ数Ｒｅは数式２で示される。

数式１と数式２から平均速度ｕを消去し、摩擦係数λについて整理した式を数式３に示す。

数式３はダルシー・ワイスバッハの式をベースとした第一管摩擦係数・レイノルズ数関数と定義する。本関数の係数を演算する第一管摩擦係数・レイノルズ数関数係数演算部４において、数式３の管摩擦係数λ、レイノルズ数Ｒｅ以外の係数を決定する。
上流圧力計１、下流圧力計２で測定した上流圧力Ｐ１、下流圧力Ｐ２を電気信号により伝送する信号伝送部８および伝送路９により伝送して第一管摩擦係数・レイノルズ数関数係数演算部４において、
ΔＰ＝Ｐ１−Ｐ２の差圧演算をおこない係数を決定する。
液体温度計３で測定した液体温度Ｔを電気信号により伝送する信号伝送部８および伝送路９により伝送して第一管摩擦係数・レイノルズ数関数係数演算部４において、液体密度、粘度を設定する液体パラメータ設定部７により設定されている基準温度における液体密度、粘度を測定した液体温度Ｔにおける液体密度、粘度に換算する。換算はあらかじめ設定されている換算テーブルを参照して換算値を求めるか、または粘度の場合は公知のアンドレード粘度換算数式により換算する。
本発明においては、上流圧力計１と下流圧力計２の距離Ｌは管内面は平滑の場合の流量測定も行うことになるために、この間の管摩擦損失を大きくして、測定精度を向上させるために距離Ｌは１ｋｍ以上となることもあり、また、流量演算装置１４は広域に設置された多数の流量計測に対応することを想定して、上流圧力計１または下流圧力計２と流量演算装置１４との間は伝送回線で接続する。
この他に第一管摩擦係数・レイノルズ数関数係数演算部４に管の水力直径として円形管の場合は管内径ｄ、上流圧力計１と下流圧力計２間の距離Ｌを管寸法パラメータ設定部により設定する。
以上により、数式３の係数はすべて決定して、第一管摩擦係数・レイノルズ数関数の管摩擦係数λはレイノルズ数Ｒｅのみの関数となる。 The invention of "Claim 1" is made to solve the above-mentioned "problem to be solved by the invention". FIG. 1 is a basic configuration diagram of the invention of claim 1.
An upstream pressure gauge 1 for measuring the upstream pressure of the pipe and a downstream pressure gauge 2 for measuring the downstream pressure are installed so that the liquid flows down in a steady flow state through the pipes arranged in the same horizontal plane with a uniform pipe cross section.
A liquid thermometer 3 for measuring the temperature of the liquid is installed at a position representing the liquid temperature of the pipe. The liquid thermometer 3 corrects the liquid viscosity and density accompanying the temperature change.
When the circular pipe shown in Fig. 1 is installed horizontally,

Pressure of upstream pressure gauge P1 [Pa]
Downstream pressure gauge pressure P2 [Pa]
Pressure loss ΔP = (P1−P2) [Pa]
Distance between upstream and downstream pressure gauges L [m]
Tube friction coefficient λ [Dimensionless number]
Liquid density ρ [kg / m ³ ]
Average flow velocity u [m / s]
Pipe inner diameter d [m]

Then, the well-known Darcy-Weissbach equation is expressed by Equation 1.

Viscosity of the liquid flowing in the pipe μ [Pa · s]
Kinematic viscosity ν = μ / ρ [m ² / s]


Then, the Reynolds number Re is expressed by Equation 2.

Formula 3 is a formula obtained by eliminating the average speed u from Formulas 1 and 2 and arranging the friction coefficient λ.

Formula 3 is defined as the first pipe friction coefficient / Reynolds number function based on the Darcy-Weissbach formula. In the first pipe friction coefficient / Reynolds number function coefficient calculation unit 4 for calculating the coefficient of this function, coefficients other than the pipe friction coefficient λ and the Reynolds number Re in Expression 3 are determined.
The upstream pressure gauge 1 and the downstream pressure gauge P2 measured by the upstream pressure gauge 1 and the downstream pressure gauge 2 are transmitted by the signal transmission section 8 and the transmission path 9 that transmit the electrical signals, and the first pipe friction coefficient / Reynolds number function coefficient calculation section 4 In
A coefficient is calculated by performing a differential pressure calculation of ΔP = P1−P2.
The liquid temperature T measured by the liquid thermometer 3 is transmitted by the signal transmission unit 8 and the transmission path 9 that transmit the electric signal, and the first pipe friction coefficient / Reynolds number function coefficient calculation unit 4 sets the liquid density and viscosity. The liquid density and viscosity at the reference temperature set by the liquid parameter setting unit 7 are converted into the liquid density and viscosity at the measured liquid temperature T. For conversion, a conversion value is obtained with reference to a conversion table set in advance, or in the case of viscosity, conversion is performed using a well-known Andrade viscosity conversion formula.
In the present invention, since the distance L between the upstream pressure gauge 1 and the downstream pressure gauge 2 also measures the flow rate when the pipe inner surface is smooth, the pipe friction loss between them is increased to improve the measurement accuracy. Therefore, the distance L may be 1 km or more, and the flow rate calculation device 14 is assumed to support a large number of flow rate measurements installed in a wide area, and the upstream pressure gauge 1 or the downstream pressure gauge 2 and the flow rate calculation. The device 14 is connected by a transmission line.
In addition, in the first pipe friction coefficient / Reynolds number function coefficient calculation section 4, in the case of a circular pipe, the pipe inner diameter d and the distance L between the upstream pressure gauge 1 and the downstream pressure gauge 2 are set as a pipe diameter parameter setting section. Set by.
Thus, all the coefficients of Equation 3 are determined, and the tube friction coefficient λ of the first tube friction coefficient / Reynolds number function is a function of only the Reynolds number Re.

乱流の場合の管摩擦係数・レイノルズ数の関数は公知の式として、レイノルズ数の適用範囲が広く、管内面の粗さにも対応できる式として、数式５に示すコールブルックの式によるものとする。ここで、εは絶対粗さで、管内径との比ε／ｄは相対粗さと呼ばれている。
ε／ｄは管相対粗さ設定部１０により設定する。
図４に管内壁の絶対粗さと相対粗さの関係を示す。

数式５においてε／ｄ＝０とすれば、管内面の粗さが滑らかな管に相当し、数式６のように変形することができる。

また、数式５においてε／ｄが大きくなり、管内面が粗く摩擦係数がレイノルズ数の影響を無視できる場合は、数式７のように変型することができる。

乱流の場合、ε／ｄの値により、数式６は滑らかな管の場合、数式７は粗い管の場合となるが、いずれもε／ｄの値を選べば数式５が適用可能なため、以下数式５により第二管摩擦係数・レイノルズ数関数係数を計算する。
第二管摩擦係数・レイノルズ数関数係数演算部５に管相対粗さを管相対粗さ設定部１０により設定し、臨界レイノルズ数を臨界レイノルズ数設定部１１により設定する。
層流から乱流に変化する遷移流の管摩擦係数に対するレイノルズ数の関数として、下記によるものとする。
（１）臨界レイノルズ数は下限、上限がある。
（２）下限、上限間のレイノルズ数と摩擦係数の関係は層流と乱流曲線を結ぶ直線近似とする。
これは下限、上限間のレイノルズ数と摩擦係数の関係は図５に示す実験データから下限、上限間のレイノルズ数と摩擦係数の関係は直線的に近似可能となるためである。
（３）遷移流となる上、下限のレイノルズ数は管と流体依存性が大きく確定できないために設定値とする。
（４）層流と遷移流、遷移流と乱流への変化時に摩擦係数対レイノルズ数曲線は不連続とならない。

層流と遷移流の境界の臨界レイノルズ数 Ｒｅ_Ｌ
遷移流と乱流の境界の臨界レイノルズ数 Ｒｅ_Ｈ
層流と遷移流の境界の摩擦係数 λ_Ｌ
遷移流と乱流の境界の摩擦係数 λ_Ｈ

とし、レイノルズ数Ｒｅを横軸、摩擦係数λを縦軸にとった時の遷移流の直線の方程式は数式８となる。
臨界レイノルズ数Ｒｅ_Ｌ およびＲｅ_Ｈは臨界レイノルズ数設定部１１により設定する。

ここで、λ_Ｌは数式４により、λ_Ｌ＝ ６４／ Ｒｅ_Ｌにより計算する。また、λ_Ｈは乱流曲線の数式５において、レイノルズ数Ｒｅ_Ｈを代入した数式９により計算される。
流量計測対象管のε／ｄの値は管の粗さ対応して設定する。

なお、実用管について直径ｄと相対粗さの例を図６に示す。
以上により数式９は乱流域と接続する摩擦係数λ_Ｈ以外の係数は与えられ、λ_Ｈについて解くことが可能である。数式９は陰関数のためλ_Ｈの値はニュートン・ラプソン法等を用いて数値的に解くか、Ｅｘｃｅｌ等の表計算ソフトであるゴールシーク、ソルバーなどを管流量計測装置１４に組込むことにより演算で求める。
λ_Ｈが求められたことにより、遷移流のλ、Ｒｅの直線の方程式の係数が求められた。
以上、第二管摩擦係数・レイノルズ数関数係数演算部５の係数と数式が求められた。図７に第二管摩擦係数・レイノルズ数関数の遷移域における直線近似の方法を示す。 The first pipe friction coefficient / Reynolds number function coefficient calculation unit 4 depends on the type of liquid, the pipe size, the distance L between the upstream pressure gauge and the downstream pressure gauge, the differential pressure ΔP between the measured upstream pressure P1 and downstream pressure P2. The coefficient of the first pipe friction coefficient and the Reynolds number function is calculated.
In the second pipe friction coefficient / Reynolds number function coefficient calculation unit 5, the mathematical formulas are different for each laminar flow, transition flow from laminar flow to turbulent flow region, and turbulent flow. The pipe friction coefficient / Reynolds number function, which depends only on the wall roughness, is defined as the second pipe friction coefficient / Reynolds number function. The coefficient and mathematical expression of the coefficient calculation unit of this function are shown below.
The function of the coefficient of tube friction and the Reynolds number in the case of laminar flow is expressed as Equation 4 as a well-known equation.

The function of the pipe friction coefficient and Reynolds number in the case of turbulent flow is a well-known formula, which is based on the Colebrook formula shown in Formula 5, as a formula that has a wide range of applicable Reynolds numbers and can cope with the roughness of the pipe inner surface. To do. Here, ε is the absolute roughness, and the ratio ε / d to the tube inner diameter is called the relative roughness.
ε / d is set by the tube relative roughness setting unit 10.
FIG. 4 shows the relationship between the absolute roughness and the relative roughness of the pipe inner wall.

If ε / d = 0 in Equation 5, it corresponds to a tube having a smooth inner surface, and can be transformed as Equation 6.

Further, when ε / d becomes large in Equation 5 and the inner surface of the tube is rough and the friction coefficient can ignore the influence of the Reynolds number, it can be modified as shown in Equation 7.

In the case of turbulent flow, depending on the value of ε / d, Equation 6 is a smooth tube, Equation 7 is a coarse tube, but in any case, Equation 5 can be applied if the value of ε / d is selected. Hereinafter, the second pipe friction coefficient and the Reynolds number function coefficient are calculated by Equation 5.
In the second pipe friction coefficient / Reynolds number function coefficient calculation unit 5, the pipe relative roughness is set by the pipe relative roughness setting unit 10, and the critical Reynolds number is set by the critical Reynolds number setting unit 11.
As a function of the Reynolds number for the tube friction coefficient of a transition flow changing from laminar to turbulent,
(1) The critical Reynolds number has a lower limit and an upper limit.
(2) The relationship between the Reynolds number and the friction coefficient between the lower limit and the upper limit is a linear approximation connecting the laminar flow and the turbulent flow curve.
This is because the relationship between the Reynolds number and the friction coefficient between the lower limit and the upper limit can be approximated linearly from the experimental data shown in FIG. 5.
(3) The upper limit of the Reynolds number for the transition flow is set to a set value because the dependence on the pipe and the fluid cannot be determined.
(4) The friction coefficient vs. Reynolds number curve does not become discontinuous when changing to laminar flow and transition flow, or transition flow and turbulence.

Critical Reynolds number at the boundary between laminar and transition flow Re _L
Critical Reynolds number at the boundary between transition and turbulent flow Re _H
Friction coefficient at the boundary between laminar flow and transition flow λ _L
Friction coefficient at the boundary between transitional flow and turbulent flow λ _H

The equation of the straight line of the transition flow when the Reynolds number Re is taken on the horizontal axis and the friction coefficient λ is taken on the vertical axis is given by Equation 8.
The critical Reynolds numbers Re _L and Re _H are set by the critical Reynolds number setting unit 11.

Here, λ _L is calculated by λ _L = 64 / Re _{L according} to Equation 4. Further, λ _H is calculated by Expression 9 in which the Reynolds number Re _H is substituted in Expression 5 of the turbulent flow curve.
The value of ε / d of the flow rate measurement target pipe is set corresponding to the roughness of the pipe.

An example of the diameter d and the relative roughness of the practical pipe is shown in FIG.
As described above, Equation 9 is given a coefficient other than the friction coefficient λ _H connected to the turbulent region, and can be solved for λ _H. Since Equation 9 is an implicit function, the value of λ _H can be calculated numerically by using the Newton-Raphson method, or can be calculated by incorporating into the tube flow measurement device 14 a goal seek, solver, etc., which is a spreadsheet software such as Excel. Ask for.
By obtaining λ _H , coefficients of linear equations of λ and Re of the transition flow were obtained.
The coefficients and mathematical formulas of the second pipe friction coefficient / Reynolds number function coefficient calculation unit 5 have been obtained. FIG. 7 shows a method of linear approximation in the transition region of the second pipe friction coefficient / Reynolds number function.

表１の第一および第二管摩擦係数・レイノルズ数関数の係数は第一および第二管摩擦係数・レイノルズ数関数係数演算部で値が求められているために、いずれの数式も管摩擦係数λおよびレイノルズ数Ｒｅのみを変数とする関数である。 In simultaneous pipe friction factor Reynolds number calculation unit 12 calculates the pipe friction coefficient and the Reynolds number and simultaneous first and second pipe friction factor Reynolds number function.
The first pipe friction coefficient / Reynolds number function is Equation 3.
The second pipe friction coefficient and Reynolds number function are based on separate equations for laminar flow, transition flow, and turbulent flow.
For laminar flow, Equation 4,
For transition flow, Equation 8
For turbulence, Equation 5
It is.
Table 1 summarizes these mathematical expressions.

For the first and coefficient of the second pipe friction factor Reynolds number functions in Table 1 are the values in the first and second pipe friction factor Reynolds number function coefficient calculation unit is demanded, also pipe friction coefficient either formula It is a function having only λ and Reynolds number Re as variables.

In the simultaneous pipe friction coefficient / Reynolds number calculation unit 12, the first pipe friction coefficient / Reynolds number function and the second pipe friction coefficient / Reynolds number function obtained for each laminar flow, transition flow, and turbulent flow are used as simultaneous equations, and the friction coefficient λ and Reynolds number Re are obtained.
The order of calculation is performed by automatically selecting the procedure shown in FIG.
First, the friction coefficient λ and the Reynolds number Re are obtained for turbulent flow.
When the Reynolds number Re is less than the critical Reynolds number Re _H upper determines that turbulence.
The critical Reynolds number Re _H at less than seek Reynolds number Re assuming transitional flow. When the Reynolds number Re determined on the assumption of a transition flow is smaller than the upper limit critical Reynolds number Re _H and equal to or higher than the lower limit critical Reynolds number Re _L , it is determined as a transition flow.
When the obtained Reynolds number Re is smaller than the lower limit critical Reynolds number Re _L , the friction coefficient λ and the Reynolds number Re are obtained for the laminar flow. When the Reynolds number Re is less than the critical Reynolds number Re _L of lower limit is determined to laminar flow.
In the case of turbulent flow, when solving the simultaneous equations of the first pipe friction coefficient / Reynolds number function and the second pipe friction coefficient / Reynolds number function, if the formula becomes an implicit function, numerically using the Newton-Raphson method etc. Solved or obtained by calculation by incorporating a goal seek, solver or the like, which is a spreadsheet software such as Excel, into the pipe flow measuring device 14.

また、Ｒｅで表現した場合は管流量Ｑは数式２を用いて、数式１１の計算により求められる。

流量演算装置１４の流量表示部１３において、数式１０または数式１１により計算した流量Ｑを表示する。 In the flow rate calculation display unit 13 for calculating and displaying the pipe flow rate, calculation is performed using the friction coefficient λ and the Reynolds number Re obtained by the simultaneous pipe friction coefficient / Reynolds number calculation unit 12. When expressed by λ, the pipe flow rate Q is obtained by Equation 10 using Equation 1.

Further, when expressed in Re, the pipe flow rate Q is obtained by the calculation of Expression 11 using Expression 2.

In the flow rate display unit 13 of the flow rate calculation device 14, the flow rate Q calculated by the formula 10 or the formula 11 is displayed.

As a method of measuring the flow rate using the pressure difference ΔP of the pressure gauge installed upstream and downstream of the pipe, regardless of the restriction mechanism such as an orifice, the Reynolds number with respect to this assumed flow rate value Q is assumed assuming the flow rate value to be measured. Re is obtained from Equation 11, the friction coefficient λ is read from a known chart called Moody diagram, ΔP measured in Equation 10 and the read λ are substituted to calculate the flow rate Q. Next, the assumed flow rate value is changed so that the calculated flow rate Q and the assumed flow rate coincide with each other, the Re and λ are obtained again using the Moody diagram, and the flow rate Q is obtained using Equation 10. A method may be considered in which this procedure is repeated until the flow rate value calculated by Equation 10 matches the assumed flow rate value and the matched flow rate is used as the flow rate measurement value.
As a method of searching for the flow rate by repetition for this purpose, there is a method in which the Reynolds number Re and the friction coefficient λ of the Moody diagram are stored as a table in the memory of the data processing device, and the flow rate measurement value is automatically searched by data processing. Conceivable.
Patent Document 1 Patent No. 4503830 adopts a method in which the Reynolds number Re and the friction coefficient λ of the above-mentioned Moody diagram are stored in a memory of a data processing device as a table, and a flow rate measurement value is automatically searched by data processing. Yes.
The present invention does not use a Moody diagram, and therefore does not require a table of the Moody diagram. The first Reynolds number Re obtained from the well-known Darcy-Weissbach equation, the functional equation of the friction coefficient λ, the liquid The Reynolds number Re and the friction coefficient λ are obtained by simultaneously combining two independent functional expressions of the second Reynolds number Re and the friction coefficient λ. Therefore, the present invention and Patent Document 1 Patent No. 4503830 are different in the processing conversion method for obtaining the flow rate.
Major differences from Japanese Patent Laid-Open No. 6-94490 are disclosed below.
Japanese Patent Application Laid-Open No. 6-94490 is a case where the pipe wall is considered to be heat insulation, and the steady flow of the compressible fluid intended for the gas considering the friction caused by the fluid is defined as the Fanno flow, and the pipe flow rate based on the well-known Fanno equation. Seeking.
In contrast, the present invention is intended for incompressible liquids, and the flow rate is obtained based on the well-known Darcy-Weissbach equation. Therefore, the present invention has a fundamental difference in the flow rate measurement method from JP-A-6-94490.
Major differences from Japanese Patent Laid-Open No. 50-36163 are described below.
As a first difference, Japanese Patent Laid-Open No. 50-36163 uses a very high frequency cavity as a method for measuring the pressure of a pipe through which liquid sodium for cooling a nuclear reactor flows, and which shows a resonance frequency response by the pressure of liquid sodium flowing through the pipe. To measure the pressure. In the present invention, it is assumed that the pressure is measured by a pressure gauge used for process control in which a diaphragm pressure sensor such as a semiconductor type or a capacitance type is inserted into a tube. In Japanese Patent Laid-Open No. 50-36163, the ultra high frequency wave is returned to the electrical signal corresponding to the pipe pressure in the processing electronics unit through the waveguide, and the differential pressure between the pressures in the pipes of the sensors installed at the first and second positions of the pipe. To obtain the flow rate. Although the pressure measurement method is different from that of the present invention, the present invention is the same as that disclosed in Japanese Patent Laid-Open No. 50-36163 in that the flow rate is converted from the differential pressure due to the electric signal.
The second difference is that Japanese Patent Application Laid-Open No. 50-36163 claims that “it has a first resonant hypersonic cavity that responds to a pressure change outside it and supplies an electrical output that indicates the pressure change. A first ultra-high frequency sensor that has a second resonant hyper-sonic cavity that is responsive to pressure changes external thereto and that provides an electrical output indicative of the pressure change; and the first and It comprises means for comparing each output supplied from the second sensor and responding to each output. " This claim automatically calculates the Reynolds number from the flow velocity each time it is measured, reads the coefficient of friction from the Moody diagram, and calculates the Darcy-Weissbach formula described as the Δp formula in the specification. The processing to be performed is not described. In addition, FIG. No part 1 performs these processes.
These processes described in the specification are not performed every time the flow rate is measured, but the flow rate of liquid sodium necessary for cooling the reactor and the differential pressure between the first and second sensors are obtained. It can be interpreted that the flow rate required for cooling is estimated by comparing the measured differential pressure with the previously determined differential pressure. In the present invention, these processes are performed in the pipe flow rate measuring device every time the flow rate is measured. Therefore, Japanese Patent Laid-Open No. 50-36163 and the present invention are basically different as a flow rate measuring device.

また、数式２のレイノルズ数Ｒｅの管内平均流速ｕを数式１２を用いて管内流量Ｑで置換えると数式２は数式１４で表すことができる。

液体の温度を測定する前記温度計３を管の液体温度を代表する位置に設置する。液体温度計３は温度変化に伴う液体粘度と密度を補正するものである。
数式１３は、管摩擦係数λ、差圧ΔＰの関数としてλ、ΔＰ以外の値は係数とし設定または演算により求める。
数式１４のレイノルズ数は演算により求める。
液体温度計３で測定した液体温度Ｔを電気信号により伝送する信号伝送部８および伝送路９により伝送して管摩擦係数・差圧関数係数演算部およびレイノルズ数演算部１７において、液体密度、粘度を設定する液体パラメータ設定部７により設定されている基準温度における液体密度、粘度を測定した液体温度Ｔにおける液体密度、粘度に換算する。換算はあらかじめ設定されている換算テーブルを参照して換算値を求めるか、または粘度の場合は公知のアンドレード粘度換算数式により換算する。
管の水力直径として円形管の場合は管内径ｄ、上流圧力設定点２２と下流圧力予測制御点間の距離Ｌを管寸法パラメータ設定部６により設定する。
また、下流圧力予測制御点１７の圧力予測は設定した管流量Ｑのもとで行うため管流量設定部１８により管流量Ｑを設定する。以上により、数式１３の係数はすべて決定して、管摩擦係数・差圧関数の変数はλとΔＰのみの関数となっている。
数式１４のレイノルズ数の値もＱ、ｄは設定値で、ρ、μは設定値を液体温度計３で測定した液体温度に換算して求められるために値が決定している。
管摩擦係数演算部１９においては、レイノルズ数演算部で数式１４により求めたレイノルズ数Ｒｅにより摩擦係数λを演算により求める。演算式はレイノルズ数Ｒｅの値により層流、層流から乱流域に遷移する遷移流、乱流毎に数式が異なる。
数式の選定はレイノルズ数の値により下記により選定する。
層流の場合（Ｒｅ＜Ｒｅ_Ｌ）は数式４
遷移流の場合（Ｒｅ_Ｈ＞Ｒｅ≧Ｒｅ_Ｌ）は数式８
乱流の場合（Ｒｅ≧Ｒｅ_Ｈ）は数式５
により演算する。
摩擦係数λの演算において数式が陰関数の場合は、請求項１の場合と同様に、
ニュートン・ラプソン法等を用いて数値的に解くか、Ｅｘｃｅｌ等の表計算ソフトであるゴールシーク、ソルバーなどを下流圧力予測制御装置２４に組込むことにより演算で求める。
管摩擦係数演算部１９に管相対粗さを管相対粗さ設定部１０により設定し、臨界レイノルズ数を臨界レイノルズ数設定部１１により設定する。
管摩擦係数演算部１９で求めた摩擦係数λは管摩擦係数・差圧関数演算部２０において、数式１３に代入して差圧ΔＰを求める。
上流設定圧力演算表示部２１において、前記差圧ΔＰに下流設定圧力設定部２３で設定している下流設定圧力を加算する。この加算した圧力は上流圧力設定値であり、上流設定圧力演算表示部２１で表示する。
同時に前記上流圧力設定値は前記上流圧力設定器１６に対して電気信号により信号伝送部８および伝送路９により伝送して前記上流圧力設定器１６で圧力設定を行う。
表２に、これらの数式を整理して示す。

FIG. 2 is a basic configuration diagram of “claim 2”.
The upstream pressure and the downstream pressure prediction control point 17 are adjusted by adjusting the pressure of the upstream pressure set point 22 of the pipe 15 where the fluid flows down in a steady flow state through the pipe 15 arranged linearly on the same horizontal plane with a uniform pipe cross section. Is controlled by the upstream pressure setter 16 installed at the upstream pressure set point 22 under a set constant pipe flow rate Q.
In the pipe friction coefficient / differential pressure function coefficient calculation unit and the Reynolds number calculation unit 17, the coefficient of the Darcy-Weissbach equation of Equation 1 is calculated. If the relationship between the u in equation (12) and the in-pipe flow rate Q is used as the average flow velocity u in equation (1), equation (1) becomes equation (13).
Can be expressed as

Further, when the in-pipe average flow velocity u of the Reynolds number Re in Formula 2 is replaced with the pipe flow rate Q using Formula 12, Formula 2 can be expressed by Formula 14.

The thermometer 3 for measuring the temperature of the liquid is installed at a position representing the liquid temperature of the pipe. The liquid thermometer 3 corrects the liquid viscosity and density accompanying the temperature change.
Equation 13 is obtained by setting or calculating the values other than λ and ΔP as functions of the pipe friction coefficient λ and the differential pressure ΔP.
The Reynolds number of Expression 14 is obtained by calculation.
The liquid temperature T measured by the liquid thermometer 3 is transmitted by a signal transmission unit 8 and a transmission path 9 that transmit electrical signals, and the pipe friction coefficient / differential pressure function coefficient calculation unit and Reynolds number calculation unit 17 perform liquid density and viscosity. The liquid density and viscosity at the reference temperature set by the liquid parameter setting unit 7 are converted into the liquid density and viscosity at the measured liquid temperature T. For conversion, a conversion value is obtained with reference to a conversion table set in advance, or in the case of viscosity, conversion is performed using a well-known Andrade viscosity conversion formula.
In the case of a circular pipe, the pipe diameter parameter setting unit 6 sets the pipe inner diameter d and the distance L between the upstream pressure setting point 22 and the downstream pressure prediction control point as the hydraulic diameter of the pipe.
Further, since the pressure prediction at the downstream pressure prediction control point 17 is performed under the set pipe flow rate Q, the pipe flow rate setting unit 18 sets the pipe flow rate Q. As described above, all the coefficients of Expression 13 are determined, and the variables of the pipe friction coefficient / differential pressure function are functions of only λ and ΔP.
The values of Reynolds number in Expression 14 are also determined because Q and d are set values, and ρ and μ are determined by converting the set values to the liquid temperature measured by the liquid thermometer 3.
In the pipe friction coefficient calculation unit 19, the friction coefficient λ is obtained by calculation using the Reynolds number Re obtained by Equation 14 in the Reynolds number calculation unit. The calculation formula varies depending on the value of the Reynolds number Re for each laminar flow, transition flow from laminar flow to turbulent flow region, and turbulent flow.
The formula is selected according to the Reynolds number as follows.
In the case of laminar flow (Re <Re _L ), Equation 4
In the case of a transition flow (Re _H > Re ≧ Re _L ), Equation 8
In the case of turbulent flow (Re ≧ Re _H ), Equation 5
Calculate by
In the calculation of the friction coefficient λ, when the mathematical expression is an implicit function, as in the case of claim 1,
It can be solved numerically using the Newton-Raphson method or the like, or can be calculated by incorporating a goal seek, solver, etc., which is a spreadsheet software such as Excel, into the downstream pressure prediction control device 24.
In the pipe friction coefficient calculation unit 19, the pipe relative roughness is set by the pipe relative roughness setting unit 10, and the critical Reynolds number is set by the critical Reynolds number setting unit 11.
The pipe friction coefficient / differential pressure function calculation unit 20 substitutes the coefficient of friction λ obtained by the pipe friction coefficient calculation unit 19 into Equation 13 to obtain the differential pressure ΔP.
In the upstream set pressure calculation display unit 21, the downstream set pressure set by the downstream set pressure setting unit 23 is added to the differential pressure ΔP. This added pressure is an upstream pressure set value and is displayed on the upstream set pressure calculation display unit 21.
At the same time, the upstream pressure set value is transmitted to the upstream pressure setter 16 by an electric signal through the signal transmission unit 8 and the transmission path 9 and the upstream pressure setter 16 sets the pressure.
Table 2 summarizes these mathematical expressions.

ただし、ζ_ｂはベンドの損失係数であり、数式１６による。

となる。

ただし、ζ_ｅはエルボの損失係数であり、数式１８による。

となる。
図１１の同一水平面に設置された曲線管に対して、上流圧力計１および下流圧力計２間の高さが基準点高さに対して、それぞれＨ１およびＨ２で上流圧力計１と下流圧力計２間に曲がりがある管の流量計測を考える。
管は一様断面の管１５に定常流状態で液体が流れている場合、流速ｕは管路内で一定である。また、上流圧力計１と下流圧力計２間の総損失Ｈ_Ｌは摩擦損失と曲がり損失の合計であり数式１９なる。

ただし、ζは曲がり損失係数であり、曲がりが複数個所の場合は損失係数ζはこれらの合計である。ｇは重力の加速度である。
速度水頭は上下流で同じであることを考慮して、上流圧力計１と下流圧力計２間にベルヌーイの定理を適用すれば数式２０が得られる。

Ｐ１−Ｐ２＝ΔＰ、Ｈ１−Ｈ２＝ΔＨとし、数式２０をΔＰについてまとめれば数式２１となる。

数式２１は上流圧力計１と下流圧力計２間に高低差ΔＨおよび曲り管がある場合の数式１に相当する式である。
数式２を用いて、数式２１からｕを消去してλについて整理すれば数式２２と
なる。

数式２２は上流圧力計１と下流圧力計２間に高低差ΔＨおよび曲り管がある場合の数式３に相当する式である。
上流圧力計１と下流圧力計２間に高低差ΔＨおよび曲り管がある場合の流量計算式は、第一管摩擦係数・レイノルズ数関数として、同一平面の直管路の式として数式３の代わりに、数式２２を用いる。
すなわち、第一および第二管摩擦係数・レイノルズ数関数を連立方程式として管摩擦係数・レイノルズ数を演算する。
第一管摩擦係数・レイノルズ数関数は数式２２である。
第二管摩擦係数・レイノルズ数関数は層流、遷移流、乱流に対して別々の数式による。
層流については数式４、
遷移流については数式８
乱流については数式５
である。
表３ に、層流、遷移流、乱流の場合について、連立方程式として、摩擦係数、レイノルズ数を求める第一管摩擦係数・レイノルズ数関数および第二管摩擦係数・レイノルズ数関数の一覧を示す。
乱流の場合において、第一管摩擦係数・レイノルズ数関数および第二管摩擦係数・レイノルズ数関数の連立方程式を解くにあたり数式が陰関数となる場合、ニュートン・ラプソン法等を用いて数値的に解くか、Ｅｘｃｅｌ等の表計算ソフトであるゴールシーク、ソルバーなどを管流量計測装置に組込むことにより演算で求める。

摩擦係数λを用いた流量計算式は数式２１より、流速uを求めることにより、数式２３
により計算する。

なお、レイノルズ数Ｒｅを用いた流量計算式は高低差ΔＨおよび曲り管がある場合についても数式１１で計算される。 In a pipeline installed in a wide area, there may be a case where a straight pipe without height difference cannot be secured for flow measurement.
As a typical example of the bent pipe, there is a bend shown in FIG. 9 which is bent at an angle of θ degrees with a radius of curvature R and an elbow shown in FIG. 10 which is bent at an angle of θ degrees without drawing a curve.
Bend loss head Delta] h _b and known Head Loss Delta] h _e elbow official, respectively shown in Equation 15 and Equation 17.

Here, ζ _b is a bend loss coefficient and is given by Equation 16.

It becomes.

Where ζ _e is the loss factor of the elbow and is given by equation 18.

It becomes.
For the curved pipes installed on the same horizontal plane in FIG. 11, the height between the upstream pressure gauge 1 and the downstream pressure gauge 2 is H1 and H2 with respect to the reference point height, respectively. Consider the flow measurement of a pipe with a bend between the two.
When the liquid is flowing in a steady flow state in the tube 15 having a uniform cross section, the flow velocity u is constant in the pipe line. The total loss H _L between the upstream pressure gauge 1 and the downstream pressure gauge 2 is the sum of the friction loss and the bending loss, and is given by Equation 19.

However, ζ is a bending loss coefficient, and when there are a plurality of bendings, the loss coefficient ζ is the sum of these. g is the acceleration of gravity.
Considering that the velocity head is the same in the upstream and downstream, Equation 20 is obtained by applying Bernoulli's theorem between the upstream pressure gauge 1 and the downstream pressure gauge 2.

When P1−P2 = ΔP and H1−H2 = ΔH, and formula 20 is summarized for ΔP, formula 21 is obtained.

Formula 21 is a formula corresponding to Formula 1 when there is a height difference ΔH and a curved pipe between the upstream pressure gauge 1 and the downstream pressure gauge 2.
Using Equation 2, when u is deleted from Equation 21 and arranged for λ, Equation 22 is obtained.

Formula 22 is a formula corresponding to Formula 3 when there is a height difference ΔH and a curved pipe between the upstream pressure gauge 1 and the downstream pressure gauge 2.
The flow rate calculation formula when there is a height difference ΔH and a curved pipe between the upstream pressure gauge 1 and the downstream pressure gauge 2 is expressed as a first pipe friction coefficient / Reynolds number function, instead of Formula 3 as a straight pipe equation in the same plane. For this, Equation 22 is used.
That is, the pipe friction coefficient / Reynolds number is calculated using the first and second pipe friction coefficient / Reynolds number functions as simultaneous equations.
The first pipe friction coefficient / Reynolds number function is Equation 22.
The second pipe friction coefficient and Reynolds number function are based on separate equations for laminar flow, transition flow, and turbulent flow.
For laminar flow, Equation 4,
For transition flow, Equation 8
For turbulence, Equation 5
It is.
Table 3 shows a list of the first pipe friction coefficient / Reynolds number function and the second pipe friction coefficient / Reynolds number function for obtaining the friction coefficient and Reynolds number as simultaneous equations for laminar flow, transition flow, and turbulent flow. .
In the case of turbulent flow, when solving the simultaneous equations of the first pipe friction coefficient / Reynolds number function and the second pipe friction coefficient / Reynolds number function, if the formula becomes an implicit function, numerically using the Newton-Raphson method etc. Solve or obtain by calculation by incorporating a goal seek, solver, etc., which is a spreadsheet software such as Excel, into the pipe flow measuring device.

The flow rate calculation formula using the friction coefficient λ is expressed by Formula 23 by calculating the flow velocity u from Formula 21.
Calculate with

Note that the flow rate calculation formula using the Reynolds number Re is calculated by Formula 11 even when there is a height difference ΔH and a curved pipe.

In the pipe flow rate measuring apparatus according to claim 1 of the present invention, pressure gauges are installed upstream and downstream of a pipe having a uniform pipe cross section found in many liquid pipelines, and the differential pressure of the upstream and downstream pressure gauges, the pipe In addition, the flow rate is measured from the liquid data. Since the pressure gauge installed in the pipe does not have a throttling mechanism such as an orifice, there is no friction loss against the fluid. According to the present invention, without using a Moody diagram, in the turbulent flow region, it is common to liquids, and the tube friction coefficient, Reynolds number function according to the Colebrook equation and the Darcy-Weissbach equation, which depends only on the roughness of the inner wall of the tube. It is now possible to obtain the pipe flow rate directly by solving both the induced pipe friction coefficient and the Reynolds number function using simultaneous equations and obtaining the friction coefficient and the Reynolds number.
The present invention can automatically measure laminar flow, transition flow, and turbulent flow to measure the pipe flow rate, prevent flow measurement errors due to reading errors in the moody diagram, and improve the accuracy and simplification of the measurement. It is possible to measure the flow rate of pipelines for agricultural water, oil, liquefied natural gas, waterworks, various industrial plants, etc.
The pipe to be measured can be applied to a curved pipe and the measurement of pipe flow with different heights.
The pipe downstream pressure prediction control apparatus according to claim 2 of the present invention calculates the pipe friction coefficient corresponding to the set flow rate and performs pipe downstream pressure prediction control, so that the accuracy of the upstream pressure setting is improved, and an excessive pressure setting is achieved. Energy loss can be reduced because it is not necessary.
In addition, by measuring the change in pipe downstream pressure value due to the aging deterioration of the inner wall surface of the pipe and comparing it with the pipe downstream pressure prediction value before aging deterioration, by grasping the change in the absolute roughness value of the pipe inner wall surface Pipe deterioration diagnosis becomes possible.
In addition, the calibration of the pipe flow measuring device can be easily performed by flowing the calibration flow at the position of the upstream pressure gauge, measuring the flow from the differential pressure with the downstream pressure gauge, and comparing it with the calibration flow. .
In addition, the pipe flow rate measuring device is composed of a general-purpose pressure gauge installed upstream and downstream, a liquid thermometer installed at a representative point, a simple telemeter, and a flow rate calculation device. In particular, when the flow rate is measured by a common flow rate calculation device, the flow rate can be measured economically.

Claims (2)

An upstream pressure gauge for measuring the upstream pressure of the pipe, and a downstream pressure gauge for measuring the downstream pressure, in which the liquid flows down in a steady flow through the pipe having a uniform pipe cross section;
A liquid thermometer for measuring the temperature of the liquid;
First pipe friction coefficient based on Darcy-Weissbach equation, first pipe friction coefficient for calculating the coefficient of the Reynolds number function, Reynolds number function coefficient calculation unit, the upstream pressure gauge, the downstream pressure gauge, and the liquid temperature A signal transmission unit and a transmission path for transmitting the upstream pressure, the downstream pressure and the liquid temperature measured by a meter to the first pipe friction coefficient, Reynolds number function coefficient calculation unit by an electrical signal;
Liquid parameter setting unit for setting the liquid density and viscosity in the first pipe friction coefficient, Reynolds number function coefficient calculation unit,
A pipe dimension parameter setting unit for setting a hydraulic diameter of the pipe and a distance between the upstream pressure gauge and the downstream pressure gauge in the first pipe friction coefficient, Reynolds number function coefficient calculation unit,
Laminar flow, transition flow from laminar flow to turbulent flow region, mathematical formulas differ for each turbulent flow, second pipe friction coefficient independent of liquid type, second pipe friction coefficient and Reynolds number for calculating coefficients of Reynolds number function A function coefficient calculation unit;
A pipe relative roughness setting unit for setting pipe relative roughness in the second pipe friction coefficient, Reynolds number function coefficient calculation unit;
A critical Reynolds number setting unit for setting a critical Reynolds number in the second pipe friction coefficient, Reynolds number function coefficient calculation unit;
Calculate the pipe friction coefficient and Reynolds number using the first and second pipe friction coefficients and the Reynolds number function obtained by calculation in the first and second pipe friction coefficients and the Reynolds number function coefficient calculation unit as simultaneous equations. Simultaneous pipe friction coefficient, Reynolds number calculation unit,
A flow rate calculation display unit that calculates and displays the pipe flow rate using the pipe friction coefficient or the Reynolds number determined by the simultaneous pipe friction coefficient, Reynolds number function calculation unit,
A pipe flow rate measuring device comprising: Upstream pressure installed at the upstream pressure set point that controls the differential pressure with the downstream pressure prediction control point by adjusting the pressure at the upstream pressure set point of the pipe where the fluid flows down in a steady flow state through the pipe with a uniform pipe cross section A setting device;
A liquid thermometer for measuring the temperature of the liquid;
A pipe consisting of a pipe friction coefficient based on the Darcy-Weissbach equation, a pipe friction coefficient for calculating the coefficient of the differential pressure function, a differential pressure function coefficient calculation section, and a Reynolds number calculation section for calculating the Reynolds number corresponding to the set flow rate. Friction coefficient, differential pressure function coefficient calculator and Reynolds number calculator,
A signal transmission section and a transmission path for transmitting the liquid temperature measured by the liquid thermometer to the pipe friction coefficient, differential pressure function coefficient calculation section and Reynolds number calculation section by an electric signal;
A liquid parameter setting unit for setting a liquid density and a liquid viscosity in the pipe friction coefficient, differential pressure function coefficient calculation unit, and Reynolds number calculation unit;
A pipe dimension parameter setting unit for setting the pipe hydraulic coefficient and the distance between the upstream pressure setter and the downstream pressure prediction control point in the pipe friction coefficient, differential pressure function coefficient calculation unit and Reynolds number calculation unit;
A pipe flow rate setting unit that sets a pipe flow rate corresponding to downstream pressure prediction control in the pipe friction coefficient, differential pressure function coefficient calculation unit, and Reynolds number calculation unit;
The pipe friction coefficient, the differential pressure function coefficient calculation unit and the Reynolds number calculation unit find the pipe friction coefficient with respect to the Reynolds number, the laminar flow, the transition flow from laminar flow to the turbulent flow region, the mathematical formula is different for each turbulent flow, the liquid Tube friction coefficient calculation unit independent of the type of
A pipe relative roughness setting unit for setting pipe relative roughness in the pipe friction coefficient calculation unit;
A critical Reynolds number setting unit for setting a critical Reynolds number in the pipe friction coefficient calculation unit;
The calculated pipe friction coefficient, the pipe friction coefficient, the differential pressure function coefficient calculation section, the pipe friction coefficient obtained by the Reynolds number calculation section, the pipe friction coefficient, the differential pressure function to obtain the differential pressure, and the differential pressure function. An arithmetic unit;
An upstream set pressure calculation display unit configured to display the pressure obtained by adding a downstream set pressure to the differential pressure obtained by the pipe friction coefficient and the differential pressure function calculation unit as an upstream set pressure;
A downstream set pressure setting section for setting a downstream set pressure with respect to the upstream set pressure calculation display section;
A signal transmission section and a transmission path for transmitting the upstream set pressure to the upstream pressure setter by an electrical signal;
A pipe downstream pressure prediction control apparatus comprising:

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