277

2.16 Pitot Tubes and Area Averaging Units

W. H. HOWE

(1969)

J. 0. HOUGHEN

(1982)

B. G. LIPTÁK, M. PTÁCNÁK

(1995)

B. G. LIPTÁK

(2003)

Types

A. Standard, single-portedB. Multiple-opening, averagingC. Area averaging for ducts

Applications

Liquids, gases, and steam

Operating Pressure

Permanently installed carbon or stainless-steel units can operate at up to 1400 PSIG(97 bars) at 100°F (38°C) or 800 PSIG (55 bars) at approximately 700°F (371°C);pressure rating of retractable units is function of the ratings of the isolating value

Operating Temperature

For permanent installations, up to 750°F (399°C) in steel and up to 850°F (454°C)in stainless-steel construction

Flow Ranges

Can be used in pipes or ducts in sizes 2 in. (50 mm) or larger; no upper limit

Materials of Construction

Brass, steel, stainless steel

Minimum Reynolds Number

In the range of 20,000 to 50,000

Rangeability

Usually limited to 3:1

Straight-Run Requirements

Twenty-five to 30 pipe diameters upstream and 5 downstream are required if the pitotsensor is located downstream of a valve or of two elbows in different planes; ifstraightening vanes are provided, this requirement is reduced to 10 pipe diametersupstream and 5 downstream

Inaccuracy

For standard industrial units: 0.5 to 5% of full scale. Industrial pitot venturies mustbe individually calibrated to obtain 1% of range performance. Full-traversing pitotventuries under laboratory conditions meeting the National Bureau of Standards canlimit the error to 0.5% of actual flow. Inaccuracies of individually calibrated multiple-opening averaging pitot tubes, when Reynolds numbers exceed 50,000, are 2% ofrange. The errors of area-averaging duct units are claimed to be between 0.5 and 2%of span. The errors listed above do not include that of the d/p cell, which is additional.

Costs

The cost of the pitot tube itself in case of a 1-in. dia. averaging tube in stainless-steelmaterials is $800 if fixed and $1500 if retractable for hot-tap installation. Hastelloy

units for smokestack applications can cost $2000 or more. A local pitot indicator cost$500; a d/p transmitter suited for pitot applications costs about $1,500. Calibrationcosts are additional and can amount to $1000/tube.

Partial List of Suppliers

ABB Automation Instrumentation (www.abb.com/us/instrumentation) (A)Air Monitor Corp. (www.airmonitor.com) (C)Alnor Instrument Co. (www.alnor.com) (A)Blue White Industries (www.bluwhite.com) (A)Brandt Instruments (www.brandt.com) (C)Dietrich Standard (www.annubar.com) (Annubar—B)Dwyer Instruments Inc. (www.dwyer-inst.com) (B)

FE

Flow Sheet Symbol

© 2003 by Béla Lipták

278

Flow Measurement

The Foxboro Co. (www.foxboro.com) (pitot venturi—A)Kobold Instruments Inc. (www.koboldusa.com) (B)Meriam Instrument (www.meriam.com) (B)Mid-West Instrument (www.midwestinstrument.com) (delta tube—B)United Electric Controls Co. (www.ueonline.com) (A)

For the measurement of the velocities of fluids, in 1732, Henride Pitot invented the pitot tube. Pitot tubes detect the flowingvelocity at a single point (standard), at several points thatlead into an averaging probe (multiported), or at many pointsacross the cross section of a pipe or duct (area-averaging).Their advantages are low cost, low permanent pressure loss,and the capability of inserting the probe-type sensors into theprocess pipes while the system is under pressure (wet- orhot-tapping). The disadvantages of pitot tube-type sensorsare low accuracy, low rangeability, and the limitation of beingsuitable only for clean liquid, gas, or vapor service unlesspurged.

THEORY OF OPERATION

The impact pressure on a body, which is immersed in amoving fluid is the sum of the static pressure and the dynamicpressure. Thus,

2.16(1)

where

P

t

=

total pressure, which can be sensed by a fixed probe when the fluid at the sensing point is in an isentropic state (constant entropy)

P

=

static pressure of the fluid whether in motion or at rest

P

v

=

dynamic pressure caused by the kinetic energy of the fluid as a continuum

With respect to the energy relation at the isentropic stag-nation point of an ideal probe,

2.16(2)

where

v

p

=

approach velocity at the probe location

ρ

=

fluid density

g

c

=

a constant

For a liquid of constant density, integration yields, at apoint,

2.16(3)

For a compressible perfect gas for which remains con-stant during an isentropic change, a similar relation emerges.

2.16(4)

where

γ

=

ratio of specific heats.Assuming isentropic stagnation at the sensing point of

the probe,

2.16(5)

where, using English units,

V

p

=

velocity of approach, ft/s

P

=

pressure, lbf/ft

2

ρ

=

fluid density, lbm/ft

3

g

c

=

32.2

If density is constant, integration yields

2.16(6)

For a compressible perfect gas, the ratio remains con-stant during an isentropic change, and a similar relation isobtained.

2.16(7)

where

γ

is the ratio of specific heats.To compute the fluid velocity at a particular point, it is

necessary to measure the values of both the static pressure

P P Pt v= +

dp v dv

gP

P

p

co

vt p

ρ∫ ∫=

( )P P PPv

gt vp

c

− = =2

2

FIG. 2.16a

The velocity at a point (in the turbulent flow range) is related to thesquare root of the pressure difference between total and static pressures.

pργ

( )( )

P P Pv

gt vp

c

− = = −ρ γγ

12

2

dp V d

gp

V

co

v

P

P pt

ρ= ∫∫

lbmlbf

fts2

( )P P Pp V

gt v

p

c

− = =( )2

2

Pργ

( )( )

P P PV

gt v

p

c

− = = − ( )γγ

ρ12

Vp Vp ∼ √Pt − P

P Pt

© 2003 by Béla Lipták

2.16 Pitot Tubes and Area Averaging Units

279

(

P

) and the total pressure (

P

t

) at that point (Figure 2.16a),whence

2.16(8)

where

C

=

a dimensional constant.

PRESSURE DIFFERENTIAL PRODUCED

One of the problems with pitot tubes is that they do notgenerate strong output signals. The d/p cells available arediscussed in Chapter 5, under “Pressure Measurement.” Theminimum span of a “smart” d/p cell is 0 to 2 in. of H

2

O (0to 0.5 kPa). These smart d/p cell units are accurate up to 0.1%of actual span. For narrower differentials, down to 0 to 0.1 in.H

2

O (0 to 25 Pa), the membrane-type d/p cells can be used.In addition to using d/p cells, one can also install elastic

element or manometer-type readout devices, variable-area flow-meters (Figure 2.16b), or thermal flowmeters (Figure 2.16c)as pitot tube detectors. The thermal detector gives the highestrangeability, but it can be used only if the pitot tube is purged.

STATIC PRESSURE MEASUREMENT

In process fluids flowing through pipes or ducts, the static pres-sure is commonly measured in one of three ways: (1) throughtaps in the wall, (2) by static probes inserted into the fluidstream, or (3) by small apertures located on an aerodynamicbody immersed in the flowing fluid.

The data of Shaw

1

(presented by Benedict

2

) show thaterrors in the measurement of static pressure are minimal forvelocities up to 200 ft/s (60 m/s) if the wall tap dimensionsconform to those in Figure 2.16d, where the tap diameter (d)is 0.0635 in., the sensing tube ID

≅

2d, and the tap length-to-diameter ratio (l/d) is 1.5

<

l/d

<

6.

Static pressure errors also depend on fluid viscosity, fluidvelocity, and whether the fluid is compressible. Shaw

1

statesthat, for incompressible fluids flowing in a circular conduitwith a pipe Reynolds number of 2

×

10

5

, an error of about1% of the mean dynamic pressure may occur using a walltap with a diameter 1/10th that of the pipe. Rayle

3

mentionsthat a tap diameter of 0.03 in. (0.75 mm) with a conicalcountersink 0.015 in. (0.34 mm) deep will ensure nearly truestatic pressure sensing.

Static pressure may also be sensed through a tube insertedinto the moving fluid. One configuration is shown in Figure2.16e.

Other static probe designs are also described in the liter-ature.

2

The aerodynamic probe is a bluff body inserted intothe flowing fluid with appropriately located holes on its sur-face through which pressure signals are obtained. The probeis oriented so that the sensed pressure is a measure of thestatic pressure. Two configurations taken from Benedict,

2

the cylinder and the wedge, are shown in Figure 2.16f. Theprobes are rotated until the pressure sensed from each holeis the same or, alternatively, the two taps may be manifoldedto obtain an averaged pressure.

FIG. 2.16b

Pitot rotameter with bypass flow entering through impact opening(facing flow) and leaving through static port on opposite side (notshown). (Courtesy of ABB Instruments, formerly Fischer & Porter Co.)

Flow Indicator

Gland Nut

ImpactOpening (Flow Inlet)

AdaptorBushing

0.5" NPTConnection

Bushing

VP P

Pt= −

C( ) .0 5

ρ

FIG. 2.16c

Pitot-tube rangeability can be increased by replacing the d/p celldetector with a thermal flowmeter.

FIG. 2.16d

Wall tap for static pressure measurement.

Purge Gas

ThermalFlowmeter

BypassOrifice

BalancingNeedle Valve

Flow

Pipe Wall

Sensing Tube

d

D

Tap L

© 2003 by Béla Lipták

280

Flow Measurement

The total pressure develops at the point where the flowis isentropically stagnated, which is assumed to occur at thetip of a pitot tube or at a specific point on a bluff bodyimmersed in the stream. Figure 2.16g illustrates a typicalpitot tube, also showing the taps for sensing static pressure.Another variation is shown in Figure 2.16h.

SINGLE-PORTED PITOT TUBE

Pitot tubes are sensitive to flow direction and must be care-fully aligned to face into the flow. This can be difficult ifthe flow direction is caused to vary by changes in turbulence.The pitot tube is made less sensitive to flow direction if theimpact aperture has an internal bevel of about 15° extendingabout 1.5 diameters into the tube. The characteristics ofvarious designs and orientations are discussed in Benedict.

2

Figure 2.16i illustrates the typical performance of a pitot tube.Pitot venturi and double-venturi elements have been

developed to amplify the pressure signals generated by thein-stream velocity sensors, as shown in Figures 2.16j and2.16k. These elements are intended to remain in a fixedposition, so their measurements must be converted to flowrate through calibration, which accounts for the properties of

FIG. 2.16f

Two shapes of aerodynamic probes used to sense static pressure.

FIG. 2.16e

Typical static pressure-sensing probe.

FIG. 2.16g

Typical pitot tube.

FlowDirection

Four Holes (Dia. = 0.04")Spaced 90° Apart

Wall

d

15 d5 d 45° 45°

Cylinder Wedge

Impact Pressure Connection

Tubing Adapter

Static Pressure HolesOuter Pipe Only

Impact Pressure Opening

Stainless Steel Tubing

FIG. 2.16h

Schematic of an industrial device for sensing static and dynamicpressures in a flowing fluid.

Impact (High Pressure)

Connection

PackingNut

Flow

StuffingBox

Static(Low Pressure)

Connection

CorporationCock

StaticOpening

Flow

ImpactOpening

Of Pipe

© 2003 by Béla Lipták

2.16 Pitot Tubes and Area Averaging Units

281

the fluid and the velocity profile (e.g., Reynolds number). Toobtain a stable velocity profile, it is recommended that asmooth, straight section of pipe, of a length equaling at least10 to 15 pipe diameters, be provided both upstream anddownstream of the probe.

To determine the average velocity in a pipe, it is necessaryto traverse it with a pitot tube. For circular pipes, such anaverage is obtained from measurements of (

P

t

−

P

) on eachside of the cross section at the following locations, expressedin percentage of the diameter measured from the center:

2.16(9)

where

N

is the number of measurements per traverse. Twomeasurements normal to each other are recommended.

To improve the measurements made near the walls ofpipes that are more than 6 in. (150 mm) in diameter, a reduc-tion nozzle is inserted into the pipeline (Figure 2.16l).

FIG. 2.16i

Center to average velocity ratios in straight and smooth pipes.

7

WATER D = 0.7125 cm.

WATER D = 2.855 cm.

AIR D = 2.855 cm.

AIR D = 0.7125 cm.

AIR D = 1.225 cm.

1.0

0.9

0.8

0.7

0.6

0.51 2 3 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90 100

x 1000 = REYNOLDS NUMBER R0

AV

ER

AG

E V

ELO

CIT

YC

EN

TE

R V

ELO

CIT

Y

FIG. 2.16j

A pitot venturi produces a higher differential pressure than thestandard pitot tube.

FIG. 2.16k

The double venturi produces a higher differential pressure than thestandard pitot tube. (Courtesy of The Foxboro Co.)

Flow

FIG. 2.16l

Reduction nozzle used to expedite velocity traverses.

1/2-1"

1/2"

Smooth, StraightApproach Sectionof at Least10 Pipe Diameters

2 1100 1 2 3

2nN

n KN−

× =

%, , ,

© 2003 by Béla Lipták

282

Flow Measurement

Calibration of Pitot Tubes

In high-precision laboratory tests, the pitot tube is traversedacross the cross-section of the pipe, thereby establishing thevelocity profile that exists in the pipe. In industrial applica-tions, the pitot tube is fixed and measures the flow velocityonly at one point on the velocity profile (Figure 2.16m). Ifthe velocity (

U

) measured by this fixed pitot tube is not theaverage velocity (

V

), a substantial error will result. This errorcannot be easily eliminated because, even if the pitot tubeinsertion is carefully set to measure the average velocity

V

under one set of flow conditions, it will still be incorrect assoon as the flow velocity changes. At Reynolds numbersunder 1000 (in the fully laminar region), the ratio betweenthe average velocity and the center velocity is 0.5 (

V

/

U

c

=

0.5 in Figure 2.16m). In fully developed turbulent flow (Re

=

50,000 or more), this same ratio is about 0.81(

V

/

Uc = 0.8).Unfortunately, the velocity profile is affected not only by

the Reynolds number but also by the pipe surface roughnessand by upstream valves, elbows, and other fittings. To reformthe velocity profile, it is recommended to provide a straightpipe length of about 25 pipe diameters between the upstreamdisturbances and the pitot element.

If the data for calculating the Reynolds number is available,and if the pitot tube is installed in a pipe with smooth innersurface, it should be possible to design a microprocessor-based smart pitot tube that measures only the center velocity(Uc) and, based on that reading, accurately calculates the flowunder all flow conditions.

The National Bureau of Standards calibrates pitot tubesby mounting them on a carriage, which is drawn throughstagnant air at a known velocity. Smoke is introduced intothe room to verify that the air is stagnant—that there is noturbulence. Such tests have shown that pitot tubes with coef-ficients very close to unity can be designed. Devices such aspitot-venturies or double venturies can provide flow rate mea-surements with less than 1% error, but only after extensivein situ calibration for each installation.

MULTIPLE-OPENING PITOT TUBES

One approach in attempting to overcome the inherent limitationof the pitot tube—that of being a point velocity sensor—wasto measure the velocities at several points and average these

readings. It was argued that, by averaging the velocitiesmeasured at four fixed points, for example (see Figure 2.16n),changes in the velocity profile will be detected, and thereforethe reading of a multiple-opening pitot tube will be moreaccurate than that of single-point sensors.

The manufacturers of averaging pitot tubes usually claimthat the flow coefficient (K) will stay within 2% between theReynolds numbers of 50,000 and 1,000,000. This is probablyso, but it might not be attributable to averaging action butrather to the fact that, in this highly turbulent region, thevelocity profile is flat and changes very little.

Critics of this device argue that it offers little improve-ment over the single-opening pitot tube, because it is inef-fective at Reynolds numbers below 50,000. This means thatit is not applicable for the measurement of a large portion ofindustrial liquid flows. The other argument made by criticsis that the averaging pitot tube openings are too large and,

FIG. 2.16mThe velocity profile becomes flatter as the Reynolds number rises (the flow becomes more turbulent), and the task of the pitot-type flowsensor is to find the insertion depth corresponding to the average velocity (V).

Flow

Laminar

Uc

U

U

V

Flow

Turbulent

FIG. 2.16nThe design of a particular averaging pitot tube. (Courtesy ofDietrich Standard.)

PH

PH

PL

PL

VelocityProfile

HighPressureProfile

LowPressureProfile

AverageVelocity

Average High(Impact) Pressure

Average LowPressure

(9.5, 22, 32, or 51 mm)

DP

A = 38/", 7

8/", 141 /" or 2"

© 2003 by Béla Lipták

2.16 Pitot Tubes and Area Averaging Units 283

consequently, these devices are not true averaging chambers;rather, the sensed pressure is dominated by the pressure atthe nearest port. For these reasons, further testing by inde-pendent laboratories is still needed.

The reason for making the ports of the averaging pitottubes so large is to prevent plugging. Some manufacturers ofarea-averaging pitot tubes do overcome this limitation bypurging, because the small port openings are kept clean bythe purge gas, and these units can act as true averagingchambers. Naturally, they can be used only on processes inwhich the introduction of a purge media is acceptable.

One advantage of the averaging pitot tubes that both itsmanufacturers and its critics agree on is their ability to beinstalled into operating, pressurized pipelines. This hot-tapping capability, and the ability to remove the sensor with-out requiring a shutdown, are important advantages of allprobe-type instruments (Figure 2.16o).

In calculating the pressure differential produced by anaveraging pitot tube, one might use the equations listed inTable 2.16p. For the metric equivalents of the units usedin this table, refer to the Appendix. The flow coefficient (K)of the pitot tube varies with its design. The K values of theaveraging pitot tube shown in Figure 2.16n are listed in Table2.16q. The distance “A” used in Table 2.16q is also definedin Figure 2.16n.

AREA-AVERAGING PITOT STATIONS

Area-averaging pitot stations have been designed for the mea-surement of large flows of low-pressure gases. Measurementsinclude the flow rate of combustion air to boilers, airflow todryers, and air movement in HVAC systems. These units are

available with circular or rectangular cross sections (Figures2.16r and 2.16s) and can be mounted in the suction or dis-charge of fans or in any other large pipes or ducts. Thesestations are designed so that one total pressure detection portand one static pressure sensing port are located in each unitarea of the cross section of the duct, and they each are

FIG. 2.16oThe hot-tap installation of an averaging pitot tube involves the samesteps, which are required in installing all “retractable” probe-typeinstruments. (Courtesy of Dietrich Standard.)

Install

DrillThruValve

Inserted

TABLE 2.16pEquations for Calculation of the Pressure Differential Produced by the Averaging Pitot TubeDescribed in Figure 2.16n*

Liquid, gas, steam (mass rate of flow) hw = differential pressure, inches of water at 68°FK = flow coefficientD = internal pipe diameter, inches

lbm/hr = pounds mass per hour

Liquid (volume rate of flow) GPM = U.S. gallons per minuteACFH = Actual cubic feet per hourSCFH = Standard cubic feet per hour (at 14.73 psia and 60°F)

Gas (standard volumetric flow) ρf = flowing density, lbm/ft3 for gas:

Gas (actual volume rate of flow) .076487 lbm/ft3 = air density at 14.73 psia and 60°FGf = specific gravity of liquidG = specific gravity of gas (molecular weight of air = 28.9644)Tf = temperature of flowing gas in degressRankine (°R = °F + 460)Pf = flowing pressure, psia

* Courtesy of Dietrich Standard.

hlb hr

KDwf

m=

1358 94 2

2

ρ/

.

h GKDw f=

( )

.GPM

5 666 2

2

hT G

p KDwf

f

=

SCFH7 711 2

2

,ρ f

f

f

p

TG= × × ×

14 73520

076487.

.

hKDw f=

( )

.ρ ACFH

358 94 2

© 2003 by Béla Lipták

284 Flow Measurement

connected to their own manifold. The manifolds act as aver-aging chambers, and they are also purged to protect thesensing ports from plugging.

The straight-run requirement of these units is reduced bythe addition of a hexagon-cell-type flow straightener and aflow nozzle in front of the area-averaging flow sensor. Thisnozzle also serves to amplify the differential pressure pro-duced by the unit (Figure 2.16s). According to the manufac-turer, this design (Figure 2.16s) reduces the straight-runrequirement of most installations to a range of 0 and 10diameters. The longest straight run (10 diameters) is recom-mended when the flow meter is installed downstream of abutterfly valve or a damper.

Because these area-averaging pitot stations generate verysmall pressure differentials, special d/p cells are requiredto detect these minute signals. One such detector is themembrane-type design (Fig. 2.16t), which can have a spanas small as 0 to 0.01 in. H2O (to 2.5 Pa). When such extremelysmall pressure differentials are detected, the pressure dropin the tubing between the d/p cell and the pitot station must

TABLE 2.16qThe Flow Coefficient K for the Averaging Pitot Tube Shown in Figure 2.16nHaving the “A” Dimension Also Defined in That Figure*

Paper Size Flow Coefficient-K

Size/Sch D-in D-mm A = 3/8" A = 7/8" A = 11/4" A = 2"

2" sch 40 2.067 52.50 5912

21/2" sch 40 2.469 62.71 .6026

3" sch 40 3.068 77.93 .6134

31/2" sch 40 3.548 90.12 .6192

4" sch 40 4.026 102.26 .6235

5" sch 40 5.047 128.19 .6297 .5934

6" sch 40 6.065 154.05 .6047

8" sch 40 7.981 202.72 .6173

10" sch 40 10.020 254.51 .6250

12" sch std. 12.000 304.80 .6298 .6186

14" sch std. 13.250 336.55 .6321 .6220

16" sch std. 15.250 387.35 .6349 .6263

18" sch std. 17.250 438.15 .6370 .6296

20" sch std. 19.250 488.95 .6387 .6321

24" sch std. 23.250 590.55 .6411 .6357 .6247

30" sch std. 29.250 742.95 .6435 .6393 .6308

36" sch std. 35.250 895.35 .6450 .6416 .6346

42" sch std. 41.250 1047.7 .6461 .6432 .6373

48" 48.00 1219.20 .6445 .6395

60" 60.00 1524.0 .6461 .6422

72" 72.00 1828.80 .6472 .6439

*Courtesy of Dietrich Standard.

FIG. 2.16rInstallation in rectangular duct of area-averaging pitot tube ensem-bles for metering the flow rate of gases. (Courtesy of Air MonitorCorp.)

© 2003 by Béla Lipták

2.16 Pitot Tubes and Area Averaging Units 285

be minimized. This is achieved by making the connectingtubes short and large in diameter. The pressure differentialgenerated by the flow element shown in Figure 2.16s canbe calculated by using the equations in Table 2.16u. For theequivalent SI units for use in these equations, refer to theAppendix.

SPECIAL PITOT TUBES FOR PULSATING FLOW

The mean velocity measurements of unsteady flows, if madeby conventional pitot tubes, are usually inaccurate.4 In suchmeasurements, one can expect errors in the range of 5 to 30%

of mean total pressure. This measurement can be improvedby using specially designed probes when the applicationinvolves unsteady or pulsating flows.

Figure 2.16v shows a design provided with a low-capac-ity capillary probe filled with silicon oil. The oil serves totransmit the process pressure to the d/p transducer. Thistype of probe was developed and is used by Deutsche For-schungs– und Versuchsanstalt für Luft und Raumfahrt inGermany.5

Figure 2.16w shows another example of a probedesigned to measure unsteady flow. This probe was devel-oped in the Aeronautical Research and Test Institute inCzechoslovakia.6 The main design challenge in this designis to equalize the resistances in the input and output openingsof the probe. Also, to protect against resonance during mea-surement, the natural frequency of the probe must be care-fully tuned.

FIG. 2.16sThe flow straightener and the nozzle serve to reduce the upstreamstraight pipe-run requirement and increase the pressure differentialgenerated. (Courtesy of Brandt Instruments.)

Exit Fitting1/4 NPTFWall

FlowStraightener Nozzle Probe

Array

Flow

Gaskets

FIG. 2.16tMembrane type d/p transmitter.

GainAdjustment

ab

HI Membrane

Output

SupplyAir

SupplyCavity

LOOrifice

TABLE 2.16uCalculation of Pressure Differentials Generated By Area Averaging Pitot Stations*

Equations for DifferentialPressure Calculation Terms Used

Area = Cross-sectional area of duct section in ft2

ACFM = Actual cubic feet per minute

DP = Differential pressure in inches w.c.

M = Mass flow in pounds per hour

SCFM = Standard cubic feet per minute

V = Velocity in feet per minute

PABS = Absolute pressure in PSIA

PATM = Atmospheric pressure in PSI

Ps = Static pressure in inches w.c.

T = Temperature in degrees F

DENS = Density at actual conditions lbs/ft3

DENSTD = Density at standard conditions lbs/ft3

*Courtesy of Brandt Instruments.

DP =

×ACFM

AreaDENS2

21096 845( . )

DP =×

SCFMArea4000 7

2

.

DP V= ×( )( . )

221096 845

DENS

DPM=

×

×

×6011096 845

2

2Area DENS ( . )

© 2003 by Béla Lipták

286 Flow Measurement

References

1. Shaw, R., The influence of orifice geometry on static pressure mea-surements, Fluid Mech., 7, pt. 4, 1960.

2. Benedict, R. P., Fundamentals of Temperature, Pressure, and FlowMeasurements, John Wiley & Sons, New York, 1969, 237.

3. Rayle, R. F., Influence of orifice geometry on static pressure measure-ments, ASME Paper 59-A-234, December 1959.

4. Becker, H. A., Reaction of pitot-tube in turbulent flow, J. Fluid Mech.,69, pt. I, 1974.

5. Weyer, L. I., Bestimmung der zeitlichen Druckmittelwerte in stark fluktui-render Strömmung, inbesondere in Turbomaschienen, Forschungsbericht

74–34, Deutsche Forschungs–und Versuchsanstalt für Luft–undRaumfahrt-Portz-Wahn, 1974.

6. Neruda, J. and Soch, P., Measurement System with a Pitot Tube,Czechoslovak patent no. 218417.

7. Spink, L. K., Principles and Practice of Flow Engineering, 9th ed.,The Foxboro Co., Invensys Systems, Inc., Foxboro, MA, 1967.

Bibliography

The Accuracy of the Pitot Tube Traverse Method of Measuring Pipe Flowat Various Distances up to 30 Diameters Downstream of a SmoothRight-Angled Bend, National Engineering Laboratory Flow Measure-ment Memo, No. 37, 1969.

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Baker, R. C., Flow Measurement Handbook, Cambridge University Press,UK, 2000.

Beitler, S. R., Present status of the art of flow measurement in the powerindustry, ASME Paper No. 68-WA/PTC-7, December 1968.

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Dyer, Ed., John Wiley & Sons, New York, 2001.Flow meter survey, Instrum. Control Syst., 42(3), 115–130, 1969, and 42(7),

100–102, 1970.Furness, R. A., Developments in pipeline instrumentation, Pipe Line Rules

of Thumb Handbook, 4th ed., Gulf Publishing, Houston, TX, 1998.Hiser, R., Increased functions and reduced costs of differential pressure

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FIG. 2.16vOn highly pulsating flow measurements a minute flow of silicon oilthrough a capillary can serve as a pressure-averaging purge.

FIG. 2.16wPitot tube designed for pulsating flow averaging using tuned naturalfrequency.6

PressureDetector

Capillary

PitotPort

Oil Supply

© 2003 by Béla Lipták