A Modified Technique of Flow Transducer Using Bourdon Tube as Primary Sensing Element

1530-437X (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. Seehttp://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/JSEN.2014.2322199, IEEE Sensors Journal

Index Terms – Bernoulli’s equation, Static pressure, Bourdon gauge, Inductive pick-up coil, Differential inductance measurement.

Abstract— The pressure head at a point inside a flowing fluid

through a pipeline decreases with the increase of flow rate according to Bernoulli’s equation. The measurement of flow rate by measuring this pressure is not generally used since decrease of pressure is very small compared to static pressure at no flow. In this paper, a modified differential inductance type technique has been developed to measure the flow rate of a fluid by measuring only this change in pressure without using any obstruction in the pipeline. A differential inductance type pressure transducer using two identical Bourdon tubes as the primary sensing elements, has been designed and developed to measure the small decrease of pressure due to flow of fluid in a horizontal pipeline. The transducer has been used to measure the flow rate of tap water through a pipeline. The basic theoretical equations describing the operation of the transducer have been derived. The transducer has been experimentally tested and the experimental results are reported in this paper. The experimental characteristic is found to follow the theoretical equations with good repeatability.

I. INTRODUCTION

Measurement of flow of a fluid through a pipeline is one of the most important requirements in any process plant in order to run the plant with optimum efficiency at lesser cost. There are various effects like effect of energy associated with a flowing fluid through a pipeline, Doppler effect, effect of speed of the fluid suction pump on the flow rate, cooling effect of flowing fluid on a heated object etc. which have been utilized in designing the various flow meters [1], [3]. For example, energy associated with the flowing fluid is described by Bernoulli’s equation and is utilized in designing obstruction type flow meters. Doppler effect is used in non-contact ultrasonic flow meters, and speed of fluid suction pump is utilized in various positive displacement flow meters and so on. The cooling effect of a flowing fluid on a heating element placed inside the fluid is utilized to find the mass flow

S. Marick is with Department of Applied Electronics and Instrumentation Engineering, Future Institute of Engineering and Management, Sonarpur Station Road, Kolkata 700150, India. Email: [email protected]. S. K. Bera is with Electronics & Communication Engineering Dept., Techno India Chaibasa, Jharkhand, India. Email: [email protected]. S.C.Bera is with Instrumentation Engineering Section, Department of Applied Physics, University of Calcutta, 92, A.P.C. Road, Kolkata 700009, India. Email: [email protected] Copyright (c) 2013 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected].

rate of the fluid in terms of change in resistance of the element. There are many other industrially accepted flow meters like electromagnetic flow meter, vortex flow meter, coriolis flow meter etc. In electromagnetic flow meter the emf induced between two diametrically opposite insulated metallic electrodes inserted into the pipeline of a flowing conducting liquid is taken as the measure of the volume flow rate of the liquid. In vortex flow meters frequency of vortices produced behind a blunt post in a pipeline under the turbulent condition is directly proportional to the volume flow rate of the fluid passing through the pipeline. In coriolis flow meters [1], [2], [6], [14] the effect of coriolis force produced by the interaction between a flowing fluid through a perpendicularly vibrating pipeline section is utilized to measure the mass flow rate of the fluid in terms of tilting frequency of the U-shaped pipeline section or in terms of phase difference between the vibrating waves produced on two sides of a straight pipeline section with respect to the location of the vibrating source. A good number of research works on flow transducer of simpler design and lesser cost with good accuracy are still being reported by various workers. T. Moazzeni et al. [5] have proposed a flow measurement technique in harsh environmental condition by estimating the time delay between two correlated thermal signals recorded by two separate thermocouples placed in the pipeline. They have applied a regression method for calibration process and have found a nearly linear relationship in comparison to the standard flow meters in the range of 0.5 to 3 gallons per minute. A modified orifice type flow transducer for a conductive liquid has been designed by S.C.Bera et al. [7] in which no differential pressure cell is needed to measure the differential pressure across the orifice. A non-contact type online flow pattern identification technique of gas-liquid two phase flow has been reported by L. Wang et al. [8]. In this technique eight statistical energy patterns are extracted from the output of a capacitively coupled contactless conductivity detector for a particular excitation signal and from this energy patterns, the flow patterns are obtained by using SVM method. D. Li et al. [9] have utilized Coventorware software based MEMS technique to fabricate a monolithic piezo-resistive sensor and have applied this sensor for simultaneous measurement of pressure and flow. S.C.Bera et al. [10] have developed a low cost inductive technique for measurement and transmission of pressure signal using a Bourdon tube as the sensing element and have found a very good linearity and repeatability. U.R.Prasanna et al. [11] have developed a null deflection type flow measurement technique by compensating the pressure drop across a flow restrictor from an external pressure source and this compensating pressure drop is taken as a measure of flow rate of the fluid. This non-disruptive flow measurement

A modified technique of flow transducer using Bourdon tube as primary sensing element

S.Marick , S.K.Bera and S.C.Bera Member IEEE



technique has been claimed to have a good resolution at very low flow rate. N. Svedin et al. [12] have developed a micro machined silicon torque sensor which senses the torque produced at the bearing surface of a static turbine placed in a flow tube and have shown that this torque is linearly related with the volume flow rate through the pipeline. Pitot tube is a very simple flow sensor and needs some corrections for accurate measurement of flow rate. S. Gh. Etemad et al. [13] have developed a neural network based model to estimate the correction factor of Pitot tubes for Newtonian and non- Newtonian fluids. M.A.Atmanand et al. [15] have established a relation between the flow rate of a fluid passing through a control valve in a pipeline and the input signal of the control valve actuator. Thus they have utilized the input signal as a measure of the volume flow rate of the fluid and have developed a flow control system without using any actual flow transmitter.

Flow of a fluid through a pipeline under a static pressure head depends on process resistance of the pipeline and the value of the static pressure as well as type of the fluid. Thus the pressure at a point inside a flowing fluid primarily depends on velocity of the fluid at that point. This pressure for a low viscous fluid follows Bernoulli’s principle which states that total mechanical energy per unit volume of a fluid element is constant at every point along a streamline, i.e. the sum of kinetic energy and potential energy remains constant. Potential energy of a fluid element in a pipeline has two parts, of which one part is due to the pressure of the fluid at the fluid element and the other part is due to the elevation of the fluid element from the reference level or the sea level. For a horizontal pipeline the elevation energy remains constant. So from the law of conservation of energy, the pressure energy of a fluid element in a horizontal pipeline completely filled with the fluid, decreases with the increase of fluid velocity. But at low or medium flow rate the decrease of pressure with the increase of flow rate may be very small compared to the static pressure at no flow. So measurement of flow rate of a fluid by measuring the online pressure of a flowing fluid in a pipeline is not generally used. In the present paper a technique has been developed by which flow rate of a fluid in a pipeline can be measured only by measuring static pressure at no flow by a pressure gauge and measuring the online pressure of a flowing fluid at a given flow rate by a second pressure gauge and then taking the difference between the two readings. Thus the effect of static pressure is eliminated in this technique. To convert the Bourdon gauge reading into electrical signal an inductance type transducer [10] has been used. The theoretical equations describing the operations of the proposed flow transducer have been derived. The transducer has been experimentally studied in both increasing and decreasing modes of flow rate and experimental results are reported in the paper. A good repeatability of experimental results has been observed.

Table 1: Nomenclature

II. METHOD OF APPROACH

Let us consider two identical Bourdon tube type pressure gauges PG1 and PG2 of suitable range connected to the horizontal pipeline at a point at suitable distance from the end connections so that the flow of a fluid at the point is free from end connection disturbances as schematically shown in Fig. 1(a) with the photographic view shown in Fig. 1(b). The pressure gauge PG2 is directly connected with the main pipeline through the isolation valve V2 and the pressure gauge PG1 is connected with the pipeline through isolation valves V1 and V2. PG1 is used to measure the static pressure of the fluid in the main pipeline under no flow condition and PG2 is used to measure the online pressure of the fluid flowing through the pipeline.

(a)

(b)

Fig. 1: (a) Schematic diagram of proposed flow sensor (b) Photographic view of proposed flow sensor

Symbols Explanations Q volume flow rate ρ density of the liquid A cross-sectional area of the horizontal pipeline V velocity of fluid flowing through the pipeline PS static pressure P online pressure

PG1 pressure gauge for measurement of static pressure PG2 pressure gauge for measurement of online pressure

r mean radius of C-type Bourdon tube δθ angle of rotation of free end of Bourdon tube δx circumferential movement of the tip of the Bourdon tube δL change in inductance of the pickup coil

δLPS change in inductance of the inductive pick-up coil attached with static pressure measuring unit (PG1)

δLP change in inductance of the inductive pick-up coil attached with online pressure measuring unit (PG2)

L0 inductance of each coil at no flow condition

L1 inductance of the coil of static pressure measuring unit (PG1)

L2 inductance of the coil of online pressure measuring unit (PG2)

L2 V2 PG2 PG1 L1

V1



Under no flow condition, the isolation valves (V1 and V2) are fully open and both PG1 and PG2 indicate the static pressure of the fluid. Now let us assume that V2 is closed and fluid is allowed to flow through the main pipeline with a velocityV , so that online pressure is reduced to P′ given by Bernoulli’s equation

2

12V P Kρ

′+ = = constant (1)

where V is the velocity of fluid flowing through the pipeline, ρ is the density of the fluid and P′ is the pressure of the fluid. If A be the area of the cross-section of the horizontal pipeline then volume flow rate Q is given by Q AV=

or Q

VA

= (2)

From equations (1) and (2), we have

2

2 12

Q PK

A ρ

′+ =

or 23 2P K K Q′ = − (3)

where 2 22K

Aρ

= and 3 1K Kρ= (4)

Now keeping V1 closed if V2 is fully open then a suction pressure P′′ will be produced in the fluid of the Bourdon gauge PG2. As stated in [16] P′′ may be assumed to be linearly related with flow rate Q, i.e.

4 5P K Q K′′ = + (5) where K4 and K5 are constants. Hence the net pressure produced in the pressure gauge PG2 is given by

26 2 4P P P K K Q K Q′ ′′= − = − − (6)

Where K6 = K3 – K5 (7) Thus, with the increase of flow rate Q , the net pressure P of the flowing fluid measured by Bourdon gauge PG2 decreases non-linearly. Now, if SP be the static pressure measured by Bourdon gauge

PG1 then the differential pressure ( P∆ ) between SP and P is given by

22 64S SQP P P K Q K P K+∆ = − = + − (8)

Thus the differential pressure non-linearly depends on volume flow rate Q but this differential pressure is very small. So the movement of Bourdon tube of each pressure gauge is converted into electrical signal by using inductive pick-up type technique [10] as stated below. Let us consider a C-type Bourdon tube (AB) with its free tip B attached with a thin U-shaped wire BCD made of ferromagnetic material as shown in Fig. 2. If the Bourdon tube mean radius r at no input pressure changes to r rδ+ at a gauge pressure P and free tip rotates through an angle δθ then the circumferential movement of the tip of the Bourdon tube is given by

( )x r r rδ δ δθ δθ= + (9) since rδ and δθ are very small. Again Pδθ ∝ or 1C Pδθ = (10)

where C1 is the proportionality constant. Thus 1x rC Pδ = (11)

Since the ferromagnetic wire is rigidly attached with the tip of the bourdon tube, so the linear movement (between D and D′ ) of the tip of the ferromagnetic wire may also be assumed to be equal to the circumferential movement xδ as shown in Fig 2. Now, this movement of the tip of the ferromagnetic wire with the variation of gauge pressure is further converted into variation of inductance of an inductive pick-up coil mounted on the base plate of the pressure gauge housing as shown in Fig. 3. Hence for a movement xδ of the ferromagnetic wire inside the pick-up coil, the variation in inductance of the coil is given by

L xδ δ∝ or 2L C xδ δ= (12)

where C2 is the constant of proportionality. Thus from equations (11) and (12), we have

1 2 7L rC C P K Pδ = = (13) where K7 = rC1C2 (14)

Fig.2. C-type Bourdon tube

Fig.3. Photographic view of C-type Bourdon gauge with inductive pick-up type sensor

Ferromagnetic wire

Bourdon tube

Inductive coil

Lead Wires



Each of the two pressure gauges PG1 and PG2 as shown in Fig. 1 are provided with identical inductive pick up type pressure sensors as shown in Fig. 3. Since PG1 measures static pressure SP and PG2 measures online pressure P and both

the pressure gauges are identical with same value of 7K so change of inductance of the two inductive pick-up coils attached with these gauges are given by

7SP SL K Pδ = (15)

and 7PL K Pδ = (16)

Hence, if 0L is the inductance of each coil at no flow condition then at volume flow rate Q the inductance of the coil of static pressure measuring unit (PG1) is given by

1 0 0 7SP SL L L L K Pδ= + = + (17) And that of coil of online pressure measuring unit (PG2) is given by

2 0 0 7PL L L L K Pδ= + = + (18) The difference between these inductances is given by

1 2 7 ( )SL L L K P P∆ = − = − (19) Thus from equations (8) and (19), we have

27 7 2 6

28 9

4

10

( )SQ

Q K

L K P K K Q K P K

K Q K

+

+

∆ = ∆ = + −

= + (20)

where 8 7 2K K K= , 9 7 4K K K= and ( )10 7 6K K P KS= − (21)

Hence the difference in inductances of the two coils non-linearly depends on volume flow rate Q . To measure this difference of inductances of the two coils a modified OPAMP based differential inductance measurement circuit is designed as shown in Fig. 4.

Fig. 4 Schematic diagram of the proposed flow transducer

For the sinusoidal ac supply voltage VS, the output of OPAMPs A1 and A2 are given by

0 11

1S

R j LV V

R

ω+= − × (22)

0 22

1S

R j LV V

R

ω+= − × (23)

where R0 is the resistance of each of the identical inductive pick-up coils.

Hence, the output of the differential amplifier circuit consisting of OPAMP A3 is given by

2 222 1 1 20

1 1

( ) ( ) ( )S Sj V R j V RRV V V L L L

R R R R R

ω ω∆ = − = − = ∆ (24)

Thus combining equations (20) and (24), we get

2 28 100

12

11 12 13

9( )S Q

Q K

j V RV K Q K K

R R

K Q K

ω+

+

∆ = +

= +

(25)

where 2 8 2 211

1 1

7S SKj V R K j V R K

KR R R R

ω ω= = [from (21)] , (26)

2 9 2 4 712

1 1

S Sj V R K j V R K K

KR R R R

ω ω== [from (21)] , (27)

2 10 2 713

1 1

6( )

S S SP Kj V R K j V R K

KR R R R

ω ω −== [from (21)] , (28)

Thus the output of the differential inductance measurement circuit almost follows a parabolic equation with flow rate. Now from equations (4), (7) and (28),

2 713

1

1 5( )

S SP K Kj V R K

KR R

ρω +−=

(29)

If the flow is obtained from a constant level overhead tank or from a constant pressure vessel then PS = ρK1 and equations (25) and (29) are independent of static pressure. But if the flow is obtained from a variable level tank or variable pressure vessel then ρK1 will not be equal to PS and an error will be introduced in the flow transducer output. In this case the error may be eliminated by connecting the pressure gauge PG1 with the liquid storage tank or pressure vessel at location having no flow of the fluid, since under this condition PS will be equal to ρK1. In other applications where static pressure changes an intermittent zero checking technique may be introduced by connecting a valve in main pipeline where the valve is operated using manual signal from the control room. Here valves V1 and V2 of the sensor system shown in Fig. 1 should also be operated by manual signal from control room. For zero checking main pipeline valve is closed and sensor valves V1 and V2 are opened. Under this condition PS is again equals to ρK1 and the transducer output become error free. After zero checking static pressure gauge valve V1 is closed and sensing pressure gauge valve V2 and main pipeline valve are opened. However, this intermittent process may be avoided by selecting a suitable range of the flow meter within tolerable limit of error or by calibrating the flow meter with respect to a standard flow meter and correcting each online data by auto calibration technique.

III. DESIGN

The proposed flow transducer consists of a main PVC pipeline section of length 90 cm, internal diameter 25 mm connected horizontally between two end connectors as shown

VS R1

R1 R

R R2

R2

∆V0

L1

L2

A1

A2

A3

V1

V2



in schematic diagram of Fig. 1(a) and in photographic view of Fig. 1(b) of the transducer. Two pressure gauges (PG1 and PG2) are provided with inductive sensors as shown in Fig. 3. These pressure gauges along with isolation valves (V1 and V2) are connected with the main pipeline through 12.5 mm Galvanized-Iron (GI) pipe. Tap water from an overhead tank of height about 4 meters is used as the process fluid. So the pressure gauge is selected in the range 0-1 Kg/cm2. A commercially available ferromagnetic GI wire of 17 SWG and 50 mm length is bent to form a U shape of unequal arms. The shorter arm is rigidly attached with the free end of the Bourdon tube using brazing technique while the longer arm is inserted into the inductive pick up coil to act as its movable core material. The inductance coil is mounted on the base plate of the Bourdon gauge by fixing bracket as shown in Fig. 3. The inductance coil is made with 5000 turns of 40 SWG super enamel copper wire wound on an insulating material former with 6 mm internal diameter and 9 mm outer diameter and a length of 60 mm. In the differential inductance measurement circuit shown in Fig. 4, the stabilized sinusoidal ac source at 5 volts, 1000 Hz has been used, with OP-07 as OPAMPs (A1, A2, and A3). R1, R and R2 are selected to be 10kΩ, 1kΩ and 100kΩ respectively of ½ watt, 1% tolerance.

IV. EXPERIMENT

The experiment is carried out with the experimental setup as shown in Fig. 5 using tap water as the process fluid. Tap water from a ground tank T1 is supplied to an overhead tank T2 by a pump. The pump supply voltage is so adjusted that its output flow rate W1 is slightly greater than the flow rate of water through the flow transducer main pipeline and the excess water is exhausted through the upper exhaust line to the ground tank T1. Thus depth of water in the overhead tank is maintained constant and static pressure in the flow transducer is also constant. From lower exhaust line of overhead tank water flows through the valve V3, proposed flow transducer’s flow head, valve V4 and rotameter to the ground tank T1.

Fig. 5 Schematic diagram of experimental setup

Before starting the experiment the valve V4 is closed, valve

V3 is open and isolation valves V1 and V2 in flow transducer shown in Fig.1 are also open. So that the pressure gauges PG1 and PG2 are filled with water at static pressure. Now the isolation valve V1 of the flow transducer is fully closed so that only pressure gauge PG2 is connected with the main pipeline.

The output terminals of inductive sensors L1 and L2 are connected with the differential inductance measurement circuit with stabilized ac source as shown in Fig. 4. The output of the circuit is measured by a 4½ digit digital multimeter. Now with the valve V3 fully open the valve V4 is opened in steps and at each step the rotameter reading and circuit output are measured in both increasing and decreasing modes. The static characteristic curve of the flow transducer is drawn by plotting the circuit output voltage ∆V against flow rate Q. The rotameter used in the experiment is pre-calibrated by direct water collection method and accuracy of ±0.5% has been observed. The static characteristic graphs in three increasing and three decreasing modes are shown in Fig. 6 and the corresponding standard deviation curve is shown in Fig. 7.

Fig. 6 Static characteristic graphs of the proposed flow transducer

Fig. 7 Standard deviation curve of the proposed flow transducer

The average value of measured data shown in Fig. 6 along with the corresponding ideal values obtained from ideal non-linear curve is now plotted against flow rate as shown in Fig. 8. The ideal data are obtained from best fit two degree polynomial obtained by using Microsoft Office Excel program. The percentage deviation of the average value of the measured data at a given flow rate from ideal best fit non-linear curve is calculated and plotted against flow rate as shown in Fig. 9.

Pump

T1

T2

Flow head

Flow transducer

V3

W1>W2

W2

Rotamete

V4



Fig. 8 Static characteristic graph of the proposed flow transducer for average

value of measured data

Fig. 9 Percentage deviation from ideal non-linearity of average value of the

measured data V. DISCUSSIONS From the static characteristic graph of the proposed flow transducer using pressure gauge as the sensing element as shown in Fig. 6 and average characteristic as shown in Fig. 8 it is observed that the characteristic almost follows the theoretical equation (25). Experimental data for three increasing and decreasing modes as shown in Fig. 6 have a good repeatability as shown in standard deviation curve in Fig. 7. From the average values of the measured data, the average static characteristic is drawn as shown in Fig. 8. The best fit ideal non-linear curve of this characteristic is also shown in the same Fig. 8. It is observed that the experimental curve and the ideal curve almost coincide with each other. The percentage deviation of the measured data from ideal curve shown in Fig. 9 is found to be within tolerable limit of ± 0.1%. The non-linear characteristic of the proposed transducer may be easily linearized by using a piece-wise hardware or software based technique. The non-linearity is due to non-linear Bernoulli’s equation regarding flow rate of a fluid through a pipe line. The proposed transducer has been tested for water flow rate up to a limiting range of 10 LPM, since facilities for testing a flow meter at higher range with both liquid and gas are not available in the laboratory. So this part

of the work is left as future scope. It may be mentioned here that the minimum detectable velocity of gases by the proposed transducer will be much more than that in water or other liquid applications. For example, the minimum detectable flow rate of water by the proposed flow transducer in the present work is 1 LPM which corresponds to water velocity of 0.034 m/sec for pipeline of 0.025 m internal diameter. At the same flow

rate the minimum detectable air velocity will be 2

w w

a

vρρ

or

0.994 m/sec at 30 oC, where w aandρ ρ are the densities of water and air respectively and wv is the velocity of water. The Bourdon tube type pressure gauges available in the market have a rugged construction. Hence the proposed flow transducer using Bourdon gauge as the primary sensing element will also have a very rugged construction. Since two identical Bourdon gauges are used and the difference of movements of the tips are sensed by two identical inductive pick-ups and Bourdon tubes are placed in atmospheric condition, so the effect of fluid temperature may be assume to be minimum. Moreover, the inductive pick up type technique converts the flow rate signal into electrical signal which can be easily transmitted to a controller after proper signal conditioning in the form of 4-20 mA current signals in analog or digital form. So the transducer can be easily incorporated in automatic flow control system of modern instrumentation. The proposed flow measurement technique does not require any obstruction in the pipe line. So the proposed technique will be free from the major defect of an obstruction type flow meter due to pressure loss across the obstruction. Thus maximum possible flow rate against a static pressure may be easily maintained by using the proposed transducer. Moreover, in obstruction type flow meter a differential pressure cell is associated with various types of maintenance and mounting problems and has complicated construction. The mounting of Bourdon gauges used in the proposed transducer is very easy compared to the DP cell. Bourdon gauges along with the proposed inductive pick-ups are also very much less costly than the DP cell used in obstruction type flow meter along with much less maintenance problems. It may be mentioned here that when a Bourdon gauge is connected with a pipeline through which a fluid is flowing, some amount of fluid is inserted into the Bourdon tube when fluid pressure is increased due to decrease of flow rate but this amount of fluid is very much negligible compared to the total volume of the fluid. Hence, this offers negligible resistance to the fluid flow rate and the error due connection of the pressure gauge with the pipeline is negligible. The differential inductance measurement technique used in the proposed transducer eliminates the effect of electromagnetic interference in the inductive pick-ups. In this technique the effect of high static pressure in the flow line is also eliminated. Bourdon tube with inductive pickup has already been used for pressure measurement by the present author [10]. The same technique is used in the present work for measurement of flow rate. But here, a modification of the design of the earlier work has been made. In the earlier work the inductive



pick up type pressure sensing element was mounted outside the Bourdon gauge which increases the overall space required for the sensor mounting, and this may be difficult in the plant atmosphere in the location consisting of a large number of pipelines. But in the present work the sensing element has been mounted inside the normal Bourdon gauge without requiring any additional space. This also provides better mechanical protection for the sensing element from being damaged by external mechanism. Since in the present work two such identical Bourdon gauges are used so required space for mounting the proposed flow sensor unit is comparatively large. The modified design helps in minimizing the space problem. Since the proposed transducer is found to have a parabolic characteristic as shown in equation (25) and experimental static characteristic graph shown in Fig. 6 and Fig. 8. So sensitivity of the transducer is different at different flow rates. At lower flow rate sensitivity is comparatively small since the movement of the Bourdon tube tip is very small at low flow rate. At higher flow rate sensitivity has a satisfactory value. However using Bourdon tube of better sensitivity with larger radius (r) of C-section, the proposed transducer sensitivity at low flow may be improved. So the proposed flow transducer will have a minimum measurable range below which flow cannot be measured accurately. At higher turbulent flow a measurement error may be introduced due to loss of energy by turbulence. This is true for every obstruction type flow meter which has limited range. Hence the proposed transducer will have a limited maximum range with turbulence error within tolerable limit.

VI. CONCLUSIONS

The proposed flow transducer has a rugged construction as mentioned earlier. It has a very simple design and hence it is less costly than the conventional flow transducer like orifice, venturi, nozzle etc. Its mounting is very simple such as a simple connection of a short length of transducer tube with the main pipe line. By using suitable signal conditioner circuit the electric signal output of the proposed transducer may be easily converted into linear 4-20 mA current output and transmitted to the remote receiver and may be incorporated in the modern computer based system.

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A Modified Technique of Flow Transducer Using Bourdon Tube as Primary Sensing Element