Baker R.C. Flow Measurement Handbook: Industrial Designs, Operating Principles, Performance, and Applications

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5.17 CHAPTER CONCLUSIONS 127

5.16 APPLICATION, ADVANTAGES AND DISADVANTAGES

The standard orifice can be used with almost any single-phase Newtonian flow,

whereas for high viscosity fluids, a quadrant or conical orifice may be used. Abrasive

fluids are likely to change the shape of the leading edge of the plate and therefore

the calibration of the orifice meter and are not to be advised. The application of the

orifice plate to two-phase flows should be attempted with great caution.

An advantage of the orifice plate flowmeter is that the experience over many

years has been well documented and is distilled in the standards, allowing a device

to be desiged and constructed with confidence. The uncertainty is, also, calculable

from the standards. Thus without calibration of the instrument, it is possible to set

a value against the uncertainty of the measurements. Few other meters offer this

possibility.

Its ease of installation in the line has to be balanced by the need for very careful

construction in order to obtain the calculable uncertainty. Some features of the

design (e.g., the edge radius of the plate inlet for small plate diameters) are very

difficult to achieve.

Another disadvantage is the nonlinear characteristic of the meter due to

Equation (5.1). This, in turn, leads to a restricted range since the differential pres-

sure measurement device will need to respond to, say, 100:1 turndown for a 10:1

flow turndown. With smart transducers, this is more possible than in the past. An-

other problem with the nonlinear characteristic is the effect of pulsation on the

reading.

The high pressure loss due to the poor pressure recovery after the plate may be a

disadvantage in many applications and will certainly lead to energy losses.

The cost of installation of the orifice will not be markedly

less

than other full-bore

flowmeters, when allowance has been made for pressure transducers, flow computer,

etc.

Maintenance will be aided if one of the commercial designs which allows the

orifice plate to be withdrawn from the line, even under operating conditions, is used.

Pressure transducers should be regularly checked. This does not ensure that the total

system has retained operational integrity or that the calibration is unchanged by

debris in the impact pipes or by fouling or rusting of the flow pipe causing changes

in roughness and hence of the profile entering the meter. However, it allows a fuller

record to be kept without removal for calibration and, with other operating data,

may give greater confidence in the integrity of the instrument.

5.17 CHAPTER CONCLUSIONS

The orifice continues to have an important and valued place in flow measurement

because of its longevity and its documentation in the standards and because custom

and practice require its use in some industries. The recent update of the standard is

evidence for this.

It will, no doubt, continue to have an important niche, and manufacturers of

orifice meter components will continue to provide a useful service particularly for

fiscal metering of natural gas and oil products (Reader-Harris 1989).

128 ORIFICE PLATE METERS

The measurement of

with upstream fittings causing distortion to the inlet

profile, of C with upstream conditioners, etc., has been, and will continue to be, the

subject of experimental programs. The value of such data may possibly decrease with

time,

as those seeking high accuracy look to other flow metering devices. However,

the orifice will continue to be specified by industry for many applications and legal

reasons. The benefit of all the work that has been done, a selection of which has

been referred to in this chapter, is that the ISO installation requirements have been

generally confirmed. In addition, data on the use of a flow conditioner do not yet

instill complete confidence in the resulting orifice performance (but cf. the work by

Laws and others reported in Chapter 2).

Users should also be conscious of the degrading of precision that results from

corrosion, wear, and deposits on the plate, in the pipe, and in the pressure tappings.

The effect of wear on the inlet edge of the plate may be substantial.

The computation of the flow, particularly if coupled with upstream distortion,

offers a considerable challenge, and the results can be sensitive to the detailed ap-

plication of computer programs. It would seem to be a prime candidate for a pertur-

bation approach, where the computer program could be used to calculate changes

from the norm rather than attempt to obtain the absolute discharge coefficient. Such

an approach might shed further light on the shape of the empirical equations and

the trends in discharge coefficient for variation in D,

f$,

and Re (cf. Reader-Harris

1989).

APPENDIX

5.A

Orifice Discharge Coefficient

I am indebted to Dr. Michael Reader-Harris for clarifying the position with regard to

the adoption of a new form of the discharge coefficient equation by

ISO.

At the time

that this book is going to press, the ISO has not been finalized, and the United States

has not changed its version to reflect the full database used in the modification.

Therefore, rather than omit the equation from the book, I have decided to include

the provisional form as set out in ISO 5167-l:Amd 1: 1998 and by Reader-Harris and

Sattary (1996).

The equation for C, which has come to be known as the Reader-Harris/Gallagher

equation, is:

for Re > 4,000 and D > 71.12 mm (2.8 in.),

C = 0.5961 + 0.0261£

- 0.216£

C^ term

(

—

0.3

Slope term

5.A ORIFICE DISCHARGE COEFFICIENT 129

+ (0.043 + 0.080e-

10L

i - 0.123e>-

\ Upstream tap term

x(l-0.11A)p

(l-p

- 0.031(M^ - 0.8M£

Downstream tap term

Where D < 71.12 mm (2.8 in.), the following term should be added:

+ 0.011(0.75 -

p)(2.8

- D/25.4) (D: mm) (5.A.1)

where

is based on the pipe diameter D,

. _,' 19,0000

>08

where L\ = h/D and h is the distance of the upstream tapping from the upstream

face of the plate, and L

and

is the distance of the downstream tapping

from the downstream face of the plate. The' signifies that the measurement is from

the downstream and not the upstream face of the plate.

The terms in A are only significant for small throat Reynolds number. M

is, in

fact, the distance between the downstream tapping and the downstream face of the

plate divided by the dam height.

For

the purposes of Equation (5.A.I) the values of

the

upstream and downstream

lengths are:

and D/2 1 0.47

Flange 25.4/D 25.4/D

[D:

mm)

Corner 0 0

The uncertainty associated with Equation (5.A.1) is

(0.7 -

p)%

for 0.1 < p

0.2

0.5%

for 0.2 < p

0.6

(1.6670 - 0.5)% for 0.6 <

P <

0.75

and for D

71.12 mm (2.8 in.), the following should be added arithmetically:

+ 0.9(0.75 -

P)(2.S

- D/25.4)

(D:

mm)

CHAPTER

Venturi Meter and Standard Nozzles

6.1 INTRODUCTION

In this chapter, we are concerned with devices defined in international standard

documents. Among these, the venturi meter is one of the oldest industrial methods

of measuring flow, although other methods may be more common. Chapter 8 deals

with other devices such as variable area meters, target meters, averaging pitot tubes,

Dall meters, and other venturi, nozzle, and orifice-like devices.

As in the case of the orifice plate, the reader should have access to a copy of the

latest version of the ISO standard (5167-1). I have refrained from repeating infor-

mation that should be obtained from the standard, and include only the minimum

information to provide an understanding of the discharge coefficients, the likely

uncertainty of the various devices, and the type of material from which they may

be constructed. However, although the amount of material published recently is not

great, there is a growing interest in the use of some of these devices for difficult

metering tasks and a reevaluation of their behavior, which may well lead to several

reports in the next few years.

Spink (1978) suggested that a standard orifice should be used unless:

• The velocity is such as to require the value of

to exceed 0.75: if higher dif-

ferential pressure or larger pipe is not possible, he suggested considering a flow

nozzle;

• The fluid contains a second phase of some sort - particulate, bubble, or droplet -

in suspension: either a venturi or a flow nozzle with vertically downward flow,

an eccentric or segmental orifice, or a different type of device such as a target

meter or electromagnetic flowmeter should be considered;

• The fluid is very viscous or results in low Reynolds number flows: the meters

already mentioned may be suitable, or a quadrant or semicircular orifice may be

worth considering;

• The flow is very low and the fluid very clean: an integral orifice or a small cali-

brated meter run may be appropriate;

• Pumping costs are a major consideration: in which case go to a lower loss device.

If a liquid or a gas flows down a pipe of decreasing cross-section, the velocity

(provided, in the case of a gas, that it is below the speed of sound) increases as the

area decreases, and the pressure also decreases with the increase in velocity. This

behavior allows the measurement of the change in pressure as a means of obtaining

130

6.2 ESSENTIAL BACKGROUND EQUATIONS 131

Upstream

tapping

Throat

tapping

Diffuser

angle

Connecting

planes

Figure 6.1. Classical venturi meter (after ISO 5167-1 1997).

Conical

divergent

Outlet

plane

the flow rate in the duct. If the duct has a smoothly varying cross-section and slowly

changing area, the pressure change for a particular flow rate can be predicted from

Equation (2.11). This is particularly so for the case of the venturi and the inlet to the

standard nozzles, and in contrast to the standard orifice plate, the flow rate can be

predicted to within about

1-1.5%

as shown from experimental data.

The inlet flow will usually be turbulent and will approach the venturi (Figure 6.1)

or nozzle (Figures

6.2-6A)

where an upstream pressure tapping (one at entry to the

flowmeter) will measure the static pressure. The convergent flow at the inlet of the

venturi or nozzles passes smoothly to the throat, except that it is possible that a small

recirculation zone may exist upstream at the corner of nozzle entry. The downstream

pressure tapping for the venturi is in the parallel throat section and is set in the wall.

In the case of the nozzles, the downstream tapping is either in the throat or in the

pipe wall. In the latter case, it senses the pressure of the jet as it leaves the outlet of

the nozzle. Downstream of the throat in the venturi, there is a controlled diffusion,

the small angle ensuring that good pressure recovery is achieved with a low total

pressure loss. The losses at the outlet of the nozzles vary according to the particular

design.

The comparison between the flow in the venturi (Figure 6.1), a duct of (relatively)

smoothly changing area, and the flow through an orifice plate (Figure 5.1) is marked.

The essential equations governing the

behavior of the venturi and the nozzles

have been given in Chapter 2 (cf. Baker

1996),

and many of the ideas are touched

on in Chapter 5. In this chapter, we shall,

as far as possible, avoid repetition.

6.2 ESSENTIAL BACKGROUND

EQUATIONS

Truncated

divergent

design

Not truncated

design

The equation relating mass flow to the dif-

ferential pressure for venturi and nozzles, is

Inlet

pressure

Throat

pressure

Figure 6.2. Venturi nozzle (after ISO 5167-1 1997).

132 VENTURI METER AND STANDARD NOZZLES

Pressure

tappings

(carrier ring)

Pressure

tappings

(corner)

Figure 6.3. ISA 1932 nozzle (after ISO 5167-1 1997).

reproduced from Chapter 5:

(5.1)

where

is the coefficient of discharge, E is the velocity of approach factor

-p

1/2

where p is the diameter ratio d/D of orifice diameter to pipe internal diameter, e is the

expansibility (or expansion) factor, Ap is the differential pressure, p\ is the density at

the upstream pressure tapping cross-section, and q

is related to q

by Equation (5.2).

The expansibility (or expansion) factor

is given in the standard for each device,

venturi or nozzle, which should be consulted for details. The expressions differ from

those in Chapter 5.

The discharge coefficients for these instruments are of the form

(6.1)

i—-

Figure 6.4. Long radius nozzle (after ISO 5167-1 1997).

6.2 ESSENTIAL BACKGROUND EQUATIONS 133

Table 6.1. Coefficient of discharge for the classical venturi

Type of

Convergent

Rough-cast

(or as-cast)

Machined

Rough-welded

sheet iron

Constraints

100 mm < D < 800 mm

0.3 <P < 0.75

2 x 10

< Re < 2 x 10

50mm< D < 250 mm

0.4 < p < 0.75

2 x 10

< Re < 1 x 10

200 mm < D < 1200 mm

0.4 < p < 0.7

2 x 10

< Re < 1 x 10

0.984

0.995

0.985

Uncertainty

(%)

0.7

1.0

1.5

For the classical venturi meter, the coefficients are given in Table 6.1. It is im-

portant to note that, although the flow in the meter is a flow that approaches

the ideal and results in a coefficient within about 1% of unity and therefore very

close to the result from Bernoulli's equation, the uncertainty is greater than for the

orifice. This reflects not on the stability of the flow but on the consistency with

which the devices can be machined and the pressure tappings formed. The expe-

rience that has been amassed of the behavior of these instruments will also relate

to this.

Shufang et

al.

(1996) reported tests outside the

ISO

limits with a

1,400-mm

design

using a maximum flow rate of 18,000 m

/h with a system uncertainty of 0.2% and

for 1,85 x 10

< Re < 5.78 x 10

obtained discharge coefficients:

for machined convergent 0.983 ± 0.003

for rough-welded 0.987 ± 0.006

The results for the rough-welded are essentially in line with the annex in the

standard, which suggests no change for the rough-welded but an uncertainty of

±2%.

However, for the machined convergent, the standard suggests a slight increase

in C and uncertainty compared with the decrease reported by Shufang et al. (1996).

For the rough-cast or as-cast version, the standard suggests that there appears to

be no change for higher Reynolds numbers. There are likely to be changes, mainly

decreases in C, for lower Reynolds numbers.

For the nozzles, the standard sets out the discharge coefficient formulas. The

reader is referred to ISO 5167-1 for the complete formulas, the conditional require-

ments and the limits of applicability. For ft = 0.5 and Re = 10

, the terms in Equa-

tion (6.1) have values:

CQO

Second Term

for the venturi nozzle 0.9771 0

for the ISA 1932 0.9768 -0.00025

for the long radius 0.9965 -0.00462

134 VENTURI METER AND STANDARD NOZZLES

The approximate uncertainty for each nozzle for a p = 0.5 is

for the venturi nozzle 1.3%

for the ISA 1932 0.8%

for the long radius 2.0%

Note that in all the equations, Re refers to the Reynolds number based on the

upstream pipe internal diameter. However, Re

based on the throat diameter

some-

times used in the standards, and the reader should be aware of this.

6.3 DESIGN DETAILS

for the orifice plate, these are set out fully in ISO 5167, which provides the detailed

requirements. The reader must refer to the standard to confirm that these are the

latest values and to obtain all other details for each of these devices.

For the Classical Venturi Meter

The main features of the venturi design are shown in Figure 6.1. In addition the

standard deals in matters such as the smoothness of the finish of the throat and the

adjacent curvature. These are required to have k/d < 10~

, where k is the roughness

and d is the throat diameter. For the machined venturi, the entrance cylinder of

length not less than D and the convergent section are required to have a finish to

the same quality. The radius of curvature between the sections must be less than the

following values:

0.25D between entrance cylinder and convergent section,

0.25d between the convergent section and the throat,

0.25d between the throat and the divergent.

In each case, the standard would prefer that the radius of curvature be zero. The

requirements for the other two methods of fabrication of the venturi are also given

in the standard.

Pressure tappings are shown in Figure

6.1,

and the standard requires that four (at

least) shall be provided at both the throat and the upstream positions and specifies

their size, finish, and precise positions.

The value of the pressure loss across the venturi meter compared with the differ-

ential pressure between inlet and throat can be taken to be in the range 5-20%.

For the Venturi Nozzles

The nozzle is shown in Figure 6.2 and must have a roughness less than 10~

d. It can

be made of any material provided it meets the requirements set out in the standard.

Obviously the material must be stable enough to retain its shape and to resist erosion

and corrosion by the fluid.

For the ISA 1932 Nozzles

The nozzle is shown in Figure 6.3 and has a roughness as for the venturi nozzle.

Again, any unchanging material is acceptable.

Flanged Nozzle Assembly

6.5 INSTALLATION EFFECTS 135

Integral Weld-in Nozzle

ISA 1932 Flow Nozzle

To BS1042 Section 1.1

Orifice Flanges

to ANSI B16.36

with Corner Taps

Long Radius Flow Nozzle

To BSI042 Section 1.1

Venturi Tube

Fabricated Flanged

Venturi Tube

To BS1O42 Section I.I

Figure 6.5. Commercially available devices

(reproduced with permission from Elsag

Bailey-Bush Beach Engineering Division).

For the Long Radius Nozzle

The nozzle is shown in Figure 6.4 and has the same roughness as the venturi nozzle.

Again any unchanging material is acceptable.

6.4 COMMERCIALLY AVAILABLE DEVICES

The standards allow prospective users to design and make their own differential

pressure device. However, various manufacturers also produce standard equipment.

Figure 6.5 shows examples of such devices.

6.5 INSTALLATION EFFECTS

Upstream Fittings

Even though the values recommended by ISO 5167-1:1997 for nozzles and venturi

nozzles are the same as those for the orifice plate, the values for the classical venturi

are generally less. For instance, for a venturi with a diameter ratio of 0.5, the ISO

allowance for an upstream bend is 1.5D, and for two or more in the same plane, it

is 2.5D. These spacings have raised questions, and, as a result, NEL (1997) provided

guidance on installation, which suggested that the ISO may need to be revised as

136 VENTURI METER AND STANDARD NOZZLES

Table 6.2. Upstream straight lengths required for zero additional uncertainty

(in diameters from the outlet of the downstream bend to the upstream pressure

tapping plane) as for ISO (old) and as proposed by NEL (1997) (new)

0.4

0.5

0.6

0.75

Single

Bend

Old

0.5

1.5

3.0

4.5

90°

.5D)

New

Two 90° Bends

Same Plane

Old

1.5

2.5

3.5

4.5

New

Two 90° Bends

Perpendicular

Planes

Old

New

Reducer

3:1 Over

3.5D

Old

2.5

5.5

8.5

11.5

4:3 Over

2.3D

New

Note: At least four throat diameters should separate the throat tapping from downstream

fittings.

Indicates that no values are given without 0.5% additional uncertainty.

indicated in Table 6.2. The guidance notes should be consulted for spacings where

0.5%

additional uncertainty is relevant.

For the venturi, Ginesi (1991) suggested that the upstream lengths, to avoid

calibration change, may be about half those for the orifice, rather than a ninth as

suggested by the standards. This agrees with Table 6.2 for a single bend and two

bends in the same plane, but there is less agreement for the other two columns. The

most surprising values in Table 6.2 are those for two bends in different planes, to

which most instruments are very sensitive.

Himpe et al. (1994) described new results for the influence of upstream bends on

the discharge coefficient of classical venturi tubes, which suggest that the influence

of disturbances does not necessarily decrease with decreasing bend angles, and the

influence of the angle between the plane of the pipe bend and the position of the

tapping is considerable.

Al-Khazraji et al. (1978) used an eccentric orifice upstream of a venturi to assess

the error that results from the flow disturbance. The orientation relative to the single

pressure tapping had

negligible effect, but

spacing of

reduced the error to about

1%.

At 10D spacing, there was, again, negligible effect, showing the same trend as

for a single bend with fi < 0.6 in Table 6.2.

Two-Phase Flows

Baker (1991a) provides several references relating to the behavior of venturi meters in

multiphase flows. Additionally, de Leeuw

(1997,

cf. 1994) proposed a new correlation

for overreading in wet gas horizontal flow which appears to give results within 2%

of the data. He claims that the improvement is, in part, because it allows for the gas

velocity. Taking q

as the volumetric flow rate deduced from the differential pressure

when liquid is present in the gas stream, q

as the liquid volumetric flow rate, and

as the gas volumetric flow rate, the overreading ratio is given by

(6.2)