SpiraxSarco-B4-Flowmetering

8/14/2019 SpiraxSarco-B4-Flowmetering

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The Steam and Condensate Loop 4.1.1

Fluids and Flow Module 4.1Block 4 Flowmetering

Module 4.1

Fluids and Flow


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The Steam and Condensate Loop4.1.2


Introduction

When you can measure what you are speaking about and express it innumbers, you know something about it; but when you cannot measure it,

when you cannot express it in numbers, your knowledge

is of a meagre and unsatisfactory kind.William Thomson (Lord Kelvin) 1824 - 1907

Many industrial and commercial businesses have now recognised the value of:

o Energy cost accounting.

o Energy conservation.

o Monitoring and targeting techniques.

These tools enable greater energy efficiency.

Steam is not the easiest media to measure. The objective of this Block is to achieve a greaterunderstanding of the requirements to enable the accurate and reliable measurement of steam

flowrate.Most flowmeters currently available to measure the flow of steam have been designed for measuringthe flow of various liquids and gases. Very few have been developed specifically for measuringthe flow of steam.

Spirax Sarco wishes to thank the EEBPP (Energy Efficiency Best Practice Programme) of ETSUfor contributing to some parts of this Block.

Fundamentals and basic data of

Fluid and Flow

Why measure steam?Steam flowmeters cannot be evaluated in the same way as other items of energy saving equipmentor energy saving schemes. The steam flowmeter is an essential tool for good steam housekeeping.It provides the knowledge of steam usage and cost which is vital to an efficiently operated plantor building. The main benefits for using steam flowmetering include:

o Plant efficiency.

o Energy efficiency.

o Process control.

o Costing and custody.

Plant efficiencyA good steam flowmeter will indicate the flowrate of steam to a plant item over the full range ofits operation, i.e. from when machinery is switched off to when plant is loaded to capacity. Byanalysing the relationship between steam flow and production, optimum working practices canbe determined.

The flowmeter will also show the deterioration of plant over time, allowing optimum plant cleaningor replacement to be carried out.

The flowmeter may also be used to:

o Track steam demand and changing trends.

o Establish peak steam usage times.

o Identify sections or items of plant that are major steam users.

This may lead to changes in production methods to ensure economical steam usage. It can alsoreduce problems associated with peak loads on the boiler plant.


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Energy efficiencySteam flowmeters can be used to monitor the results of energy saving schemes and to comparethe efficiency of one piece of plant with another.

Process controlThe output signal from a proper steam flowmetering system can be used to control the quantityof steam being supplied to a process, and indicate that it is at the correct temperature and

pressure. Also, by monitoring the rate of increase of flow at start-up, a steam flowmeter can beused in conjunction with a control valve to provide a slow warm-up function.

Costing and custodySteam flowmeters can measure steam usage (and thus steam cost) either centrally or at individualuser points. Steam can be costed as a raw material at various stages of the production processthus allowing the true cost of individual product lines to be calculated.

To understand flowmetering, it might be useful to delve into some basic theory on fluidmechanics, the characteristics of the fluid to be metered, and the way in which it travels throughpipework systems.

Fluid characteristicsEvery fluid has a unique set of characteristics, including:

o Density.

o Dynamic viscosity.

o Kinematic viscosity.

DensityThis has already been discussed in Block 2, Steam Engineering Principles and Heat Transfer,however, because of its importance, relevant points are repeated here.

Density (r) defines the mass (m) per unit volume (V) of a substance (see Equation 2.1.2).

Equation 2.1.2( ) =0DVVPNJ

'HQVLW\ 9ROXPH9P 6SHFLILFYROXPH

J

Y

Steam tables will usually provide the specific volume (vg) of steam at various pressures/temperatures, and is defined as the volume per unit mass:

9ROXPH96SHFLILFYROXPH P NJ

0DVVP=

J

Y

From this it can be seen that density (r) is the inverse of specific volume (vg):

=

'HQVLW\ NJ P6SHFLILFYROXPH

J

Y

The density of both saturated water and saturated steam vary with temperature. This is illustratedin Figure 4.1.1.


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Fig. 4.1.1 The density (r) of saturated water (rf) and saturated steam (rg) at various temperatures

Dynamic viscosityThis is the internal property that a fluid possesses which resists flow. If a fluid has a high viscosity(e.g. heavy oil) it strongly resists flow. Also, a highly viscous fluid will require more energy topush it through a pipe than a fluid with a low viscosity.

There are a number of ways of measuring viscosity, including attaching a torque wrench to apaddle and twisting it in the fluid, or measuring how quickly a fluid pours through an orifice.

A simple school laboratory experiment clearly demonstrates viscosity and the units used:

A sphere is allowed to fall through a fluid under the influence of gravity. The measurement of the

distance (d) through which the sphere falls, and the time (t) taken to fall, are used to determinethe velocity (u).

The following equation is then used to determine the dynamic viscosity:

Equation 4.1.1 JU

'\QDPLFYLVFRVLW\ X

0700

50 100 150 200 250 300

800

900

1000

Den

sity(r)kg/m

Temperature (C)

Saturated water

0

10

20

30

40

50

0 50 100 150 200 250 300

Density(r)kg/m

Temperature (C)

Saturated steam

Where: = Absolute (or dynamic) viscosity (Pa s)Dr = Difference in density between the sphere and the liquid (kg /m3)g = Acceleration due to gravity (9.81 m/ s2)

r = Radius of sphere (m)

u =

Note: The density of saturated steam increases with temperature (it is a gas, and is compressible) whilst thedensity of saturated water decreases with temperature (it is a liquid which expands).

G'LVWDQFHVSKHUHIDOOVP

9HORFLW\W7LPHWDNHQWRIDOOVHFRQGV


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There are three important notes to make:

1. The result of Equation 4.1.1 is termed the absolute or dynamic viscosity of the fluid and ismeasured in Pascal/second. Dynamic viscosity is also expressed as viscous force.

2. The physical elements of the equation give a resultant in kg/m, however, the constants(2 and 9) take into account both experimental data and the conversion of units to Pascalseconds (Pa s).

3. Some publications give values for absolute viscosity or dynamic viscosity in centipoise (cP),e.g.: 1 cP = 10-3 Pa s

Example 4.1.1It takes 0.7 seconds for a 20 mm diameter steel (density 7800 kg /m3) ball to fall 1 metre throughoil at 20C (density = 920 kg/m3).

Determine the viscosity where:Dr = Difference in density between the sphere (7800) and the liquid (920) = 6880 kg/m3g = Acceleration due to gravity = 9.81 m/s2

r = Radius of sphere = 0.01 m

u = Velocity = 1.43 m/s

( )

( )

JU'\QDPLFYLVFRVLW\

X

[[['\QDPLFYLVFRVLW\ 3DV

[

G W

Dynamicviscosity()x

10

kg/m

-6

0 50 100 150 200 250 3000

500

1000

1500

2000

Temperature (C)

Saturated water

D

ynamicviscosity()x

10

kg/m

-6

05

10

15

20

50 100 150 200 250 300

Temperature (C)

Saturated steam

Fig. 4.1.2 The dynamic viscosity of saturated water (mf) and saturated steam (mg) at various temperatures

Note: The values for saturated water decrease with temperature, whilst those for saturated steam increase with temperature.

Values for the dynamic viscosity of saturated steam and water at various temperatures are givenin steam tables, and can be seen plotted in Figure 4.1.2.


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[[

H

5H\QROGVQXPEHU5

From looking at the above Reynolds number it can be seen that the flow is in the laminar region(see Figure 4.1.7).

Equation 4.1.3

Reynolds number (Re)The factors introduced above all have an effect on fluid flow in pipes. They are all drawntogether in one dimensionless quantity to express the characteristics of flow, i.e. theReynolds number (Re).

X'5H\QROGVQXPEHU5

H

Where:r = Density (kg /m3)u = Mean velocity in the pipe (m/s)

D = Internal pipe diameter (m) = Dynamic viscosity (Pa s)

Analysis of the equation will show that all the units cancel, and Reynolds number (Re) is thereforedimensionless.

Evaluating the Reynolds relationship:

o For a particular fluid, if the velocity is low, the resultant Reynolds number is low.

o If another fluid with a similar density, but with a higher dynamic viscosity is transported throughthe same pipe at the same velocity, the Reynolds number is reduced.

o For a given system where the pipe size, the dynamic viscosity (and by implication,

temperature) remain constant, the Reynolds number is directly proportional to velocity.

Example 4.1.3The fluid used in Examples 4.1.1 and 4.1.2 is pumped at 20 m/s through a 100 mm bore pipe.

Determine the Reynolds number (Re) by using Equation 4.1.3 where: r = 920 kg /m3

= 1.05 Pa s

Equation 4.1.3X'

5H\QROGVQXPEHU5

H

Kinematic viscosityThis expresses the relationship between absolute (or dynamic) viscosity and the density of the fluid(see Equation 4.1.2).

Where:Kinematic viscosity is in centistokesDynamic viscosity is in Pa sDensity is in kg/m3

Example 4.1.2In Example 4.1.1, the density of the oil is given to be 920 kg /m3 - Now determine the kinematicviscosity:

[.LQHPDWLFYLVFRVLW\ FHQWLVWRNHVF6W

=

Equation 4.1.2'\QDPLFYLVFRVLW\ [

.LQHPDWLFYLVFRVLW\ 'HQVLW\


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Fig. 4.1.3 Velocity profile ignoring viscosity and friction

Fig. 4.1.4 Velocity profile with viscosity and friction

However, this is very much an ideal case and, in practice, viscosity affects the flowrate of the fluidand works together with the pipe friction to further decrease the flowrate of the fluid near thepipe wall. This is clearly illustrated in Figure 4.1.4:

At low Reynolds numbers (2300 and below) flow is termed laminar, that is, all motion occursalong the axis of the pipe. Under these conditions the friction of the fluid against the pipe wallmeans that the highest fluid velocity will occur at the centre of the pipe (see Figure 4.1.5).

Fig. 4.1.5 Parabolic flow profile

Flow

Flow

Flow

Flow regimesIf the effects of viscosity and pipe friction are ignored, a fluid would travel through a pipe in auniform velocity across the diameter of the pipe. The velocity profile would appear as shown inFigure 4.1.3:


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As the velocity increases, and the Reynolds number exceeds 2300, the flow becomes increasinglyturbulent with more and more eddy currents, until at Reynolds number 10000 the flow iscompletely turbulent (see Figure 4.1.6).

Saturated steam, in common with most fluids, is transported through pipes in the turbulentflow region.

Fig. 4.1.7 Reynolds number

Turbulent flow region(Re: above 10 000)

Transition flow region(Re: between 2300 - 10000)

Laminar flow region(Re: between 100 - 2300)

Flow

Fig. 4.1.6 Turbulent flow profile

Stagnation


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The examples shown in Figures 4.1.3 to 4.1.7 are useful in that they provide an understandingof fluid characteristics within pipes; however, the objective of the Steam and Condensate LoopBook is to provide specific information regarding saturated steam and water (or condensate).

Whilst these are two phases of the same fluid, their characteristics are entirely different. This hasbeen demonstrated in the above Sections regarding Absolute Viscosity (m) and Density (r).The following information, therefore, is specifically relevant to saturated steam systems.

Example 4.1.4A 100 mm pipework system transports saturated steam at 10 bar g at an average velocity of 25 m /s.

Determine the Reynolds number.

The following data is available from comprehensive steam tables:

Tsat at 10 bar g = 184C

Density (r) = 5.64 kg /m3

Dynamic viscosity of steam () at 184C = 15.2 x 10-6 Pa s

Equation 4.1.3

X'

5H\QROGVQXPEHU5 H

Where:r = Density = 5.64 kg /m3

u = Mean velocity in the pipe = 25 m/sD = Internal pipe diameter = 100 mm = 0.1 m

= Dynamic viscosity = 15.2 x 10 -6 Pa s

=[[

5[

H

Re = 927 631 = 0.9 x 106

o If the Reynolds number (Re) in a saturated steam system is less than 10000 (104) the flowmay be laminar or transitional.

Under laminar flow conditions, the pressure drop is directly proportional to flowrate.

o If the Reynolds number (Re) is greater than 10000 (104) the flow regime is turbulent.Under these conditions the pressure drop is proportional to the square root of the flow.

o For accurate steam flowmetering, consistent conditions are essential, and for saturated steamsystems it is usual to specify the minimum Reynolds number (Re) as 1 x 105 = 100000.

o At the opposite end of the scale, when the Reynolds number (R e) exceeds 1 x 106, the head

losses due to friction within the pipework become significant, and this is specified as themaximum.


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[X[

[

[ [[

[

=

=

H

5 [

X P V

Volumetric flowrate may be determined using Equation 4.1.4:

Equation 4.1.4T $X=Y

Equation 4.1.5T

T = YPJY

Equation 4.1.6$X

T =PJY

Example 4.1.5Based on the information given above, determine the maximum and minimum flowrates forturbulent flow with saturated steam at 10 bar g in a 100 mm bore pipeline.

Equation 4.1.3X'

5H\QROGVQXPEHU5

H

Where:r = Density = 5.64 kg/m3

u = Mean velocity in the pipe (To be determined) m/ sD = Internal pipe diameter = 100 mm (0.1 m)

= Dynamic viscosity = 15.2 x 10-6 Pa s

For minimum turbulent flow, Re of 1 x 105 should be considered:

P NJ

J

Y

Where:qv = Volume flow (m3/s)A = Cross sectional area of the pipe (m2)

u = Velocity (m / s)

Mass flowrate may be determined using Equations 4.1.5 and 4.1.6:

Where:qm = Mass flow (kg/ s)qv = Volume flow (m3/s)vg = S pecific volume (m3/kg)

Equation 4.1.6 is derived by combining Equations 4.1.4 and 4.1.5:

Where:qm = Mass flow (kg/ s)A = Cross sectional area of the pipe (m2)u = Velocity (m /s)vg = Specific volume (m3/kg)


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Returning to Example 4.1.5, and inserting values into Equation 4.1.6:

$X 'T ZKHUH$

' XT

[ [NJV

[

[X[5

[

[ [[[

T

=

=

= =

= =

=

P

J

P

J

P

H

T NJK

[

X P V

Y

Y

p

$X

' XT

[ [NJV

[

=

=

= =

P

J

P

J

P

T NJ K

Y

Y

Similarly, for maximum turbulent flow, Re = 1 x 10 6 shall be considered:

and:

Summary

o The mass flow of saturated steam through pipes is a function of density, viscosity and velocity.

o For accurate steam flowmetering, the pipe size selected should result in Reynolds numbers ofbetween 1 x 10 5 and 1 x 10 6 at minimum and maximum conditions respectively.

o Since viscosity, etc., are fixed values for any one condition being considered, the correctReynolds number is achieved by careful selection of the pipe size.

o If the Reynolds number increases by a factor of 10 (1 x 10 5 becomes 1 x 10 6), then so does thevelocity (e.g. 2.695 m/s becomes 26.95 m/s respectively), providing pressure, density andviscosity remain constant.


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Questions

1. 100 mm bore pipe carries 1000 kg/h of steam at 10 bar g.What is the Reynolds number at this flowrate?

a| 23.4 x 104

b| 49 x 105

c| 0.84 x 106

d| 16.8 x 104

2. If a flowrate has a Reynolds number of 32 x 104, what does it indicate?

a| Flow is turbulent and suitable for flowmetering

b| Flow is laminar and any flowmeter reading would be inaccurate

c| The pipe is oversized and a much smaller flowmeter would be necessary

d| The steam must be superheated and unsuitable for flowmetering

3. A 50 mm bore pipe carries 1100 kg/ h of steam at 7 bar g.How would you describe the flow condition of the steam?

a| Laminar

b| It has a dynamic viscosity of 130 Pa s

c| Transitional

d| Turbulent

4. The dynamic viscosity of saturated steam:a| Increases as pressure increases

b| Remains constant at all temperatures

c| Reduces as pressure increases

d| Is directly proportional to velocity

5. The Reynolds number (Re) of steam:

a| Is directly proportional to the steam pressure and temperature

b| Is directly proportional to the pipe diameter and velocity

c| Is directly proportional to the pipe diameter and absolute viscosity, flowrate and density

d| Is directly proportional to density, temperature and dynamic viscosity

6. For accurate flowmetering of steam, flow should be:

a| Either turbulent or transitional

b| Laminar

c| Turbulent

d| Either laminar or turbulent

Answers 1:a,2:a,3:d,4:a,5:c,6:c


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Principles of Flowmetering Module 4.2Block 4 Flowmetering

Module 4.2

Principles of Flowmetering


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Principles of Flowmetering

TerminologyWhen discussing flowmetering, a number of terms, which include Repeatability, Uncertainty,

Accuracy and Turndown, are commonly used.

RepeatabilityThis describes the ability of a flowmeter to indicate the same value for an identical flowrateon more than one occasion. It should not be confused with accuracy i.e. its repeatability maybe excellent in that it shows the same value for an identical flowrate on several occasions,but the reading might be consistently wrong (or inaccurate). Good repeatability is important,where steam flowmetering is required to monitor trends rather than accuracy. However, thisdoes not dilute the importance of accuracy under any circumstances.

UncertaintyThe term uncertainty is now becoming more commonly referred to than accuracy. This isbecause accuracy cannot be established, as the true value can never be exactly known.However uncertainty can be estimated and an ISO standard exists offering guidance on thismatter (EN ISO/ IEC 17025). It is important to recognise that it is a statistical concept andnot a guarantee. For example, it may be shown that with a large population of flowmeters,95% would be at least as good as the uncertainty calculated. Most would be much better,but a few, 5% could be worse.

AccuracyThis is a measure of a flowmeters performance when indicating a correct flowrate value againsta true value obtained by extensive calibration procedures. The subject of accuracy is dealtwith in ISO 5725.

The following two methods used to express accuracy have very different meanings:

o Percentage of measured value or actual readingFor example, a flowmeters accuracy is given as 3% of actual flow.

At an indicated flowrate of 1000 kg / h, the uncertainty of actual flow is between:1000 - 3% = 970 kg/ hAnd1000 + 3% = 1030 kg / hSimilarly, at an indicated flowrate of 500 kg / h, the error is still 3%, and the uncertaintyis between:500 kg/ h - 3% = 485 kg/ hAnd500 kg / h + 3% = 515 kg / h

o

Percentage of full scale deflection (FSD)A flowmeters accuracy may also be given as 3% of FSD. This means that the measurementerror is expressed as a percentage of the maximum flow that the flowmeter can handle.

As in the previous case, the maximum flow = 1000 kg/h.At an indicated flowrate of 1000 kg/h, the uncertainty of actual flow is between:1000 kg/ h - 3% = 970 kg/ hAnd1000 kg / h + 3% = 1030 kg / hAt an indicated flowrate of 500 kg /h, the error is still 30 kg /h, and the actual flow is between:500 kg / h - 30 kg /h = 470 kg / h an error of - 6%

And500 kg / h + 30 kg/ h = 530 kg / h an error of + 6%

As the flowrate is reduced, the percentage error increases.

A comparison of these measurement terms is shown graphically in Figure 4.2.1


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Example 4.2.1A particular steam system has a demand pattern as shown in Figure 4.2.2 The flowmeter hasbeen sized to meet the maximum expected flowrate of 1000 kg/ h.

Equation 4.2.1=H h v s y

U q

H v v s y

Fig. 4.2.2 Accumulated losses due to insufficient turndown

Instantaneous

flowrate

900

800

700

600

500

400

300

200

100

00 1 2 3 4 5 6 7 8

1000

Flowrate(kg/h)

Elapsed time (hours)

Accumulated

error (lost flow)

Turndown limit

on flowmeter

The turndown of the flowmeter selected is given as 4:1. i.e. The claimed accuracy of the flowmetercan be met at a minimum flowrate of 1 000 4 = 250 kg/ h.When the steam flowrate is lower than this, the flowmeter cannot meet its specification, so largeflow errors occur. At best, the recorded flows below 250 kg / h are inaccurate - at worst they arenot recorded at all, and are lost.

In the example shown in Figure 4.2.2, lost flow is shown to amount to more than 700 kgof steam over an 8 hour period. The total amount of steam used during this time is approximately2700 kg, so the lost amount represents an additional 30% of total steam use. Had the steamflowmeter been specified with an appropriate turndown capability, the steam flow to the processcould have been more accurately measured and costed.

30%

20%

10%

-10%

-20%

-30%

0%

0 125 250 500 750 1000

Uncertainty

offlowratereading

Actual flowrate (kg/ h)

Error expressed as 3% of maximum flow

Error expressed as +3% of full

scale deflection

Error expressed as -3% of full

scale deflection

Fig. 4.2.1 Range of error

TurndownWhen specifying a flowmeter, accuracy is a necessary requirement, but it is also essential toselect a flowmeter with sufficient range for the application.

Turndown or turndown ratio, effective range or rangeability are all terms used to describethe range of flowrates over which the flowmeter will work within the accuracy and repeatabilityof the tolerances. Turndown is qualified in Equation 4.2.1.


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Bernoullis Theorem

Many flowmeters are based on the work of Daniel Bernoulli in the 1700s. Bernoullis theoremrelates to the Steady Flow Energy Equation (SFEE), and states that the sum of:

o Pressure energy,

o Kinetic energy and

o Potential energy

will be constant at any point within a piping system (ignoring the overall effects of friction).This is shown below, mathematically in Equation 4.2.2 for a unit mass flow:

Equation 4.2.2

Q Q

u u

t ! t t ! t+ + = + +

If steam flow is to be accurately metered, the user must make every effort to build up a true andcomplete assessment of demand, and then specify a flowmeter with:

o The capacity to meet maximum demand.

o A turndown sufficiently large to encompass all anticipated flow variations.

Fig. 4.2.3 Table showing typical turndown ratios of commonly used flowmeters

Flowmeter type Turndown (operating) range

Orifice plate 4:1 (Accurate measurement down to 25% of maximum flow)

Shunt flowmeter 7:1 (Accurate measurement down to 14% of maximum flow)

Vortex flowmeters 25:1 down to 4:1 (Accurate measurement from 25% to 4%of maximum flow depending on application)

Spring loaded variable area meter, Up to 50:1 (Accurate measurement down to 2% of maximum flow)position monitoring

Spring loaded variable area meter, Up to 100:1 (Accurate measurement down to 1% of maximum flow)differential pressure monitoring

Where:P1 and P2 = Pressure at points within a system (Pa)u1 and u2 = Velocities at corresponding points within a system (m/s)h1 and h2 = Relative vertical heights within a system (m)

r = Density (kg/m3)g = Gravitational constant (9.81 m/s)

Bernoullis equation ignores the effects of friction and can be simplified as follows:

Pressure energy + Potential energy + Kinetic energy = Constant

Equation 4.2.3 can be developed from Equation 4.2.2 by multiplying throughout by rg.

Equation 4.2.3

Q t u 2 Q t u

! !

Friction is ignored in Equations 4.2.2 and 4.2.3, due to the fact that it can be considerednegligible across the region concerned. Friction becomes more significant over longer pipelengths. Equation 4.2.3 can be further developed by removing the 2nd term on either sidewhen there is no change in reference height (h). This is shown in Equation 4.2.4:

Equation 4.2.4

Q 2 Q

! !


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Example 4.2.2Determine P2 for the system shown in Figure 4.2.4, where water flows through a diverging sectionof pipe at a volumetric rate of 0.1 m3/ s at 10C.

The water has a density of 998.84 kg /m3 at 10C and 2 bar g.

From Equation 4.1.4:

Equation 4.1.4 2 6

Y

Where:qv = Volumetric flowrate (m/ s)A = Cross-sectional area (m2)u = Velocity (m / s)

By transposing the Equation 4.1.4, a figure for velocity can be calculated:

W r y p v

6

#

W r y p v v u r ' r p v s v r x ( (

'

#

W r y p v v u r $ r p v s v r x $ % %

$

! i h t h t r r r Q 2 " "

=

= =

= =

Y

! $ i h h i y r r r Q

" " ! $ i h h " " ! $ x Q h 2 " " ! $ Q h =

2 bar g

Horizontal pipe

r= 998.84 kg/ m3

Ignore frictional losses

0.1 m3/s of water at 10C

? bar g

80 mm diameter

150 mm diameter

Fig. 4.2.4 System described in Example 4.2.2

P1

P2

Equation 4.2.4

Q 2 Q

! !

+

Q 2 Q

!

( ( $ % %

Q 2 " " ! $ ( ( ' ' #

!

Q 2 # ' " Q h

Q 2 # ' " i h h

Q 2 " ' ' i h t

Equation 4.2.4 is a development of Equation 4.2.3 as described previously, and can be usedto predict the downstream pressure in this example.



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Example 4.2.2 highlights the implications of Bernoullis theorem. It is shown that, in a divergingpipe, the downstream pressure will be higher than the upstream pressure. This may seem odd atfirst glance; it would normally be expected that the downstream pressure in a pipe is less than theupstream pressure for flow to occur in that direction. It is worth remembering that Bernoullistates, the sum of the energy at any point along a length of pipe is constant.

In Example 4.2.2, the increased pipe bore has caused the velocity to fall and hence the pressure

to rise. In reality, friction cannot be ignored, as it is impossible for any fluid to flow along a pipeunless a pressure drop exists to overcome the friction created by the movement of the fluid itself.In longer pipes, the effect of friction is usually important, as it may be relatively large.A term, hf, can be added to Equation 4.2.4 to account for the pressure drop due to friction, andis shown in Equation 4.2.5.

Equation 4.2.5

Q 2 Q u

! !

I

Equation 4.2.6Q Q 2 u

I

With an incompressible fluid such as water flowing through the same size pipe, the densityand velocity of the fluid can be regarded as constant and Equation 4.2.6 can be developedfrom Equation 4.2.5 (P1 = P2 + hf).

Equation 4.2.6 shows (for a constant fluid density) that the pressure drop along a length ofthe same size pipe is caused by the static head loss (hf) due to friction from the relative movementbetween the fluid and the pipe. In a short length of pipe, or equally, a flowmetering device, thefrictional forces are extremely small and in practice can be ignored. For compressible fluids likesteam, the density will change along a relatively long piece of pipe. For a relatively short equivalentlength of pipe (or a flowmeter using a relatively small pressure differential), changes in densityand frictional forces will be negligible and can be ignored for practical purposes. This means that

the pressure drop through a flowmeter can be attributed to the effects of the known resistanceof the flowmeter rather than to friction.

Some flowmeters take advantage of the Bernoulli effect to be able to measure fluid flow, anexample being the simple orifice plate flowmeter. Such flowmeters offer a resistance to theflowing fluid such that a pressure drop occurs over the flowmeter. If a relationship exists betweenthe flow and this contrived pressure drop, and if the pressure drop can be measured, then itbecomes possible to measure the flow.

Quantfying the relationship between flow and pressure dropConsider the simple analogy of a tank filled to some level with water, and a hole at the side ofthe tank somewhere near the bottom which, initially, is plugged to stop the water from flowingout (see Figure 4.2.5). It is possible to consider a single molecule of water at the top of the tank(molecule 1) and a single molecule below at the same level as the hole (molecule 2).

With the hole plugged, the height of water (or head) above the hole creates a potential to forcethe molecules directly below molecule 1 through the hole. The potential energy of molecule 1relative to molecule 2 would depend upon the height of molecule 1 above molecule 2, themass of molecule 1, and the effect that gravitational force has on molecule 1s mass. Thepotential energy of all the water molecules directly between molecule 1 and molecule 2 isshown by Equation 4.2.7.

Equation 4.2.7Q r v h y r r t 2 t u

Where:m = Mass of all the molecules directly between and including molecule 1 and molecule 2.g = Gravitational constant (9.81 m/s2)h = Cumulative height of molecules above the hole


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Fig. 4.2.5 A tank of water with a plugged hole near the bottom of the tank

Initial

water

level

Water molecule 1

Height of

molecule 1 above

hole (h)

Potentialenergy = 100 units

Pressureenergy = 0 units

Plug

Water molecule 2

Potentialenergy = 0 units

Pressureenergy = 100 units

Molecule 1 has no pressure energy (the nett effect of the air pressure is zero, because the plug atthe bottom of the tank is also subjected to the same pressure), or kinetic energy (as the fluid inwhich it is placed is not moving). The only energy it possesses relative to the hole in the tank ispotential energy.

Meanwhile, at the position opposite the hole, molecule 2 has a potential energy of zero as it hasno height relative to the hole. However, the pressure at any point in a fluid must balance theweight of all the fluid above, plus any additional vertical force acting above the point ofconsideration. In this instance, the additional force is due to the atmospheric air pressure abovethe water surface, which can be thought of as zero gauge pressure. The pressure to which molecule2 is subjected is therefore related purely to the weight of molecules above it.

Weight is actually a force applied to a mass due to the effect of gravity, and is defined as mass xacceleration. The weight being supported by molecule 2 is the mass of water (m) in a line ofmolecules directly above it multiplied by the constant of gravitational acceleration, (g). Therefore,molecule 2 is subjected to a pressure force m g.

But what is the energy contained in molecule 2? As discussed above, it has no potential energy;neither does it have kinetic energy, as, like molecule 1, it is not moving. It can only thereforepossess pressure energy.

Mechanical energy is clearly defined as Force x Distance,so the pressure energy held in molecule 2 = Force (m g) x Distance (h) = m g h, where:m = Mass of all the molecules directly between and including molecule 1 and molecule 2g = Gravitational acceleration 9.81 m/ s2

h = Cumulative height of molecules above the holeIt can therefore be seen that:

Potential energy in molecule 1 = m g h = Pressure energy in molecule 2.

This agrees with the principle of conservation of energy (which is related to the First Law ofThermodynamics) which states that energy cannot be created or destroyed, but it can changefrom one form to another. This essentially means that the loss in potential energy means anequal gain in pressure energy.


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Fig. 4.2.6 The plug is removed from the tank

Water molecule 1

Plug removed

Molecule 3 has no pressure energy for the reasons described above, or potential energy (as thefluid in which it is placed is at the same height as the hole). The only energy it has can only bekinetic energy.

At some point in the water jet immediately after passing through the hole, molecule 3 is to befound in the jet and will have a certain velocity and therefore a certain kinetic energy. As energycannot be created, it follows that the kinetic energy in molecule 3 is formed from that pressureenergy held in molecule 2 immediately before the plug was removed from the hole.

It can therefore be concluded that the whole of the kinetic energy held in molecule 3 equals the

pressure energy to which molecule 2 is subjected, which, in turn, equals the potential energyheld in molecule 1.

The basic equation for kinetic energy is shown in Equation 4.2.8:

Consider now, that the plug is removed from the hole, as shown in Figure 4.2.6. It seems intuitivethat water will pour out of the hole due to the head of water in the tank.

In fact, the rate at which water will flow through the hole is related to the difference in pressureenergy between the molecules of water opposite the hole, inside and immediately outside thetank. As the pressure outside the tank is atmospheric, the pressure energy at any point outsidethe hole can be taken as zero (in the same way as the pressure applied to molecule 1 was zero).

Therefore the difference in pressure energy across the hole can be taken as the pressure energycontained in molecule 2, and therefore, the rate at which water will flow through the hole isrelated to the pressure energy of molecule 2.

In Figure 4.2.6, consider molecule 2 with pressure energy of m g h, and consider molecule 3having just passed through the hole in the tank, and contained in the issuing jet of water.

Water molecule 2

with pressure energy m g h

Molecule 3 with kinetic

energy mu2

Equation 4.2.8

F v r v p r r t 2

!

Where:m = Mass of the object (kg)u = Velocity of the object at any point (m/s)


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If all the initial potential energy has changed into kinetic energy, it must be true that thepotential energy at the start of the process equals the kinetic energy at the end of the process.To this end, it can be deduced that:

Equation 4.2.9

t u 2

!


! t u

2

2 ! t u

Equation 4.2.10 2 ! t u

Therefore:

Equation 4.2.10 shows that the velocity of water passing through the hole is proportional to thesquare root of the height of water or pressure head (h) above the reference point, (the hole).The head h can be thought of as a difference in pressure, also referred to as pressure drop or

differential pressure.Equally, the same concept would apply to a fluid passing through an orifice that has beenplaced in a pipe. One simple method of metering fluid flow is by introducing an orifice plateflowmeter into a pipe, thereby creating a pressure drop relative to the flowing fluid. Measuringthe differential pressure and applying the necessary square-root factor can determine the velocityof the fluid passing through the orifice.

The graph (Figure 4.2.7) shows how the flowrate changes relative to the pressure drop acrossan orifice plate flowmeter. It can be seen that, with a pressure drop of 25 kPa, the flowrate isthe square root of 25, which is 5 units. Equally, the flowrate with a pressure drop of 16 kPa is4 units, at 9 kPa is 3 units and so on.

Fig. 4.2.7 The square-root relationship of an orifice plate flowmeter

0 1 2 3 4 5

25

20

15

10

5

0

Differentialpressure(kPa)

Flowrate (mass flow units)

Knowing the velocity through the orifice is of little use in itself. The prime objective of anyflowmeter is to measure flowrate in terms of volume or mass. However, if the size of the holeis known, the volumetric flowrate can be determined by multiplying the velocity by the area ofthe hole. However, this is not as straightforward as it first seems.

It is a phenomenon of any orifice fitted in a pipe that the fluid, after passing through the orifice,will continue to constrict, due mainly to the momentum of the fluid itself. This effectively meansthat the fluid passes through a narrower aperture than the orifice. This aperture is called the venacontracta and represents that part in the system of maximum constriction, minimum pressure,and maximum velocity for the fluid. The area of the vena contracta depends upon the physicalshape of the hole, but can be predicted for standard sharp edged orifice plates used for suchpurposes. The ratio of the area of the vena contracta to the area of the orifice is usually in theregion of 0.65 to 0.7; consequently if the orifice area is known, the area of the vena contractacan be established. As a matter of interest, the vena contracta occurs at a point half a pipediameter downstream of the orifice. The subject is discussed in the next Section.


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The orifice plate flowmeter and Bernoullis Theorem

When Bernoullis theorem is applied to an orifice plate flowmeter, the difference in pressureacross the orifice plate provides the kinetic energy of the fluid discharged through the orifice.

Fig. 4.2.8 An orifice plate with vena contracta

However, it has already been stated, volume flow is more useful than velocity (Equation 4.1.4):

Substituting for u from Equation 4.2.10 into Equation 4.1.4:

6 ! t u

=Y

In practice, the actual velocity through the orifice will be less than the theoretical value for velocity,due to friction losses. This difference between these theoretical and actual figures is referred to asthe coefficient of velocity (C v).

6 p h y r y p v

8 r s s v p v r s r y p v 8

U u r r v p h y r y p v

=Y

Orifice diameter (do)

Orifice plate

Flow

Pressure drop

across the orifice (h)

Vena

contracta

diameter

do/2

Pipe diameter (D)

As seen previously, the velocity through the orifice can be calculated by use of Equation 4.2.10:

Equation 4.2.10 2 ! t u

Equation 4.1.4 2 6 Y


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Also, the flow area of the vena contracta will be less than the size of the orifice. The ratio of thearea of the vena contracta to that of the orifice is called the coefficient of contraction.

The coefficient of velocity and the coefficient of contraction may be combined to give a coefficient

of discharge (C) for the installation. Volumetric flow will need to take the coefficient of discharge(C) into consideration as shown in Equation 4.2.11.

Equation 4.2.11 8 6 ! t u

=Y

Where:qv = Volumetric flowrate (m3/s)C = Coefficient of discharge (dimensionless)A = Area of orifice (m2)g = Gravitational constant (9.8 m/s2)

h = Differential pressure (m)This may be further simplified by removing the constants as shown in Equation 4.2.12.

Equation 4.2.12

Y

Equation 4.2.12 clearly shows that volume flowrate is proportional to the square root of thepressure drop.

Note:The definition of C can be found in ISO 5167-2003, Measurement of fluid flow by means ofpressure differential devices inserted in circular cross-section conduits running full.

ISO 5167 offers the following information:

The equations for the numerical values of C given in ISO 5167 (all parts) are based on datadetermined experimentally.

The uncertainty in the value of C can be reduced by flow calibration in a suitable laboratory.

6 r h s u r r h p h p h

8 r s s v p v r s p h p v 8

6 r h s u r v s v p r

=F


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Fig. 4.2.9 The simple Pitot tube principle

The Pitot tube and Bernoullis Theorem

The Pitot tube is named after its French inventor Henri Pitot (1695 1771). The device measuresa fluid velocity by converting the kinetic energy of the flowing fluid into potential energy at whatis described as a stagnation point. The stagnation point is located at the opening of the tube asin Figure 4.2.9. The fluid is stationary as it hits the end of the tube, and its velocity at this point iszero. The potential energy created is transmitted though the tube to a measuring device.

The tube entrance and the inside of the pipe in which the tube is situated are subject to the samedynamic pressure; hence the static pressure measured by the Pitot tube is in addition to thedynamic pressure in the pipe. The difference between these two pressures is proportional to thefluid velocity, and can be measured simply by a differential manometer.

Where:P1 = The dynamic pressure in the pipeu1 = The fluid velocity in the pipeP2 = The static pressure in the Pitot tubeu2 = The stagnation velocity = zeror = The fluid density

Because u2 is zero, Equation 4.2.4 can be rewritten as Equation 4.2.13:

X

X

Q Q

!

Q Q

!

! Q

+ =

=

=

Equation 4.2.13

! Q

=

Equation 4.2.4

Q 2 Q

! !

The fluid volumetric flowrate can be calculated from the product of the pipe area and the velocitycalculated from Equation 4.2.13.

Bernoullis equation can be applied to the Pitot tube in order to determine the fluid velocity fromthe observed differential pressure (DP) and the known density of the fluid. The Pitot tube can beused to measure incompressible and compressible fluids, but to convert the differential pressureinto velocity, different equations apply to liquids and gases. The details of these are outside thescope of this module, but the concept of the conservation of energy and Bernoullis theorem appliesto all; and for the sake of example, the following text refers to the relationship between pressureand velocity for an incompressible fluid flowing at less than sonic velocity. (Generally, a flow can be

considered incompressible when its flow is less than 0.3 Mach or 30% of its sonic velocity).From Equation 4.2.4, an equation can be developed to calculate velocity (Equation 4.2.13):

Fluid

flowStagnation point

DP


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The effect of the accuracy of the differential cell upon

uncertainty

Example 4.2.3In a particular orifice plate flowmetering system, the maximum flow of 1000 kg / h equates to adifferential pressure of 25 kPa, as shown in Figure 4.2.10.

The differential pressure cell has a guaranteed accuracy of 0.1 kPa over the operating range ofa particular installation.

Demonstrate the effect of the differential cell accuracy on the accuracy of the installation.

Fig. 4.2.10 Square root characteristic

Determine the flowmeter constant:At maximum flow (1000 kg / h), the differential pressure = 25 kPa

x t u ! $ x Q h

x t u 8 h ! $ x Q h

x t u

8 h !

! $ x Q h

=

= =

or

If the differential pressure cell is over-reading by 0.1 kPa, the actual flowrate (qm):

8 h ! $ x Q h

! ! # ( x Q h ( ( ' x t u

=

= =

P

P

The percentage error at an actual flowrate of 1 000 kg/ h: ( ( ' x t u

r !

x t u

= =

Similarly, with an actual mass flowrate of 500 kg / h, the expected differential pressure:

$ x t u ! Q x Q h

Q % ! $ x Q h

=

=

If the differential pressure cell is over-reading by 0.1 kPa, the actual flowrate (qm):

! % ! $ x Q h

# ( % x t u

=

=

P

P

The percentage error at an actual flowrate of 500 kg / h:

$ # ( % x t u

r '

$ x t u

= =

0 100 200 300 400 500 600 700 800 900 1000

25

20

15

10

5

0Differentialpressure(kPa)

Flowrate (kg/ h)



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Review of results:At maximum flowrate, the 0.1 kPa uncertainty in the differential pressure cell reading representsonly a small proportion of the total differential pressure, and the effect is minimal.

As the flowrate is reduced, the differential pressure is also reduced, and the 0.1 kPa uncertaintyrepresents a progressively larger percentage of the differential pressure reading, resulting in theslope increasing slowly, as depicted in Figure 4.2.12.

At very low flowrates, the value of the uncertainty accelerates. At between 20 and 25% of maximumflow, the rate of change of the slope accelerates rapidly, and by 10% of maximum flow, the rangeof uncertainty is between +18.3% and -22.5%.

Figure 4.2.11 shows the effects over a range of flowrates:

Actual flowrate kg/h 100 200 300 400 500 600 700 800 900 1000

Calculated flow using DP cell

(Under-reading) kg/h77 190 293 395 496 597 697 797 898 998

Uncertainty

(Negative)% 22.5 5.13 2.25 1.26 0.80 0.56 0.41 0.31 0.25 0.20

Calculated flow using DP cell(Over-reading) kg/h

118 210 307 405 504 603 703 302 902 1002

Uncertainty

(Positive)% 18.3 4.88 2.20 1.24 0.80 0.55 0.41 0.31 0.25 0.20

Fig. 4.2.11 Table showing percentage error in flow reading resulting from

an accuracy limitation of 0.1 kPa on a differential pressure cell

Fig. 4.2.12 Graph showing percentage uncertainty in flow reading resulting

from an accuracy limitation of 0.1 kPa on a differential pressure cell

100 300 500 700 900 1000

30%

20%

10%

0%

-10%

-20%

-30%

Error(%)

Actual flowrate (kg/h)

Conclusion

To have confidence in the readings of an orifice plate flowmeter system, the turndown ratio mustnot exceed 4 or 5:1.

Note:o Example 4.2.3 examines only one element of a steam flowmetering installation.

o The overall confidence in the measured value given by a steam flowmetering system willinclude the installation, the accuracy of the orifice size, and the accuracy of the predicatedcoefficient of discharge (C) of the orifice.


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Questions

1. An orifice plate flowmeter has been selected for a maximum flowrate of 2 500 kg /h.The flowmeter has a published accuracy of 2% of actual flow. For a flowof 700 kg /h, over what range of flow will accuracy be maintained?

a| 650 - 750 kg /h

b| 686 - 714 kg/ h

c| 675 - 725 kg /h

d| 693 - 707 kg/ h

2. An orifice plate flowmeter has been selected for a maximum flowrate of 2500 kg /h.The flowmeter has a published accuracy of 2% of FSD. For a flow of 700 kg /h,over what range of flow will accuracy be maintained?

a| 675 - 725 kg /h

b| 693 - 707 kg /h

c| 650 - 750 kg /h

d| 686 - 714 kg/ h

3. An orifice plate flowmeter is selected for a maximum flow of 3000 kg / h.The minimum expected flow is 300 kg/h. The accuracy of the flowmeter is 2%of actual flow. Over what range of flow at the minimum flow condition willaccuracy be maintained?

a| Range unknown because the turndown is greater than 8:1

b| Range unknown because the turndown is greater than 4:1

c| 294 - 306 kg /h

d| 240 - 360 kg/ h

4. Why is an orifice plate flowmeter limited to a turndown of 4:1?

a| At higher turndowns, the vena contracta has a choking effect on flow through an orifice

b| At higher turndowns the differential pressure across an orifice is too smallto be measured accurately

c| At low flowrates, the accuracy of the differential pressure cell has a larger effect

on the flowmeter accuracy

d| The orifice is too large for flow at higher flowrates

5. An orifice plate flowmeter is sized for a maximum flow of 2000 kg /h.What is the effect on accuracy at a higher flow?

a| The accuracy is reduced because the turndown will be greater than 4:1

b| The flowmeter will be out of range so the indicated flow will be meaningless

c| None

d| The characteristics of an orifice plate flowmeter mean that the higher the flow,the greater the accuracy, consequently accuracy will be improved


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6. What would be the effect on accuracy of a DN100 orifice plate flowmeter if thedownstream differential pressure tapping was 25 mm after the flowmeter,instead of the expected d/2 length.

a| Accuracy would be improved because the flow is now laminar

b| Accuracy would be reduced due to a higher uncertainty effect causedby a lower differential pressure

c| Accuracy would be much reduced because flow is now turbulent

d| None

Answers 1:b,2:c,3:b,4:c,5:b,6:b


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Block 4 Flowmetering Types of Steam Flowmeter Module 4.3

Module 4.3

Types of Steam Flowmeter


30/76


Types of Steam Flowmeter Module 4.3Block 4 Flowmetering

Types Of Steam Flowmeter

There are many types of flowmeter available, those suitable for steam applications include:

o Orifice plate flowmeters.

o Turbine flowmeters (including shunt or bypass types).

o Variable area flowmeters.o Spring loaded variable area flowmeters.

o Direct in-line variable area (DIVA) flowmeter.

o Pitot tubes.

o Vortex shedding flowmeters.

Each of these flowmeter types has its own advantages and limitations. To ensure accurate andconsistent performance from a steam flowmeter, it is essential to match the flowmeter to theapplication.

This Module will review the above flowmeter types, and discuss their characteristics, their

advantages and disadvantages, typical applications and typical installations.

Fig. 4.3.1 Orifice plate

Fig. 4.3.2 Orifice plate flowmeter

Tabhandle

Measuringorifice

Orificeplate

Drainorifice

Orifice plate

Vena contractadiameter

Downstream presuretrappingUpstream pressuretrapping

Orifice diameter

DP (Differential pressure) cell

Orifice plate flowmeters

The orifice plate is one in a group known as head lossdevices or differential pressure flowmeters. In simpleterms the pipeline fluid is passed through a restriction,and the pressure differential is measured across thatrestriction. Based on the work of Daniel Bernoulli in 1738(see Module 4.2), the relationship between the velocityof fluid passing through the orifice is proportional tothe square root of the pressure loss across it. Otherflowmeters in the differential pressure group includeventuris and nozzles.

With an orifice plate flowmeter, the restriction is in theform of a plate which has a hole concentric with thepipeline. This is referred to as the primary element.

To measure the differential pressure when the fluid isflowing, connections are made from the upstream anddownstream pressure tappings, to a secondary deviceknown as a DP (Differential Pressure) cell.


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From the DP cell, the information may be fed to a simple flow indicator, or to a flow computeralong with temperature and/or pressure data, which enables the system to compensate for changesin fluid density.

In horizontal lines carrying vapours, water (or condensate) can build up against the upstream faceof the orifice. To prevent this, a drain hole may be drilled in the plate at the bottom of the pipe.Clearly, the effect of this must be taken into account when the orifice plate dimensions are

determined.Correct sizing and installation of orifice plates is absolutely essential, and is well documented inthe International Standard ISO 5167.

Fig. 4.3.3 Orifice plate flowmeter installation

Orifice plate

Pressure sensor(for compensation)

Temperature sensor(for compensation)

Differentialpressurecell

Flow computer

Local readout

Impulse lines

InstallationA few of the most important points from ISO 5167 are discussed below:

Pressure tappings - Small bore pipes (referred to as impulse lines) connect the upstream anddownstream pressure tappings of the orifice plate to a Differential Pressure or DP cell.

The positioning of the pressure tappings can be varied. The most common locations are:

o From the flanges (or carrier) containing the orifice plate as shown in Figure 4.3.3. This isconvenient, but care needs to be taken with tappings at the bottom of the pipe,because theymay become clogged.

o One pipe diameter on the upstream side and 0.5 x pipe diameter on the downstream side.This is less convenient, but potentially more accurate as the differential pressure measuredis at its greatest at the vena contracta, which occurs at this position.


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Corner tappings - These are generally used on smaller orifice plates where space restrictionsmean flanged tappings are difficult to manufacture. Usually on pipe diameters including orbelow DN50.

From the DP cell, the information may be fed to a flow indicator, or to a flow computer alongwith temperature and/or pressure data, to provide density compensation.

Pipework - There is a requirement for a minimum of five straight pipe diameters downstreamof the orifice plate, to reduce the effects of disturbance caused by the pipework.

The amount of straight pipework required upstream of the orifice plate is, however, affected by anumber of factors including:

o The ratio; this is the relationship between the orifice diameter and the pipe diameter(see Equation 4.3.1), and would typically be a value of 0.7.

Equation 4.3.1GRULILFHGLDPHWHU

'SLSHGLDPHWHU=

o The nature and geometry of the preceeding obstruction. A few obstruction examples are

shown in Figure 4.3.4:

Fig. 4.3.4 Orifice plate installations

(b)

(a)

(c)

5 pipe

diameters

5 pipe

diameters

5 pipe

diameters(a)

(b) (c)

Table 4.3.1 brings the ratio and the pipework geometry together to recommend the number ofstraight diameters of pipework required for the configurations shown in Figure 4.3.4.

In particularly arduous situations, flow straighteners may be used. These are discussed in more

detail in Module 4.5.

Table 4.3.1 Recommended straight pipe diameters upstream of an orifice plate for various ratios and preceding

obstruction

See Recommended straight pipe diameters upstream of an

Figure orifice plate for various ratios and preceding obstruction

4.3.4


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Advantages of orifice plate steam flowmeters:

o Simple and rugged.

o Good accuracy.

o Low cost.

o No calibration or recalibration is required provided calculations, tolerances and installationcomply with ISO 5167.

Disadvantages of orifice plate steam flowmeters:

o Turndown is limited to between 4:1 and 5:1 because of the square root relationship betweenflow and pressure drop.

o The orifice plate can buckle due to waterhammer and can block in a system that is poorlydesigned or installed.

o The square edge of the orifice can erode over time, particularly if the steam is wet ordirty. This will alter the characteristics of the orifice, and accuracy will be affected. Regularinspection and replacement is therefore necessary to ensure reliability and accuracy.

o The installed length of an orifice plate flowmetering system may be substantial; a minimumof 10 upstream and 5 downstream straight unobstructed pipe diameters may be needed foraccuracy.

This can be difficult to achieve in compact plants. Consider a system which uses 100 mmpipework, the ratio is 0.7, and the layout is similar to that shown in Figure 4.3.4(b):

The upstream pipework length required would be = 36 x 0.1 m = 3.6 m

The downstream pipework length required would be = 5 x 0.1 m = 0.5 m

The total straight pipework required would be = 3.6 + 0.5 m = 4.1 m

Typical applications for orifice plate steam flowmeters:o Anywhere the flowrate remains within the limited turndown ratio of between 4:1 and 5:1.

This can include the boiler house and applications where steam is supplied to many plants,some on-line, some off-line, but the overall flowrate is within the range.


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Since a turbine flowmeter consists of a number of moving parts, there are several influencingfactors that need to be considered:

o The temperature, pressure and viscosity of the fluid being measured.

o The lubricating qualities of the fluid.

o The bearing wear and friction.

o The conditional and dimensional changes of the blades.

o The inlet velocity profile and the effects of swirl.

o The pressure drop through the flowmeter.

Because of these factors, calibration of turbine flowmeters must be carried out under operationalconditions.

In larger pipelines, to minimise cost, the turbine element can be installed in a pipework bypass,or even for the flowmeter body to incorporate a bypass or shunt, as shown in Figure 4.3.6.

Bypass flowmeters comprise an orifice plate, which is sized to provide sufficient restriction fora sample of the main flow to pass through a parallel circuit. Whilst the speed of rotation ofthe turbine may still be determined as explained previously, there are many older units stillin existence which have a mechanical output as shown in Figure 4.3.6.

Clearly, friction between the turbine shaft and the gland sealing can be significant with thismechanical arrangement.

Turbine flowmeters

The primary element consists of a multi-bladed rotor which is mounted at right angles to the flowand suspended in the fluid stream on a free-running bearing. The diameter of the rotor is slightlyless than the inside diameter of the flowmetering chamber, and its speed of rotation is proportionalto the volumetric flowrate.

The speed of rotation of the turbine may be determined using an electronic proximity switchmounted on the outside of the pipework, which counts the pulses, as shown in Figure 4.3.5.

Fig. 4.3.5 Turbine flowmeter

Output to pulse counter

Pulse pick-up

Bearings

Flow

RotorSupporting web


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Advantages of turbine flowmeters:

o A turndown of 10:1 is achievable in a good installation with the turbine bearings in goodcondition.

o Accuracy is reasonable ( 0.5% of actual value).

o Bypass flowmeters are relatively low cost.

Disadvantages of turbine flowmeters:

o Generally calibrated for a specific line pressure. Any steam pressure variations will leadto inaccuracies in readout unless a density compensation package is included.

o Flow straighteners are essential (see Module 4.5).

o If the flow oscillates, the turbine will tend to over or under run, leading to inaccuracies dueto lag time.

o Wet steam can damage the turbine wheel and affect accuracy.

o Low flowrates can be lost because there is insufficient energy to turn the turbine wheel.

o Viscosity sensitive: if the viscosity of the fluid increases, the response at low flowrates deterioratesgiving a non-linear relationship between flow and rotational speed. Software may be available

to reduce this effect.

o The fluid must be very clean (particle size not more than 100 mm) because:

Clearances between the turbine wheel and the inside of the pipe are very small.

Entrained debris can damage the turbine wheel and alter its performance.

Entrained debris will accelerate bearing wear and affect accuracy, particularly at low flowrates.

Typical applications for turbine flowmeters:

o Superheated steam.

o Liquid flowmetering, particularly fluids with lubricating properties. As with all liquids, care

must be taken to remove air and gases prior to them being metered.

Fig. 4.3.6 Bypass or shunt turbine flowmeter

Air bleed

TurbineBypass

Orificeplate(restriction)

Output

Flow


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Fig. 4.3.7 Variable area flowmeter

Variable area flowmeters

The variable area flowmeter (Figure 4.3.7), often referred to as a rotameter, consists of a vertical,tapered bore tube with the small bore at the lower end, and a float that is allowed to freely movein the fluid. When fluid is passing through the tube, the floats position is in equilibrium with:

o The dynamic upward force of the fluid.

o The downward force resulting from the mass of the float.o The position of the float, therefore, is an indication of the flowrate.

In practice, this type of flowmeter will be a mix of:

o A float selected to provide a certain weight, and chemical resistance to the fluid.

The most common float material is grade 316 stainless steel, however, other materials such asHastalloy C, aluminium or PVC are used for specific applications.

On small flowmeters, the float is simply a ball, but on larger flowmeters special shaped floatsare used to improve stability.

o

A tapered tube, which will provide a measuring scale of typically between 40 mm and250 mm over the design flow range.

Usually the tube will be made from glass or plastic. However, if failure of the tube could presenta hazard, then either a protective shroud may be fitted around the glass, or a metal tube maybe used.

With a transparent tube, flow readings are taken by observation of the float against a scale. Forhigher temperature applications where the tube material is opaque, a magnetic device is usedto indicate the position of the float.

Because the annular area around the float increases with flow, the differential pressure remainsalmost constant.

High flows

Tapered tube

Low flows

Magneticallycoupled indicator

Float

Flow


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Advantages of variable area flowmeters:

o Linear output.

o Turndown is approximately 10:1.

o Simple and robust.

o Pressure drop is minimal and fairly constant.

Disadvantages of variable area flowmeters:

o The tube must be mounted vertically (see Figure 4.3.8).

o Because readings are usually taken visually, and the float tends to move about, accuracyis only moderate. This is made worst by parallax error at higher flowrates, because the floatis some distance away from the scale.

o Transparent taper tubes limit pressure and temperature.

Typical applications for variable area flowmeters:

o Metering of gases.

o Small bore airflow metering - In these applications, the tube is manufactured from glass, withcalibrations marked on the outside. Readings are taken visually.

o Laboratory applications.

o Rotameters are sometimes used as a flow indicating device rather than a flow measuring device.

Fig. 4.3.8 Variable area flowmeter installed in a vertical plane

Flow

Larger diameter

Graduated scale

Float

Smaller diameter


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However, another important feature is also revealed: if the pass area (the area between the floatand the tube) increases at an appropriate rate, then the differential pressure across the springloaded variable area flowmeter can be directly proportional to flow.

To recap a few earlier statements

With orifice plates flowmeters:

o As the rate of flow increases, so does the differential pressure.

o By measuring this pressure difference it is possible to calculate the flowrate through the flowmeter.

o The pass area (for example, the size of the hole in the orifice plate) remains constant.

With any type of variable area flowmeter:

o The differential pressure remains almost constant as the flowrate varies.

o Flowrate is determine from the position of the float.

o The pass area (the area between the float and the tube) through which the flow passes increases

with increasing flow.

Figure 4.3.10 compares these two principles.

Spring loaded variable area flowmeters

The spring loaded variable area flowmeter (an extension of the variable area flowmeter) uses aspring as the balancing force. This makes the meter independent of gravity, allowing it to beused in any plane, even upside-down. However, in its fundamental configuration (as shown inFigure 4.3.9), there is also a limitation: the range of movement is constrained by the linearrange of the spring, and the limits of the spring deformation.

Fig. 4.3.9 Spring loaded variable area flowmeters

Flow

Flow

Float

Float

SpringTapered tube

Manometer

Anchor

Anchor


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Advantages of spring loaded variable area flowmeters:

o Robust.

o Turndowns of 25:1 are achievable with normal steam velocities (25 m/s), although highvelocities can be tolerated on an intermittent basis, offering turndowns of up to 40:1.

o Accuracy is 2% of actual value.

o Can be tailored for saturated steam systems with temperature and pressure sensors to providepressure compensation.

o Relatively low cost.

o Short installation length.

Disadvantages of spring loaded variable area flowmeters:

o Size limited to DN100.

o Can be damaged over a long period by poor quality (wet and dirty) steam, at prolonged highvelocity (>30 m/s).

Typical applications for spring loaded variable area flowmeters:

o Flowetering of steam to individual plants.

o Small boiler houses.

Fig. 4.3.11 Spring loaded variable area flowmeter monitoring the position of the float

Flow

Pressuretransmitter Temperaturetransmitter Flappositiontransmitter

Spring loaded flap (float)

Position varies with flowrate

Flow

computer

Signal conditioning unit

Stopvalve

Separator

Strainer Flowmeter

Flow

Steam trap set

3D6D

Fig. 4.3.12 Typical installation of a spring loaded variable area flowmeter measuring steam flow


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In Option 2 (Figure 4.3.10), namely, determining the differential pressure, this concept can bedeveloped further by shaping of the float to give a linear relationship between differential pressureand flowrate. See Figure 4.3.13 for an example of a spring loaded variable area flowmetermeasuring differential pressure. The float is referred to as a cone due to its shape.

Fig. 4.3.13 Spring Loaded Variable Area flowmeter (SLVA) monitoring differential pressure

Advantages of a spring loaded variable area (SLVA) flowmeter:

o High turndown, up to 100:1.

o Good accuracy 1% of reading for pipeline unit.

o Compact a DN100 wafer unit requires only 60 mm between flanges.

o Suitable for many fluids.

Disadvantages of a variable area spring load flowmeter:

o Can be expensive due to the required accessories, such as the DP cell and flow computer.

Typical applications for a variable area spring load flowmeter:

o

Boiler house flowmetering.o Flowmetering of large plants.

Fig. 4.3.14 Typical installation of a SVLA flowmeter monitoring differential pressure

Flow

Spring loaded cone (float)

Differentialpressure cell

Temperature transmitterSLVA

flowmeter

Flow

Pressure transmitter

Computer unit

DP cell


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The DIVA system will also:

o Provide process control for certain applications.

o Monitor plant trends and identify any deterioration

and steam losses.

Traditional flowmetering system DIVA flowmetering system

4-20 mA output

Differentialpressure

transmitter

Temperaturesensor

Isolation valves

Flowcomputer

Direct In-Line Variable Area (DIVA) flowmeter

The DIVA flowmeter operates on the well established spring loaded variable area (SLVA) principle,where the area of an annular orifice is continuously varied by a precision shaped moving cone.This cone is free to move axially against the resistance of a spring.

However, unlike other SLVA flowmeters, the DIVA does not rely on the measurement of differential

pressure drop across the flowmeter to calculate flow, measuring instead the force caused by thedeflection of the cone via a series of extremely high quality strain gauges. The higher the flow ofsteam the greater the force. This removes the need for expensive differential pressure transmitters,reducing installation costs and potential problems (Figure 4.3.15).

The DIVA has an internal temperature sensor, which provides full density compensation forsaturated steam applications.

Flowmetering systems will:

o Check on the energy cost of any part of the plant.

o Cost energy as a raw material.

o

Identify priority areas for energy savings.o Enable efficiencies to be calculated for processes or power generation.

Fig. 4.3.15 Traditional flowmetering system versus a DIVA flowmetering system

Flow

Flow

The DIVA steam flowmeter (Figure 4.3.16) has a system uncertainty in accordance withISO 17025, of:

o 2% of actual flow to a confidence of 95% (2 standard deviations) over a range of 10% to

100% of maximum rated flow.o 0.2% FSD to a confidence of 95% (2 standard deviations) from 2% to 10% of the maximum

rated flow.

As the DIVA is a self-contained unit the uncertainty quoted is for the complete system. Manyflowmeters claim a pipeline unit uncertainty but, for the whole system, the individual uncertaintyvalues of any associated equipment, such as DP cells, need to be taken into account.

The turndown of a flowmeter is the ratio of the maximum to minimum flowrate over which it willmeet its specified performance, or its operational range. The DIVA flowmeter has a high turndownratio of up to 50:1, giving an operational range of up to 98% of its maximum flow.


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Integral Pt100temperature sensor.

High quality strain gauges tomeasure stress, and henceforce, proportional to flow.

Integral electronics convertthe measured strain and

temperature into a steammass flowrate.

All wetted parts stainlesssteel or Inconel.

Integrated loop-powereddevice - no additionalequipment required.

Over-range stop preventsdamage from surges orexcessive flow.

Precision design of theorifice and cone minimizesupstream velocity profile

effects.

Fig. 4.3.16 The DIVA flowmeter

Flow orientation:Vertically downwards

Turndown:Up to 50:1

Pressure limitation:11 bar g

Flow orientation:Vertically upwards

Turndown:Up to 30:1


Flow orientation:Horizontal

Turndown:Up to 50:1


Flow orientationsThe orientation of the DIVA flowmeter can have an effect on the operating performance. Installedin horizontal pipe, the DIVA has a steam pressure limit of 32 bar g, and a 50:1 turndown.As shown in Figure 4.3.17, if the DIVA is installed with a vertical flow direction then thepressure limit is reduced, and the turndown ratio will be affected if the flow is vertically upwards.

Fig. 4.3.17 Flow orientation

Flow

Flow

Flow

Flow


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Pitot tubes

In large steam mains, the cost of providing a full bore flowmeter can become extremely high bothin terms of the cost of the flowmeter itself, and the installation work required.

A Piot tube flowmeter can be an inexpensive method of metering. The flowmeter itself is cheap,it is cheap to install, and one flowmeter may be used in several applications.

Pitot tubes, as introduced in Module 4.2, are a common type of insertion flowmeter.Figure 4.3.18 shows the basis for a Pitot tube, where a pressure is generated in a tube facing theflow, by the velocity of the fluid. This velocity pressure is compared against the reference pressure(or static pressure) in the pipe, and the velocity can be determined by applying a simple equation.

Fig. 4.3.18 A diagrammatic pitot tube

Because the simple Pitot tube (Figure 4.3.19) only samples a single point, and, because the flowprofile of the fluid (and hence velocity profile) varies across the pipe, accurate placement of thenozzle is critical.

Fig. 4.3.19 A simple pitot tube

d

Totalpressure

hole

Staticpressure

holes

Stem

Static pressure

Flow

DP

Static + velocity pressure

8d

In practice, two tubes inserted into a pipe would be cumbersome, and a simple Pitot tube willconsist of one unit as shown in Figure 4.3.19. Here, the hole measuring the velocity pressure andthe holes measuring the reference or static pressure are incorporated in the same device.

Manometer


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Note that a square root relationship exists between velocity and pressure drop (see Equation 4.2.13).This limits the accuracy to a small turndown range.

Equation 4.2.13

3X =

D

r

Where:u1 = The fluid velocity in the pipeDp = Dynamic pressure - Static pressurer = Density

The averaging Pitot tubeThe averaging Pitot tube (Figure 4.3.20) was developed with a number of upstream sensing tubesto overcome the problems associated with correctly siting the simple type of Pitot tube. Thesesensing tubes sense various velocity pressures across the pipe, which are then averaged withinthe tube assembly to give a representative flowrate of the whole cross section.

Fig. 4.3.20 The averaging pitot tube

Advantages of the Pitot tube:

o Presents little resistance to flow.

o Inexpensive to buy.

o Simple types can be used on different diameter pipes.

Disadvantages of the Pitot tube:

o Turndown is limited to approximately 4:1 by the square root relationship between pressureand velocity as discussed in Module 4.2.

o If steam is wet, the bottom holes can become effectively blocked. To counter this, some modelscan be installed horizontally.

o Sensitive to changes in turbulence and needs careful installation and maintenance.

o The low pressure drop measured by the unit, increases uncertainty, especially on steam.

o Placement inside the pipework is critical.

Typical applications for the Pitot tube:

o Occasional use to provide an indication of flowrate.

o Determining the range over which a more appropriate steam flowmeter may be used.

DP output

Total pressure

Static pressure Equalannularflowareas

Flow


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Vortex shedding flowmeters

These flowmeters utilise the fact that when a non-streamlined or bluff body is placed in afluid flow, regular vortices are shed from the rear of the body. These vortices can be detected,counted and displayed. Over a range of flows, the rate of vortex shedding is proportional tothe flowrate, and this allows the velocity to be measured.

The bluff body causes a blockage around which the fluid has to flow. By forcing the fluidto flow around it, the body induces a change in the fluid direction and thus velocity. Thefluid which is nearest to the body experiences friction from the body surface and slowsdown. Because of the area reduction between the bluff body and the pipe diameter, thefluid further away from the body is forced to accelerate to pass the necessary fluid throughthe reduced space. Once the fluid has passed the bluff body, it strives to fill the space producedbehind it, which in turn causes a rotational motion in the fluid creating a spinning vortex.

Fig. 4.3.21 Vortex shedding flowmeter

Vortex shedder

IX

N=

Equation 4.3.26UX

IG

Where:f = Shedding frequency (Hz)

Sr = Strouhal number (dimensionless)u = Mean pipe flow velocity (m/s)d = Bluff body diameter (m)

The Strouhal number is determined experimentally and generally remains constant for a widerange of Reynolds numbers;which indicates that the shedding frequency will remain unaffectedby a change in fluid density, and that it is directly proportional to the velocity for any given bluffbody diameter. For example:

f = k x u

Where:

k = A constant for all fluids on a given design of flowmeter.Hence:

The fluid velocity produced by the restrictionis not constant on both sides of the bluff body.As the velocity increases on one side itdecreases on the other. This also applies to

the pressure. On the high velocity sidethe pressure is low, and on the low velocityside the pressure is high. As pressureattempts to redistribute itself, the highpressure region moving towards the lowpressure region, the pressure regions changeplaces and vortices of different strengths areproduced on alternate sides of the body.

The shedding frequency and the fluidvelocity have a near-linear relationship whenthe correct conditions are met.

The frequency of shedding is proportionalto the Strouhal number (Sr), the flowvelocity, and the inverse of the bluff bodydiameter. These factors are summarised inEquation 4.3.2.

Vortex shedder


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Fig. 4.3.22 Vortex shedding flowmeter - typical installations

Flow

Upstream Downstream

10D 5D

Temperature tap

Pressure tap

1D to2D

3.5D to7.5D

Upstream

Downstream

D = Nominal Vortex flowmeter diameter

Then the volume flowrate qv in a pipe can be calculated as shown in Equation 4.3.3:

Equation 4.3.3I

T $N

=Y

Where:A = Area of the flowmeter bore (m)

Advantages of vortex shedding flowmeters:

o Reasonable turndown (providing high velocities and high pressure drops are acceptable).

o No moving parts.

o Little resistance to flow.

Disadvantages of vortex shedding flowmeters:

o At low flows, pulses are not generated and the flowmeter can read low or even zero.

o Maximum flowrates are often quoted at velocities of 80 or 100 m/s, which would give severe

problems in steam systems, especially if the steam is wet and/or dirty. Lower velocities foundin steam pipes will reduce the capacity of vortex flowmeters.

o Vibration can cause errors in accuracy.

o Correct installation is critical as a protruding gasket or weld beads can cause vortices toform, leading to inaccuracy.

o Long, clear lengths of upstream pipework must be provided, as for orifice plate flowmeters.

Typical applications for vortex shedding flowmeters:

o Direct steam measurements at both boiler and point of use locations.

o Natural gas measurements for boiler fuel flow.

Flow

Vortex shedding flowmeter

Vortex shedding flowmeter


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Questions

1. A 50 mm bore steam pipe lifts up and over a large industrial doorway. An orifice flowmeteris fitted in the horizontal pipe above the doorway, with a 1.6 m straight run before it.The b ratio is 0.7. What will be the effect of the straight run of pipe before the flowmeter?

a| No effect. 1.45 m is the recommended minimum length of upstream pipe

b| The accuracy of the flowmeter will be reduced because the flow will be laminar,not turbulent

c| The accuracy of the flowmeter will be reduced because of increased turbulencefollowing the preceding pipe bend

d| The accuracy will be reduced because of the swirling motion of the flow

2. Why are turbine flowmeters frequently fitted in a bypass aroundan orifice plate flowmeter?

a| To minimise cost

b| To improve accuracy

c| To avoid the effects of suspended moisture particles in the steam

d| Because in a bypass, turbine flowmeters will be less susceptible to inaccuracies dueto low flowrates

3. What is the likely effect of a spring loaded variable area flowmeter(installed as in Figure 4.3.14) on steam for long periods?

a| The cone (float) can be damaged by wet steam if no separator is fitted

b| The turndown will be less than 25:1

c| No effect

d| The differential pressure across the flowmeter will be higher,so accuracy will be reduced

4. What feature makes the differential pressure type of spring loadedvariable area flowmeter suitable for a turndown of 100:1?

a| The pass area, which remains constant under all flow conditions

b| The pass area, which reduces with increasing flow

c| The moving cone which provides an increase in differential pressure as the rateof flow increases

d| The moving cone which provides a decrease in flowrate as thedifferential pressure increases

5. Which of the following is a feature of the Vortex shedding flowmeter againstan orif

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SpiraxSarco-B4-Flowmetering