Orifice plate.docx

8/10/2019 Orifice plate.docx

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5 #ermanent pressure drop for incompressi(le fluids

! See also

" 4eferences

'3ternal links

Description

$n orifice plate is a thin plate %ith a hole in the middle& It is usually placed in a pipe in %hich

fluid flo%s& When the fluid reaches the orifice plate, the fluid is forced to converge to go through

the small hole6 the point of ma3imum convergence actually occurs shortly do%nstream of the

physical orifice, at the so-called vena contracta point 7see dra%ing to the right8& $s it does so, thevelocity and the pressure changes& +eyond the vena contracta, the fluid e3pands and the velocity

and pressure change once again& +y measuring the difference in fluid pressure (et%een the

normal pipe section and at the vena contracta, the volumetric and mass flo% rates can (eo(tained from +ernoullis e9uation&

Uses

Orifice plates are most commonly used for continuous measurement of fluid flo% in pipes& heyare also used in some small river systems to measure flo% rates at locations %here the river

passes through a culvert or drain& Only a small num(er of rivers are appropriate for the use of the

technology since the plate must remain completely immersed i&e& the approach pipe must (e full,and the river must (e su(stantially free of de(ris&

Incompressible flow through an orifice

+y assuming steady-state, incompressi(le7constant fluid density8, inviscid, laminarflo% in a

hori*ontal pipe 7no change in elevation8 %ith negligi(le frictional losses,+ernoullis e9uation

reduces to an e9uation relating the conservation of energy (et%een t%o points on the samestreamline:

or:
http://en.wikipedia.org/wiki/Orifice_plate#Permanent_pressure_drop_for_incompressible_fluidshttp://en.wikipedia.org/wiki/Orifice_plate#See_alsohttp://en.wikipedia.org/wiki/Orifice_plate#Referenceshttp://en.wikipedia.org/wiki/Orifice_plate#External_linkshttp://en.wikipedia.org/wiki/Incompressible_flowhttp://en.wikipedia.org/wiki/Inviscid_flowhttp://en.wikipedia.org/wiki/Laminar_flowhttp://en.wikipedia.org/wiki/Bernoulli's_principlehttp://en.wikipedia.org/wiki/Bernoulli's_principlehttp://en.wikipedia.org/wiki/Orifice_plate#Permanent_pressure_drop_for_incompressible_fluidshttp://en.wikipedia.org/wiki/Orifice_plate#See_alsohttp://en.wikipedia.org/wiki/Orifice_plate#Referenceshttp://en.wikipedia.org/wiki/Orifice_plate#External_linkshttp://en.wikipedia.org/wiki/Incompressible_flowhttp://en.wikipedia.org/wiki/Inviscid_flowhttp://en.wikipedia.org/wiki/Laminar_flowhttp://en.wikipedia.org/wiki/Bernoulli's_principle


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> cross-sectional area of the pipe, mA

> cross-sectional area of the orifice hole, mA

> diameterof the pipe, m

> diameter of the orifice hole, m

> ratio of orifice hole diameter to pipe diameter, dimensionless> upstream fluid velocity, m@s

> fluid velocity through the orifice hole, m@s

> fluid upstreampressure, #a %ith dimensions of kg@7mBsA 8

> fluid do%nstream pressure, #a %ith dimensions of kg@7mBsA 8

> fluid density, kg@m?

eriving the a(ove e9uations used the cross-section of the orifice opening and is not as realistic

as using the minimum cross-section at the vena contracta& In addition, frictional losses may not

(e negligi(le and viscosity and tur(ulence effects may (e present& For that reason, the coefficient

of discharge is introduced& ;ethods e3ist for determining the coefficient of discharge as afunction of the 4eynolds num(er&


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he e3pansion factor , %hich allo%s for the change in the density of an ideal gas as it e3pands

isentropically,is given (y: '3pansion factor, dimensionless

>

> specific heatratio 7 8, dimensionless

Su(stituting e9uation 718 into the mass flo% rate e9uation 708:

and:

and thus, the final e9uation for the non-choked 7i&e&, su(-sonic8 flo% of ideal gases through an

orifice for values of D less than C&.5:

/sing the ideal gas la%and the compressi(ility factor7%hich corrects for non-ideal gases8, a

practical e9uation is o(tained for the non-choked flo% of real gasesthrough an orifice for valuesof D less than C&.5:


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%here:

> specific heatratio 7 8, dimensionless

> mass flo% rateat any section, kg@s

> upstream real gas flo% rate, m?@s

> orifice flo% coefficient, dimensionless

> cross-sectional area of the orifice hole, mA

> upstream real gas density, kg@m?

> upstream gaspressure, #a %ith dimensions of kg@7mBsA8

> do%nstream pressure, #a %ith dimensions of kg@7mBsA8

> the gas molar mass, kg@mol

> the /niversal Eas a% 2onstant> &015 J@7molBG8> a(solute upstream gas temperature, G

> the gas compressi(ility factor at and , dimensionless

$ detailed e3planation of choked and non-choked flo% of gases, as %ell as the e9uation for the

choked flo% of gases through restriction orifices, is availa(le at2hoked flo%&

he flo% of real gases through thin-plate orifices never (ecomes fully choked& 2unningham

7H58 first dre% attention to the fact that choked flo% %ill not occur across a standard, thin,s9uare-edged orifice&

do%nstream pressure is lo%ered to a perfect vacuum, though the mass flo% rate increases slo%lyas the do%nstream pressure is reduced (elo% the critical pressure&


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2.2 Flow Measurement

Flo% measurement is critical to determine the amount of material purchased and sold, and in

these applications, very accurate flo% measurement is re9uired& In addition, flo%s throughoutthe process should the regulated near their desired values %ith small varia(ility6 in these

applications, good reproduci(ility is usually sufficient& Flo%ing systems re9uire energy,

typically provided (y pumps and compressors, to produce a pressure difference as the driving

force, and flo% sensors should introduce a small flo% resistance, increasing the process energyconsumption as little as possi(le& ;ost flo% sensors re9uire straight sections of piping (efore

and after the sensor6 this re9uirement places restrictions on accepta(le process designs, %hich

can (e partially compensated (y straightening vanes placed in the piping& he sensors discussedin this su(section are for clean fluids flo%ing in a pipe6 special considerations are re9uired for

concentrated slurries, flo% in an open conduit, and other process situations&

Several sensors rely on the pressure drop or headoccurring as a fluid flo%s (y a resistance6 an

e3ample is given in Figure & he relationship (et%een flo% rate and pressure difference isdetermined (y the +ernoulli e9uation, assuming that changes in elevation, %ork and heat transfer

are negligi(le&

Figure 1& Orifice flo% meter


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Bernoulli's euation

!"#

%here Sf represents the total friction loss that is usually assumed negligi(le& his e9uation can

(e simplified and rearranged to give 7Foust et& al, H6 Janna, HH08

general head meter

euation

!$#

he meter coefficient, 2meter, accounts for all non-idealities, including friction losses, and

depends on the type of meter, the ratio of cross sectional areas and the 4eynolds num(er& hecompressi(ility factor, , accounts for the e3pansion of compressi(le gases6 it is &C for

incompressi(le fluids& hese t%o factors can (e estimated from correlations 7$S;', H5H6

Janna, HH08 or can (e determined through cali(ration& '9uation 708 is used for designing headflo% meters for specific plant operating conditions&

When the process is operating, the meter parameters are fi3ed, and the pressure difference is

measured& hen, the flo% can (e calculated from the meter e9uation, using the appropriate

values for 2meterand & $ll constants are com(ined, leading to the follo%ing relationship&

relationship for installed

head meter

!%#

In the usual situation in %hich only reproduci(ility is re9uired, the fluid density is not measured

and is assumed constant6 the simplified calculation is %here the density is assumed to (e itsdesign value of ro& his is a good assumption for li9uid and can provide accepta(le accuracy for

gases in some situations& $gain, all constants can (e com(ined 7including ro8 into 2to give the

follo%ing relationship&

relationship for installed

head meter with constant

densit&

!#


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If the density of a gas varies significantly (ecause of variation in temperature and pressure 7(ut

not average molecular %eight8, correction is usually (ased on the ideal gas la% using lo% cost

sensors to measure and # according to

relationship for installedhead meter( gas with

constant )*( changing +

and P

!,#

%here the density 7assumed constant at ro8, temperature 7o8 and pressure 7#o8 %ere the (ase casevalues used in determining 2o& If the density varies significantly due to composition changes and

high accuracy is re9uired, the real-time value of fluid density 7r8 can (e measured (y an on-

stream analy*er for use as roin e9uation 718 72levett, H58&

he flo% is determined from e9uation 758 (y taking the s9uare root of the measured pressuredifference, %hich can (e measured (y many methods& $ /-tu(e manometer provides an

e3cellent visual display for la(oratory e3periments (ut is not typically used industrially& For

industrial practice a diaphragm is used for measuring the pressure drop6 a diaphragm %ith one

pressure on each side %ill deform according to the pressure difference&

ote that the pressure in the pipe increases after the vena contracta %here the flo% cross section

returns to its original value, (ut (ecause of the meter resistance, the pressure do%nstream of the

meter 7#08 is lower than upstream pressure 7#8& his is the -non.reco/erable0 pressure dropof the meter that re9uires energy, e&g&, compressor %ork, to overcome and increases the cost of

plant operation& he non-recovera(le pressure losses for three important head meters are given

in Figure 5&

he lo% pressure at the point of highest velocity creates the possi(ility for the li9uid to partiallyvapori*e6 it might remain partially vapori*ed after the sensor 7called flashing8 or it might return

to a li9uid as the pressure increases after the lo%est pressure point 7called ca/itation8& We %ant

to avoid any vapori*ation to ensure proper sensor operation and to retain the relationship

(et%een pressure difference and flo%& )apori*ation can (e prevented (y maintaining the inletpressure sufficiently high and the inlet temperature sufficiently lo%&

Some typical head metersare descri(ed (riefly in the follo%ing&

Orifice $n orifice plate is a restriction %ith an opening smaller than the pipe diameter %hich isinserted in the pipe6 the typical orifice plate has a concentric, sharp edged opening, as sho%n inFigure & +ecause of the smaller area the fluid velocity increases, causing a corresponding

decrease in pressure& he flo% rate can (e calculated from the measured pressure drop across the

orifice plate, #-#0& he orifice plate is the most commonly used flo% sensor, (ut it creates arather large non-recovera(le pressure due to the tur(ulence around the plate, leading to high

energy consumption 7Foust, H8&


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Venturi Tube: he venturi tu(e sho%n in Figure . is similar to an orifice meter, (ut it is

designed to nearly eliminate (oundary layer separation, and thus form drag& he change in

cross-sectional area in the venturi tu(e causes a pressure change (et%een the convergent sectionand the throat, and the flo% rate can (e determined from this pressure drop& $lthough more

e3pensive that an orifice plate6 the venturi tu(e introduces su(stantially lo%er non-recovera(le

pressure drops 7Foust, H8&

Figure "& )enturi flo% meter

Flow Nozzle $ flo% no**le consists of a restriction %ith an elliptical contour approach section

that terminates in a cylindrical throat section& #ressure drop (et%een the locations one pipe

diameter upstream and one-half pipe diameter do%nstream is measured& Flo% no**les providean intermediate pressure drop (et%een orifice plates and venturi tu(es6 also, they are applica(le

to some slurry systems&

Elbow meter $ differential pressure e3ists %hen a flo%ing fluid changes direction due to a pipe

turn or el(o%, as sho%n in Figure 0 (elo%& he pressure difference results from the centrifugalforce& Since pipe el(o%s e3ist in plants, the cost for these meters is very lo%& Ko%ever, the

accuracy is very poor6 there are only applied %hen reproduci(ility is sufficient and other flo%

measurements %ould (e very costly&


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Figure & Flo% meter non-recovera(le pressure losses 7$ndre%s and Williams, )ol , H"H8

he follo%ing flo% sensors are (ased on physical principles other than head&

Turbine $s fluid flo%s through the tur(ine, it causes the tur(ine to rotate %ith an angular

velocity that is proportional to the fluid flo% rate& he fre9uency of rotation can (e measured

and used to determine flo%& his sensor should not (e used for slurries or systems e3periencinglarge, rapid flo% or pressure variation&

Vortex shedding Fluid vortices are formed against the (ody introduced in the pipe& hesevortices are produced from the do%nstream face in a oscillatory manner& he shedding is sensedusing a thermistor and the fre9uency of shedding is proportional to volumetric flo% rate&

Positive displacement In these sensors, the fluid is separated into individual volumetric

elements and the num(er of elements per unit time are measured& hese sensors provide high

accuracy over a large range& $n e3ample is a %et test meter&

For an excellent concise discussion on flow sensors

!including man& not discussed here# with good

figures of meters( select this button to be directed

to a site on the ***2


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For an excellent in.depth discussion of flow

sensors( select this button to be directed to a site

on the *** and select 3olume %2

+able "2 4ummar& of flow sensors

4ensor 5angeabilit&1 6ccurac&"D&namics

!s#6d/antages Disad/antages

orifice 0&5: .-1L of fullspan

-

-lo% cost

-e3tensive

industrial

practice

-high pressure

loss

-plugging %ith

slurries

/enturi 0&5:L of full

span-

-lo%er pressureloss than

orifice

-slurries do not

plug

-high cost

-line under 5 cm

flow no77le 0&5: .L full span -

-good for

slurry service

-intermediatepressure loss

-higher cost than

orifice plate

-limited pipesi*es

elbow meter 0:5-CL of full

span-

-lo% pressure

loss

-very poor

accuracy

annubar 0:C&5-&5L of

full span-

-lo% pressure

loss

-large pipediameters

-poorperformance %ith

dirty or sticky

fluids


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turbine .C:C&.5L of

measurement-

-%ide

rangea(ility

-good accuracy

-high cost

-strainer needed,

especially for

slurries

/ortex

sheddingC:

L ofmeasurement

-

-%ide

rangea(ility

-insensitive to

variations in

density,

temperature,pressure, and

viscosity

-e3pensive

positi/e

displacement

C: or

greater

C&5L of

measurement-

-high

reangea(ility

-good accuracy

-high pressure

drop

-damaged (y flo%surge or solids

otes:

& 4angea(ility is the ratio of full span to smallest flo% that can (e measured %ith sufficientaccuracy&

.& $ccuracy applies to a cali(rated instrument&

Orifice plate.docx

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