DKE292_Ch05

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Air Requirements

1 INTRODUCTIONThe selection of a fan, blower or compressor is probably one of the most importantdecisions to be made in the design and specification of a pneumatic conveyingsystem. It is often th e largest single item of capital expenditure and the potentialconveying capacity of the plan t is dependent upon the correct choice being made.The output capabil i ty of the air mover is a major con s idera tion in selection. Therating of the fan, blow er or compressor is expressed in terms of the sup ply pres-sure required and the volumetric flow rate. A ny error in this specification wil l re-sult in a system that is either over-rated or is not capab le of ach ievin g the desiredmaterial flow rate [1].

For an existing pneumatic conveying system it is often necessary to checkth e performance, part icularly if operating problems are encountered, or changes inmaterial or conveying dis tance need to be considered. Here it is the conveying l ineinlet air velocity that is important. Since the determinat ion of conveying line inletai r velocity and the specification of air requirements is so important for the suc-cessful operation of pneumatic conveying systems, all the appropriate models arederived and presented for reference purposes. In add itio n to the influe nc e of pres-sure, temperature and pip eline bore, w hich are the prim ary variables, hu m id ity isalso considered.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

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144 Chapters

1.1 Supply PressureThe delivery pressure, or vacuum , required depends essent ial ly upon the workingpressure drop needed over the length of the conveying pipe l ine . The pressure dropacross th e gas-solids separation devic e can usual ly be neglected, but if a blow tankis used fo r feeding the material into th e pipe l ine then an al lowance for the pressuredrop across the feeding device will have to be made. Con siderat ion wil l also haveto be given to the pressure drop in any air supply and extraction lines, and to theneed for a margin on the value of conveying l ine pressure drop required to conveyth e m aterial through the pipel ine at the specified rate.The magnitude of the conveying line pressure drop, whether for a posi t ive ora negative pressure system, depends to a large extent on the con veyin g dis tanceand on the solids loading ratio at which the material is to be conveyed. For shortdistance dilute phase conveying a fan or blower would be satisfactory, but fordense phase conveying or long distance dilute phase conveying, a reciprocating orscrew compressor would be required. The pressure drop is also dependent uponthe conveying gas velocity and a mult i tude of properties associated w ith the con-veyed material.1.2 Volumetric Flow RateThe volumetric flow rate required from the fan, b lower or compressor dependsupon a combination of the velocity required to convey the material and the diame-ter of the pipeline to be used. Pipes and fittings are generally available in a rangeof standard sizes, but velocity is not so clearly defined .

For convenience th e velocity at the end of the pipeline could be specified,for in the majori ty of cases compressors are rated in terms of ' free ai r delivered' ,and the pressure at the end of a pipeline, in posi t ive pressure systems, in mo s t ap-plications, wil l be sufficiently close to atmospher ic fo r this purpose. It is, however ,th e velocity at the start of the l ine that needs to be ascertained fo r design purposes.The problem is that air, and any other gas that is used for the conveying of materi-als, is compressible and so its density, an d hence volumetr ic flow rate, is influ-enced by both pressure and temperature.In negative pressure systems the air at the start of the conveying line is ap-proximately at atmospheric pressure, and it decreases along the conveying line tothe exhauster. Fo r this type of c on ve yin g system, therefore, the m i n i m u m velocitythat needs to be specified occurs at the free air con dition s. Exhausters, however,are generally specified in terms of the volumetr ic flow rate of the air that is drawninto the air mover, and not free air conditions, and so it is essentially the sameproblem in evaluating air flow rates as with positive pressure con veyin g systems.1.3 The Influence of VelocityA conveying plant is usually designed to achieve a specified material flow rate.M aterial flow rate can be equated to the so lid s loa din g ratio and air mass flow rate.


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Air Requirements 145

Compressor Rat ing, | ,I ISupply Pressure Volumetr ic Flow Rate

conveying LinePressure Drop

IMaterial ConveyingProperties DistanceIMaterial Concentrationor Solids Loading RatioI

IConveyingG as Veloci ty

I

PipBo\Material Flow Rate

Figure 5 .1 Parameters relating compressor rating with material flow rate.The air mass flow rate is proportional to the volumetric air flow rate and

this , in turn, is proportional to the air velocity and pipe l ine bore. Since these threeparameters also have an inf luence on the compressor rating, it is extremely impor-tant that the correct air mover specif icat ion is made. The re la t ionsh ip between thevar ious parameters that l ink the compressor rating and material f low rate is dem-onstrated with the path analysis shown in Figure 5 . 1 .

Figure 5.1 also illustrates the importance of conveying air velocity in thisrelationship, as it influences both the supply pressure and the volumetric flow rateof the compressor. This helps to explain why conveying air is one of the mostimportant variables in pneumatic conveying, and why it need to be controlledfairly precisely.

If , in a di lu te phase conveying system, the velocity is too low it is possiblethat the material being conveyed w i l l drop out of suspension and block the pipe-line. If, on the other hand, the velocity is too h igh , bends in the pipeline wi l l erodeand fail if the material is abrasive, and the material w i l l degrade if the particles arefriable.

Velocity also has a major influence on the conveying l ine pressure drop, andhence on the mass flow rate of the material conveyed through a pipeline. Therange of velocity, therefore, is relat ively narrow, part icularly in dilute phase sys-tems, varying from a m i n i m u m of about 3000 f t /min to a m a x i m u m of around6000 f t /min. This includes the compressibility effect, for the 3000 f t /min relates tothe pipeline inlet and the 6000 f t /min relates to the p i p e l i n e outlet .1.4 Air MoversA wide range of air movers are available, but it is essential that the correct type ofmachine is chosen for the given duty. It is the characteristics of the air mover, interms of the variation of the air flow rate with change of delivery pressure, at agiven rotational speed, that are important for pneumatic conveying, as discussed inChapter 3 on System Components.


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146 Chapters

In th e majority of pneu m atic conv eying sys tems the air mover is driven at aconstant speed, and design and operation is based on ac hie vin g a giv en co nv eyi ngline inlet air velocity. If the material feed rate into the pipel ine was to increase by10%, there would be a similar increase in pressure demand. Even if the same airflow rate was delivered there would be a reduction in conveying l ine inlet air ve-locity because of the higher pressure. Motor sizes and air flow rate should bespecified to take this type of fluctuation in to account .

Ideally an air mover is required that will del iver the same air flow rate at thehigher pressure. In practice a smal l reduct ion in air flow rate wil l result, an d hencea further lowering in air velocity, and so this should be accommodated. With someair movers, a 10% increase in pressure demand will result in an even greater re-duction in air flow rate. Air movers with this type of operating characteristic areunlikely to be acceptable.

The vast majority of the power required by a pneumatic conveying system istaken by the air mover . If a conveying sys tem requires a large bore pipeline and ahigh pressure air supply , th e power required is l ikely to be very high. Power re-quirements, and hence th e cost of operation fo r pn eum atic conveying, does tend tobe much higher than fo r other conveying systems, particularly fo r materials con-veyed in dilute phase. It must also be recognized that as a result of the high speedof compression, the air wil l be del ivered at an increased tem perature and so a deci-sion wil l have to be taken on whether or not to cool the air .

1.5 Air Humidity and MoistureAir is a mixture of gases. Oxygen and nitrogen are the main constituents, but it isalso capable of absorbing a certain amount of water vapor. There is , however, alimit to the amount of water that air can hold in gaseous form as vapor. Relativehumidity is a measure of the amount of moisture that air contains at a given pres-sure and temperature. It is expressed as a percentage. Relative humidity gives anindication of how dry the air is, and hence how m uch more vapor the air is capableof holding. 100% represents the l imit fo r relative humidity and at this value the airis said to be saturated.

Specific hum idi ty is a m easure of how m u c h moisture the air actually con-tains, and is usually expressed in terms of Ib of water per Ib of dry air. Relativehumidity cannot rise above 100% and so if changes occur such that saturationconditions are exceeded, condensation will occur. The amount of m oisture that aircan support increases with increase in temperature and decreases with increase inpressure. Thus an increase in temperature wil l result in air becoming drier. A de-crease in temperature wil l result in the relative humidi ty increasing.

If saturation conditions are reached then condensat ion wil l occur with anysubsequent decrease in temperature . Comp ress ion of air is l ikely to result in con-densation if there is no change in temperature. Across a compressor there is usu -ally an increase in temperature, as well as pressure, and so at out le t the air is l ikelyto be dry, as temperature generally has an over-r id ing effect in this situation .


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Air Requirements 1471.6 Compressibility EffectsThe volumetric flow rate of air required to convey a material through a pipelinecan be evaluated from the cross section al area of the p ipe l ine and the air velocityrequired to convey the material . Consideration mu st be given, however, to the factthat air is compressible, an d that it is compressible with respect to both pressurean d temperature, and if the plant is not located at sea level, the inf luence of eleva-tion may also have to be taken into account. As a result of the com pressibil i ty w ithrespect to pressure, stepped bore pipelines are often employed and these are givendue consideration.

Although it is air that is generally referred to , materials can be conveyedwith any suitable gas. Constants are included in the equations that will correctlyaccount for the type of gas used when evaluating th e volumetr ic flow rate re-quired. Air mass flow rate is also considered, as it is a useful working parameter,since it s value remains constant in a pipeline, and is required for evaluating th esolids loading ratio.1.6.1 Conveying Air VelocityFor the pneum atic conveying of bu lk paniculate materials, one of the critical pa-rameters is the minimum conveying air velocity necessary to convey a material.For dilute phase conveying this is typ ically about 3000 ft/min, but it does dependvery much upon the size and size distr ibution, shape and dens i ty of the particles ofthe bulk material .For dense phase conveying it can be as low as 600 f t /min, but this dependsupon the solids loading ratio at which the material is conveyed and the nature ofthe conveyed m aterial. If the velocity drops below the m in im um value the pip elin eis likely to block. It is important, therefore, that the volumetric flow rate of air,specified for any conveying system, is sufficient to maintain the required mini-mum value of velocity throughou t the conveyin g system.1.6.2 M aterial InfluencesIt should be noted that in evaluating conveying air velocities and volumetric ai rflow rates in pneumatic conveying applications, the presence of the material isdisregarded in all cases, whether fo r dilute or dense phase conveying. The convey-ing air velocity is essentially the superficial value, derived sim ply by dividing thevolumetric flow rate by the pipe section area, w itho ut taking accoun t of any parti-cles that may be conveyed.

In dilute phase conveying, and at low va lues of solids loading ratio, the in-fluence of the conveyed material wil l have negligible effect in this respect. A t asolids loading ratio of 100, however, the material will occup y approximately 1 0%of the vo lume at atmospheric pressure and so the actual air velocity will be about10% higher. At increased air pressures and solids loading ratios th e percentagedifference wi l l be correspondingly h igher.


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148 Chapters

I t wo uld be a very complex and t im e co ns um ing process to evaluate actualai r velocities and so for convenience th e superficial ai r velocity is universally em -ployed. Critical values such as the m in im um conveying air velocity and conv eyingline inlet air velocity are most ly der ived from exper ience and experimental work.In such cases it is the superficial air velocity that is used .

A s with th e flow of air only in a pipeline, or single phase f low, th e flow of agas-solid mixture wil l also result if there is a pressure difference, provided that aminimum value of conveying air velocity is maintained. Material flow wil l be inthe direction of decreasing pressure, whether it is a positive pressure or a vacuumconveying system. Since air is com pressib le, the volum etric flow rate of the airwill gradually increase, from the material feed point at the start of the pipeline, toth e material discharge point at the end of the pipe l ine . In a single bore pipe l ine theconveying air velocity will also grad ually incre ase over the length of the pip elin e.

This means that it is the value of the convey ing air velocity at the mater ia lfeed point, or the start of the p ipel ine , that is critic al, sin ce the va lue of the convey-ing air velocity will be the lowest at this point, in a single bore pipeline. In deter-mining the necessary volumetric flow rate of air, therefore, it is the conditionsprevailing at the start of the pipeline, in terms of pressure and temperature, thatmus t be taken into account.

2 VOLUMETRIC FLOW RATEVolumetric flow rate in ftVmin has been chosen for use in all the mathematicalmodels developed and on all graphical plots presented in this Handbook. Althoughit is not the basic fps unit , f tVmin is more widely quoted in trade literature onblowers and compressors. It is also m ore com patib le w ith the use of ft/min for airvelocity. Inch es have been used for all pipe l ine bore references.2.1 Presentation of EquationsThe m ajority of the equations that follow are presented in terms of both v olum etricflow rate and conveying air velocity. The reason for this is the need to providemodels that can be used for both the design of future systems and for the checkingof existing systems. In the design of a system a specific value of conveying airvelocity wil l generally be recommended, together with a pipe bore, and it is thevalue of volumetr ic flow rate that is required fo r specification of the blower orcompressor.

In order to check an exis ting system it is usual ly necessary to determine th econveying air velocity for the particular conditions. In addition to providing theappropriate models for the evaluation of air requirements and conveying air ve-locities, graphical representation of these models is also presented. With pro-grammable calculators and computers, models such as these can be handled quiteeasily and quickly .


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Graphs, however, do have the advantage of showing visual ly the relative ef-fects of the various parameters, and in some cases can be used very effectively toillustrate particular processes, and have been adopted widely in this Handbook.The main equations that are developed are addit ional ly presented in SI units, andreference to the equivalent SI units for all symbols an d dimensions is given in theNomenclature at the end of this chapter.2.2 The Influence of Pipe BoreThe diameter of a pipeline probably has the most significant effect of any singleparameter on volumetric flow rate. The volumetric flow rate through a pipelinedepends upon the mean velocity of flow at a given point in the pipeline and thepipe section area. The relationship is :

V = C x A144 frVmin (1 )where V = volumetr ic flow rate - ft / m i n

C = conveying air velocity - ft/minand A = pipe section area - in 2

so that

for a circular pipewhere d = pipe bore - n

n d2CV =- ft/mn (2)or

C _ _ 576 V f t /min (3)

A graphical representation of the above models is presented in Figure 5.2.This is a plot of volumetric air flow rate against conveying air velocity, with aseries of lines representing the relationship fo r different sizes of pipe. Conveyingair velocities from about 500 ft/min to 10,000 ft/min have been considered in orderto cover the two extremes of minimum velocity in dense phase conveying andmaximum velocity in dilute phase conveying, although velocities as high as10,000 f t/min would not n orm ally be recomm ended.


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150 C h a p t e r 5

5000

4000

u 3000I22000

1000

0

pfipetinerBore - in.10

0 8000 10,000000 4000 6000Conveying Air V elocity fi/minFigure 5.2 The influence of air velocity and pipeline bore on volumetric flow rate.2.2.1 Reference ConditionsIt should be noted that the volumetric flow rate on this graph is not related to anyreference condition. It is the actual flow rate at any given condi t ion of air pressureand temperature. E qua t ions 5.1 to 5.3 and F igure 5.2 can be used either to deter-mine the resulting velocity for a given flow rate in a given p ipe size, or to deter-mine the required volumetric flow rate knowing the velocity and pipe bore.

Blowers and compressors are usually rated in terms of ' free air delivered'.This means that the volumetric flow rate is related to ambient conditions for refer-ence purposes - usually a pressure of 14-7 lbf/ in 2 absolute and a temperature of59F (519 R). The influence of pressure and temperature on volumetric flow rate,and hence velocity, is discussed in the fo l lowing sections.2.2.2 Pipeline InfluencesThe air at the start of a conveying line wil l always be at a higher pressure than thatat the end of the line because of the pressure drop necessary for air and materialflow. Air density decreases with decrease in pressure and so, in a constant borepipeline, the air velocity wil l gradually increase from the start to the end of thepipeline. The air mass flow rate wi l l remain constant at any section along a pipe-line, but as the rat ing of blowers and compressors is generally expressed in volu-metric flow rate terms, then knowledge of the air mass flow rate is of little value inthis situation.2.3 The Ideal Gas LawThe relationship between mass and volumetric flow rate, pressure and temperaturefor a gas can be determined from the Ideal Gas Law:


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144 p v = m a R T (4)where p = absolu te pressure of gas - I b f / i n

V = actual volumetric f low rateof the gas at the pressu re, p - f tVmin

ma - mass flow rate of gas - Ib /minR = characteris t ic gas constant - ft Ibf / lb R

and T = absolute temp era ture of gas - R= ? F + 460

R earranging th is g ives :

P VT 144

For a given gas and constant mass flow rate:P V

T = constantso that

T Twhere subscripts , and 2 can relate to any twoanyw here a long the conveying pipe l ine

or in terms of ' free air condi t ions '

P (6)

where subscript 0 refers to reference co nditio nsusua l ly pu = 14-7T0 = 519Ibf/in 2 absoluteR

and V0 = free air delive red in ft3/minan d subscript i refers to actual conditions, anywherea long the convey ing pipe l in e


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152 C h a p ters

2.3.1 Working RelationshipsSubstituting reference v alues into Eq uatio n 6 and rearranging gives:

51 9 x p.V0 = x F,1 4 - 7 x T }

P^ V,= 35-3 x 1L fWmin (7)

P^ V,= 2-843 x 1 mV s (7 si)

or alternativelyT, VF, = 0-0283 x - f t 3 /min - - - - - (8)

T v= 0-352 x -- m3/s (8 si)

2.3.2 Gas ConstantsThe constant, R, in Equation 4 has a specif ic v alue for every gas and is obtainedfrom:

r >

R = ftlbf/lbR - - - (9)Mwhere , / ? = universal gas constant - ft Ibf/lb-mol R= 1545 ft Ibf/lb-mol R= 8-3143 kJ /kg-molK SIand M = mo lecular weight - mol

Values for air and some commonly employed gases are presented in Table 5.1:Whichever gas is used, the appropriate valu e of R fo r that gas is simplysub-stituted into Equation 4 and the d esign process is exac tly the sam e.


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Table 5.1 Values of Characteristic Gas Constant

G as

AirNitrogenOxygenCarbon dioxideSteamArgon

Equat ion

N 202C02H20Ar

Molecula r WeightM

28-9628 - 0132-0044-0118-0139-95

Gas ConstantR - ft Ibf/ lb R

53-355-248-335-185-838-7

2.3.2.1 The Use of NitrogenIt wil l be noticed that there is little more than 3% difference between the values ofR for air and nitrogen. This is not surprising since about 7 8 % o f air, by volume, isnitrogen, and the two constituent gases have very similar molecular weights. As aconsequence little error would result if a system in which nitrogen gas was usedfo r conveying a material, was to be inadvertently designed on the basis of air.

If carbon dioxide or superheated steam was to be used to convey the mate-rial, however, there would be a very significant error. Gases other than air andnitrogen are often used fo r specific pneumatic conveying duties.3 THE I N F L U E N C E OF PRESSUREThe influence that air pressure has on volumetric flow rate is shown graphically inFigures 5.3 to 5.5 to highlight the influence of compressibility. These are plots ofvolumetric flow rate, at the reference atmospheric pressure of 14-7 lbf / in2 absolute,against actual volumetric flow rate.

To s impl i fy the problem an isothermal situation has been assumed in orderto isolate the in f luence of pressure i.e. T, = T u. Once again this is a linear relation-ship. A series of lines representing th e relationship fo r different air pressures isgiven on each graph, and each one illustrates the relationship for a different type ofsystem.3.1 System InfluencesIn Figure 5.3 the pressures considered range from 0 (atmospheric) to 12 lbf / in2gauge and so is appropriate to low pressure, typ ical ly d i lu te phase, conveying sys-tems. If an air flow rate of 1500 ft 3/min at free air conditions is considered it canbe seen from Figure 5.3 that the actual volumetric flow rate of the air at the mate-rial feed point, at the start of the conveying line, will be reduced to about 825fVVmin if the air pressure is 12 lbf/ in 2 gauge.

Pipeline bore is not included at this stage since it is simply the effect ofchanges in air pressure that are being illustrated.


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154 Chap ter 5

2000.3

1500II3000

&Hta|(2 500o

Air Pressuregauge

O L400 800 1200 1600 2000

Volumetric Flow R ate - ftV min at 14-7 Ibf7in2 absFigure 5.3 The influence of air pressure on volumetric flow rate for low pressure sys-tems.

Alternatively, the flow rate can be determined from Equ ation 5.8:0 - 0 2 8 3 x 519 x 1500

1 ( l 4 - 7 + 12J= 825 f V V m i n

In Figure 5.4 the pressure ranges from 0 to 50 lbf/in2 gauge and so is rele-vant to high pressure conveying systems. If the air at the material feed point is at50 Ibf/in2 gauge, a free air flow rate of 1500 ft3/min will be reduced to about 340frVmin, as can be seen from Figure 5.4. In both of these cases the air wil l expandthrough the co n v ey in g l ine back, approx imate ly , to the free air value of 1500ft /min, at the discharge hopper and filtration unit at the en d of the pipe l ine .

In th e case of a vacuum system, free air condi t ions prevail at the materialfeed point. The air then expands beyond this and so, if the exhaust is at -8 lbf/in2gauge, 1500 ftVmin of free air wil l increase to about 3290 f tVmin, as can be seenfrom Figure 5.5. Alternat ively , the air flow rate can be determined from Equat ion5.8 once again:

0 - 0 2 8 3 x 5 1 9 x 1500( l4 -7 - g)

= 3288 ftVmin


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2000.sJ1500

3000

I500oE 0

Pipeline Exit- 1 5 0 0 f t 3 / m inFlow

Air Pressure- l f > f / i n 2 .gjjuge j

Pipeline Inlet- 340 ftVrnin

400 800 1200 1600Volumetric Flow Rate - ftV min at 14-7 lbf/in2 ab s

2000

Figure 5.4 The influence of air pressure on volumetric flow rate fo r high pressure sys-tems.It can be seen from this range of values that it is extremely important to take

this compressibility effect into account in the sizing of pipelines, and particularlyso in the case of combined positive and negative pressure systems.

35003000

I 2500u 20005t / i

(S 1500|1000I 500

Air Pressure- lbf/in 2 gaugefipeiineiExit-]3290 ftj/min

400 800 1200 1600Volumetric Flow Rate - ftV min at 14-7 lbf/in2 abs

2000

Figure 5.5 The influence of air pressure on volumetric flow rate fo r negative pressuresystems.


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156 Chapters

An additional po int to note is one of the m any fu nd am ent al differences be-tween pos it ive pressure and vacuu m con veying systems. With positive pressureconveying systems the filtration plant can be sized on the basis of the free air flowrate value. For negative pr essure con vey ing systems, how ever, this is not the case,as wil l be seen from Figure 5.5.

If th e system exhausts at a vacuum of 8 Ibf/in2 , fo r example, th e flow rate tobe handled by the filter will be about 3290 f t '/mm which is more than double thefree air flow rate value, and the filter w i l l have to be sized on 3290 and not 1500f V V m i n .3.2 Velocity DeterminationIfFigures 5.3 to 5.5 are used in conjunction with Figure 5.2, it w i l l be possible todetermine the resulting conveying air velocities for given conditions. An alterna-tive to this procedure is to combine the models for actual volumetric flow rate andconveying air velocity.3. 2. 7 Working RelationshipsFrom Equation 2 the actual vo lum etr ic flow rate:

V] =~576~

and from Equation 7 free air delivered:

v. - 3 5 - 3 * \and substituting Equation 2 into Equation 7 gives:

,2 f~ 3000t-,

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158 Chap ter 5

Figure 5 .6 clearly i l lustrates the inf luence of pressure on conveying air ve-locity in a single bore pipe l ine . The slope of the constant p ipe bore curves increaseat an increasing rate with decrease in pressure. The reason fo r this can be seenfrom Equation 1 1 . Conveying l ine inlet air pressure, ph is on the bottom of theequation, and so as its value gets lower, small changes in its value have a moresignificant effect. This is particularly so for negative pressure systems, and is quitedramatic at high vacuum, as shown on Figure 5.6.3.2.3 Suck-Blow SystemsO n Figure 5.7 the expansion l ines for a typica l combined positive and negativepressure system are superimposed. This illustrates the problems of both pipelinesizing, with this type of system, and the relative expansion effects at different airpressures.

With 1000 ft3/min of free air, a 6 in bore pipeline would be required for thevacuum line. This would give an air velocity of about 3560 f t /min at the materialfeed point and would expand to approximately 4900 ft/min if the exhaust was at -4Ibf7in2 gauge. If the pressure on the delivery side of the blower was 6 lbf / in2 gauge,a 5 in bore pipeline would be requi red . This w o u l d give pick-up and exit air ve-locities of about 3640 and 5130 ft/min respectively.

It w i l l be noted that the pick-up and exit air velocities are very similar forthe two parts of the system, but different size pipelines are required.

7000

| 60005 2if 5000_ o< ut4000

3000

2000

-4 -2 0 10 12Air Pressure - Iblfin gauge

Figure 5.7 Velocity profile for a typical combined posit ive and negative pressure(suck-blow) system with a free air flow rale of 1000 ftVmin.


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The free air flow rate is clearly the same for the two parts of the system andso it wil l be seen that it is entirely due to the in f luence of the conveying line inletair pressure on the compressibility of the air.

In the above case it has been assumed that the material is conveyed in dilutephase suspension f low and that the m i n i m u m conveying air velocity for the mate-rial is about 3000 ft/min. If a 20% margin is allowed when spec i fy ing a conveyingline inlet air velocity, th is would need to be about 3600 f t /min.3.2.4 Low Pressure SystemsIn Figure 5.8 a typical velocity profi le for a low pressure dilute phase conveyingsystem is shown. In this case the minimum conveying air velocity for the materialis approximately 2700 ft/min and so with a 20% margin the conveying l ine inletair velocity needs to be about 3240 ft/min. With a free air flow rate of 900 ftVmin,and a conveying line inlet air pressure of 14 lbf/in 2 gauge, a 5 in bore pipelinewould be required.

The resulting conveying l ine inlet air velocity is about 3380 ft/min, and itwill be seen that the air velocity gradually increases along the length of the pipe-line as the air pressure decreases. At the end of the pipeline, at atmospheric pres-sure, the conveying line exit air velocity wi l l be about 6600 ft/min in this 5 in borepipe l ine .

The above is s i mp l y an example to i l lustrate the variation in conveying airvelocity from feed point to mater ia l discharge in a pipel ine . For the design of aconveying system Equation 5 .10 would be used to evaluate the free air require-ments.

.70006000

I 5000< u

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160 Chap ter 5

For a 5 in bore pipeline, and with a conveying l ine inlet air pressure of 14lbf/in 2 gauge (28-7 lbf/in2 absolute) and a conveying l ine inlet air velocity of 3240ft/min, with air at 59F, this would come to 862 ftVmin. If the influence of pres-sure was not taken into account, and the volumetric flow rate was evaluated on thebasis of an air velocity of 3240 ft/min, effectively at the end of the pipeline, theconveying line inlet air velocity that would result at a pressure of 14 lbf/ in 2 gaugewould be about 1660 ft/min, and the pipeline would almost certainly block.

The influence of air pressure on conveying air velocity is illustrated furtherwith Figure 5.9. This is a plot of conveying air velocity plotted against air pres-sure, and is drawn for a free air flow rate of 1000 ftVmin in a 6 in bore pipeline.During the operation of a pneumatic conveying system the conveying line inlet airpressure may vary slightly, particularly if there are variations in the feed rate of thematerial into the pipeline. If the feed rate increases for a short period by 10%, theconveying line inlet air pressure will also have to increase by about 10% in orderto meet the increase in demand.

If the minimum conveying air velocity for the material was 3000 ft/min, andit w as being conveyed with a conveying l ine inlet air pressure of 8 lbf/ in 2 gauge,an increase in pressure to only 1 2 lbf/ in gauge would probably be suff icient toresult in a pipeline blockage. At low values of air pressure, conveying air velocityis very sensitive to changes in pressure, and so due consideration must be given tothis when deciding upon a safety margin for conveying line inlet air velocity, andhence the volumetric flow rate of free air, to be specified for the system.

3600

B13200M 2800Iu

2400

Pipeline Bore - 6 in|Air Temperature - 59 F

10 12 14Air Pressure - lbf/in 2 gauge

16

Figure 5.9 The influence of air pressure on conveying ai r velocity for a free ai rrate of 1000 ft3/min.

18

flow


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3.2.5 Stepped PipelinesIn the low pressure case illustrated inFigure 5.8 the m i n i m u m conveying air ve-locity for the material was about 2700 f t /min and with a 20% margin this was3240 f t /min. With the blower available del iver ing 900 ft3 / m in of free air at 14lbf / in2 gauge, the resulting conveying l ine inlet air velocity in a 5 in bore pipelinecame to 3380 ft/min. As a pick-up velocity this is quite acceptable but the velocityat the end of the pipeline is quite unnecessarily high at 6600 ft/min.

The velocity profile for a 6 in bore pipeline is also included on Figure 5.8. Itcan be seen from this that if the pipeline was expanded from 5 to 6 inches at apoint in the flow where the pressure was about 5 lbf / in 2 the maximum value ofconveying air velocity in the pipeline could be limited to about 5000 ft/min. TheFigure 5 .8 p ipe l ine is re-drawn in Figure 5.10 with such a step.

From Figure 5.10 it wi l l be seen that the velocity profi le has been main-tained between very much narrow limits as a result of the step to 6 inch bore. Thevelocity profile for an 8 inch bore pipeline has also been added and it wil l be seenthat expansion into such a bore would not have been possible. At the step into the6 inch bore line the velocity drops from 4920 to 3420 ft/min and this is quite ac-ceptable.

Problems arise when the step in bore is incorrectly positioned and the veloc-ity in the larger bore section of pipel ine falls below the m i n i m u m value for thematerial. The fact that the velocity at exit from the pipe l ine is lower than that atentry to the step is of no consequence.

7000.3

60008 5000I

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162 Chapters

Stepped pipelines ar e considered in more detail in Chapter 9. Equations fo rthe evaluation of pressure and velocity are developed and steps for both positivepressure and vacu um co nve yin g systems are considered.

4 THE INFLUENCE OF TEMPERATUREIn the above figures the influence of temperature was not included, so that theinfluence of pressure alone could be illustrated, and so it was assumed that al lflows and expansions were isothermal and at the standard reference temperature.In Equations 7 and 8 the inf luence of pressure and tem perature on actual volum et-ric flow rate is presented . If the influence of pres sur e is neglected, in order to sepa-rate the effect of temperature, the equation reduces to :

V } = - - f t 3 / m i n - - - - - - - - - (12)

The influence that air temperature can have on vo lumet r ic flow rate isshown graphically in Figure 5.1 1. This is a plot of volumetr ic flow rate at the ref-erence temperature of 59F, against actual volumetric flow rate at a given tem-perature. It should be noted that in Equat ion 12 and Figure 5.1 1 all pressures arestandard atmospheric so that the influence of temperature can be considered inisolation from that of pressure.

It can be seen from Figure 5.1 1 that changes in temperature do not have thesignificant effect on volu m etric flow rate that changes in pressure can have. This isbecause the influence of temperature is in terms of the ratio of absolute tempera-tures and the 460 that has to be added to the Fahrenhei t temp erature has a consid-erable dampening effect. Figure 5.11 illustrat es the inf luence of temperature overthe range of temperatures from -40F to 200F.Air temperatures higher than 200F can be experienced, however. Air at atemperature of 200F wil l result from the compression of air in a positive dis-placement blower operating at about 14 lbf/in2 gauge, and from a screw compres-sor del iver ing air at 45 lbf/in2 gauge it could be more than 400F. In some casesthe m ateri al to be convey ed m ay be at a high temperature and this could have amajor influence on the c o n v e y in g air veloci ty .

It will be seen from Equation 1 1 that if the tem perature is reduc ed, then thevelocity will fall. This is because the density of the air increases with decrease intemperature. The volumetric flow rate of air that is specified m ust be sufficient tomaintain the desired conveying line inlet air velocity at the lowest temperatureanticipated. D ue account, therefore, must be taken of cold start-up and winter op-erating conditions, particularly with vacuum conveying systems which draw inatmospheric air. This point is illustrated qui te forcefully in Figure 5.12.


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1200|1000cII 800I600H a 400

E 200

.200

0 100000 400 600 800Volumetric Flow Rate at 59F - ftVmin

Figure 5.11 The influence of air temperature on volumetric flow rate.Figure 5.12 is drawn for a 6 in bore pipeline and an inlet air pressure of 15

lbf / in2 gauge. It wil l be seen from this that conveying air velocity can be very sen-sitive to temperature. The average gradient on this plot is about 5 ft /min per Ftemperature change, and so if the temperature of the conveying air was reduced forsome reason it could result in pipeline blockage in a system operating with a pick-up velocity close to the minimum conveying air velocity for the given material.

0 20 40 80 120Air Temperature - F 160 200Figure 5.12 The influence of air temperature on conveying ai r velocity for a free ai rflow rate of 1000 frVmin.


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164 Chapters

4.1 Conveyed Material InfluencesThe above analysis refers to the situation with regard to the air on ly . For the con-veying line, however, th e material also has to be taken into account , and althoughthe air may be at 60F, the m ateri al to be convey ed m ay be at 400F or more. Inorder to determine the temperature of the conveyed suspension it is necessary tocarry out an energy b alance. If a control surface is taken around the m aterial feed-in g device and the imm ediate pipelin es, an energy balance gives:

(m Cp t) + (m Cp t ] = (m Cp t ] ..... (13)V / p \ la \ 'swhere m = mass flow rate - Ib/h

Cp = specific heat - Btu/Ib Rand t = temperature - Fand the subscripts refer to :p = conveyed material or product

a = airan d s = suspensionif heat exchanges with the surroundings, kinetic energies and other minor energyquantities are neglected.

It is the temperature of the suspension, ts, that is required and so a rear-rangement gives:

mt Cps > m x Cp, a

From continui tym s = m a + mp I b / h (14)

and by definitionmp = < / > m a I b / h ........ (15)

where < j > is the solid s loading ratio of the conveyed materialan d

Cps = Btu/lbm a + m p


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Air Requirements 165Substituting these gives:

0 Cpp tp + Cpa ta(16)

With so many variables it is diff icul t to i l lustrate the re la t ionsh ip graphi-cally. One case has been selected, however, for a conveyed material at a tempera-ture of 60F, having a specific heat of 0-24 Btu / lb R and this is presented in Figure5.13. This illustrates the influence that conveying l ine in le t air temperature andsolids loading ratio can have on the resulting suspension temperature.

Figure 5.13 relates to the dilute phase conveying of a material with a posi-tive displacement blower, where the conveying l ine inlet air temperature might beup to about 220F. This shows that the solids loading ratio has a dominating effecton the suspension temperature, even with dilute phase conveying. Unless the con-veyed material has a very low specific heat value, and is conveyed in very dilutephase, the temperature of the conveyed suspension will be close to that of the ma-terial to be conveyed. If cold air is used to convey a hot material, therefore, thecooling effect on the material of the cold air wil l be minimal. This is illustrated inmore detail in Figure 5.14 where material and air in let temperatures of 1000F and60F respectively have been considered.

Solids Loading Ratio120

I 100908070

60

Material: ! i :Inlet Temperature - 60 F \Specific heat - 0-24 Btu/lb R

60 100 140 180Air Inlet Temperature - F

Figure 5.13 The influence of air inlet temperature and solids loading ratio onthe equilibrium temperature of the suspension.


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166 Chapter 5

1000

' 800I

! 600I

I 4 0 0}

[ 200II! 0

Material:Inlet Temperature - iqOOF"Specific Heat - b'24BtC7Ib R

12 16Solids Loading Ratio 20

Figure 5.14 Influence of solids loading ratio on the eq u i l i b r iu m temperature of thesuspension.

Figure 5.14 is also drawn for a material having a specific heat value of 0-24Btu/lb R and shows the influence of solids loading ratio. It must be stressed thatthe suspension of material and air will only reach the equilibrium temperature atsome distance from the pipeline feeding point, fo r thermal transient effects have tobe taken into account.

The heat transfer process depends addit ional ly upon the thermal conductiv-ity and shape and size of the particles. It is a time dependent process and with thehigh velocities required in dilute phase conveying, eq uil ibr iu m will not be fullyestablished by the end of the pipeline with many materials. Since volumetric flowrate decreases with decrease in temperature, if there is any doubt with regard to thetemperature of the air at the start of a conveying line, the lowest likely valueshould be used fo r design purposes.

Particular care should be taken with vacuum conveying systems that are re-quired to convey hot materials. There are several points that need to be taken intoconsideration here. At the material feed point into the pipel ine air at atmospherictemperature will generally apply. At any steps in the pipeline, however, the air willbe at a significantly higher temperature as a result of the heat transfer. Care mustalso be exercised with the specification of the exhauster, fo r this is generally basedon the volumetric flow rate of the air drawn into the exhauster.4.1.1 Specific HeatSpecific heat is clearly an im portan t property in this analysis and typical v alues aregiven in Table 5.2 and specific heat values for air and water are also added fo rreference purposes. That for air is a basic element in the model, of course.


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Table 5.2 Typical Specific Heat V aluesMaterial

Metals CopperNickelSteelA l u m i n u mMagnesium

Non-Metals Sand, dryFi rebr ickCoalCottonBakel i teCork

Note A irWater

Specific HeatBtu / lb R

0-090 - 1 10 - 1 10-210-240- 190-230-310-310-380450-241-00

It will be noted that water has a very much h igher specific heat value thanany of the other materials listed, and so if a material has a high moisture contentthis could have a considerable inf luence on the specific heat of the material.

5 THE INFLUENCE OF ALTITUDEA s elevation increases, pressure naturally decreases, and so the elevation of a plantabove sea level should a lways be noted fo r reference. With increase in elevationthere is a corresponding drop in the va lue of the local atmospheric pressure andthis wil l inf luence many of the velocit ies and volumetric flow rates in the calcula-tions. There is, of course, a direct inf luence on the performance of vacuum con-veying systems, s ince any reduction in atmosp heric pressure auto m atically reducesth e available pressure difference. The var ia t ion of the local value of atmosphericpressure with the elevation of a plan t above sea level is presented in Figure 5 .15 .5.1 Atmospheric PressureFigure 5.15 shows that for a plant located 3000 ft above sea level there is a reduc-tion of more than 10% in atmospheric pressure, and equates to a reduction in pres-sure of about 1-6 lbf/in 2 or 3-3 in Hg. It wil l be seen from this that the influ enc e ofaltitude should be considered in detail for plants located above about 1000 ft, par-ticularly if a vacuum conveying sys tem is to be considered. The normal atmos-pheric pressure at sea level can fluctuate quite n atu rally by 1 in Hg on a day today basis , w hic h equates to a change in e leva t ion of about 1000 ft .


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168 Chapter 5

0 2000 8000 10,000000 6000Plant Elevation - ft

Figure 5.15 The influence of plant elevation on the local value of atmospheric pressure.

6 MOISTURE AND CO NDENSATIO NAir natu rally contains a certain amount of water vapor. The amount of water vaporthat air can contain depends upon both temperature an d pressure. A decrease intemperature or an increase in pressure can result in condensation occurring whenthe air passes through the saturation point. The problem with condensation, how-ever, is that it can sometimes be very difficult to predict. The presence of moisturemay even be unknown if it cannot be seen, although its effects will certainly beevident.

The addition of water to a bulk solid can have a significant effect on itsflowability. Condensation usu ally occurs on the walls of containing vessels andsurfaces such as hoppers, silos and p ipel ine s. A ltho ugh the effect might be local-ized, the material/surface interface is critical to the smooth operation of most bulksolids handling plants. Some materials ar e hygroscopic an d will naturally absorbmoisture from the air without condensation occurring. For these materials it isgenerally necessary to dry the air, that comes into contact with the material, to avalue of relative h um idity below that at which the material is capable of absorbingatmospheric moisture.

Equations are derived and presented that will enable the amount of moistureassociated with air to be evaluated. Graphs an d charts are also included, to i l lus-trate the influence of the main variables, and to give some idea of the order ofmagnitude of the potential problem. From the data presented it will be possible todetermine rates of condensation an d evaporation in processes such as the compres-sion an d expansion of air, as wel l as heating and cooling.


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6.1 HumidityThe amount of water vapor that air can support is not constant but varies with bothtemperature and press ure. Once air is saturated, a change in either temperature orpressure can result in condensation occurring. The terms used here are relativehumidi ty and specific humidi ty , and the Ideal G as Law, commonly used fo r air,provides th e basis fo r modeling moist air.

Specific humidity is the ratio of the mass of water vapor to the mass of dryair in any given volume of the mixture . It is usu ally expressed in terms of Ib ofwater per Ib of dry air.Relative humidity is the ratio of the partial pressure of thevapor actually present to the partial pressure of the vapor when the air is saturatedat the same temperature. It is us ua lly expressed as a percentage, with 100% repre-senting saturated air.

Thus, specific humid i ty is a measure of the mo isture content of the air, andrelative humid i ty is a measure of the ease with which the atmosphere wil l take upmoisture. R elative hu m idity is usu ally obtained by means o f wet- and dry-b ulbthermometers, or some other form of hygrometer, and specific humidity can becalculated.6.1.1 Specific H um iditySpecific humidity, c o , is the ratio of the mass of water vapor to the mass of dry airin any given volume of the mix tu re :

mvc o = - lbv/ lb a - (17)m awhere m v = mass of vapor - Iban d m a = mass of air - Ib

From the Ideal G as L aw:1 4 4 p a V = maRaT (18)At low values of partial pressure, water vapor can also be treated as an Ideal

Gas, and so:144 pv V = mvRvT - - - (19)

where pa = partial pressure of air - lbf/in 2pv = partial press ure of water vapor - l b f / i n

2V = volume of mix ture - f t 3R = characteristic gas constant - ft Ibf/lb Rand T = absolute temperature of mixture - R


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170 Chapter 5

and note that V and T w i l l be the same fo r both the air and the vapor, sincethe two constituents are intimately mixed.The partial pressure of water vapor, pm varies with temperature. For refer-ence, values are given on Figure 5.16. The partial pressure of water vapor in -creases exponen tially with increase in tempe rature and so the partial pressure axison Figure 5.16 is split in two. The axis on the right hand side, for high temperatureair, is magnified by a factor of ten, compared with that on the l e f t hand side forlow temperature air. It will also be seen that at 32F, the freezing point for water,that a significant quantity of vapor s t i l l exists in the air.At temperatures below 32F, therefore, water vapor w i l l precipitate as iceonto cold surfaces, without passing through the liquid phase. By the same reason-ing, wet surfaces that are frozen can be dried, for the ice evaporates directly intovapor, without the surface becoming wet.The characteristic gas constants for the two constituents can be obtainedfrom Equation 9 and values for various gases, including steam, are given in Table5.1. By substituting for R from Equation 9 into Equations 18 and 19 gives:

144 pa V M amn = I b (20)

and mv =144 pv V Mv

ITr lb (21)I.00.1

o

EftJO

I-20 0 20 40 60 80 100 120 140

Saturation Temperature of Air - FFigure 5.16 The Variat ion of saturation vapor pressure with temperature.


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Substituting Equations 20 and 21 into Equation 17 gives:

C O = " 1Mb. - - - - - - - - (22)Pa Ma

since V and T are common to both cons tituents .From Dalton's Law of Partial Pressures:

P = P a + P v l b f / i n 2 - - - - - - - (23)where p = total pressure, which for most applications= atmospheric pressure - l b f / i n 2 abs

Thus Specific H u m i d i t y , C O , i s given b y :

C O = - , r I b v / l b a (24)29 (p-pv)Alternatively:

0'622 pvc o = 1Mb. - - - - - - - (25)P-Pv

6.1.1.1 T he Inf luence of TemperatureA graphical representation of this equation is given in Figure 5.17. This is a graphof the moisture content of saturated air, in pounds of water per 1000 cubic feet ofair, plotted against air temperature. This graph is also plotted with a split moisturecontent axis in a s i m i l a r manner to Figure 5.16.The moisture content, in volum etric terms, is obtained simply by multiply-ing Equation 25 by the density of air. Figure 5.17 is derived for saturated air atatmospheric pressure, which means that this is the maximum value possible for agiven value of temperature. It is drawn with two sections, one covering cold airand the other warm air. It will be seen from these that the capability of air for ab-sorbing moisture increases very considerably with increase in temperature.The moisture con tent of air can also be expressed in flow rate terms. This isdetermined simply by using the flow rate f o r m of the I d e a l G as Law, as presentedin Equation 5.4, rather than the static f o r m in Equations 18 and 19. Figure 5.18 issuch a plot and shows the magnitude of the potential moisture problem, of waterassociated with air, very well.


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172 Chap ter 5

0 .60.5

2 0.4X)

1 3 0.3u0.2

0 .10

Saturated Aid atAtmospheric Pressure6

5i3 ~

I-40 -20 0 20 40 60 80 100 120 140

Air Temperature - FFigure 5.17 The influence of temperature on the moisture content of saturated air.

Figure 5.18 is drawn for saturated air at standard atmospheric pressure andshows how the quantity of water in the air is influenced by both the volumetricflow rate of the air and its temperature.

400 800 1200 1600 2000Volumetric Flow Rate of Air - ftVmin at 14-7 lbf/in2 ab s

Figure 5.18 The influence of temperature on the flow rate of moisture associated withsaturated air.


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Air Requirements 173The influence of the volumetr ic ai r flow rate is linear, of course, but that oftemperature is not, as i l lustrated w ith Figure 5 .17 . For air at atmospheric pressurethis represents the worst case, in terms of the flow rate of water associated withair, since it is drawn fo r saturated air.6.1.1.2 T he In f luence of PressureTw o further graphical representations of Equat ion 25 are given in Figures 5.19 and5.20. These are graphs of moisture content of air , in pou nd s of water per poun d of

air, drawn to illustrate th e influence of air pressure. Figu re 5.19 is a graph of spe-cific humidity plotted against temperature, with lines of constant pressure drawn.The pressures cover a range from -10 to 50 lbf/in2 gauge and so are appropriate toboth positive and negative pressure conveying systems.

Figure 5.20 is a sim ilar plot, but wit h the x-axis and the family of curves in-terchanged. Both plots are for saturated air. These show that pressure also has asignificant effect on the a m o u n t of water vapor that air can absorb, decreasing withincrease in pressure. Figure 5.20 shows th e influence of pressure on the moisturecontent capability of air very well , part icular ly at low pressures and under vacuumconditions.

These plots can be used to determine w hether condensation is likely to occurin processes such as the compression an d cooling of air. For air that is not initiallysaturated, however, account has to be taken of the initial relative hu mid i ty of theair.

0-3

.o

.o 0-2

3 3o< a 0 - 1

-10 -5 0 5 10 15

40 80 120 160Saturated Air Temperature - F

200

Figure 5.19 The influence of temperature and pressure on the moistu re content of satu-rated air.


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174 Chapter 5

-10 -5 10 20 30 40Air Pressure I b f / i n 2 gauge

Figure 5.20 The influence of pressure an d temperature on the moisture content of satu-rated ai r.6.1.2 Relative HumidityRelative humidity, (p, is the ratio of the partial pressure of the vapor actually pre-sent, to the partial pressure of the vapor when the air is saturated at the same tem-perature:

(26)

where pv = partial pressure of vaporan d pg = partial pressure of vapor at saturationThis is usually expressed as a percentage.

This si tuation can be best represented with lines of constant pressure super-imposed on a temperature vs. entropy plot for H20. Such a plot is presented inFigure 5.21. This also shows the saturation lines fo r both liquid an d vapor and howthese separate the various phases or regions. Air saturated with water vapor, andhaving a relative humidity of 100%, will lie on the saturated vapor line, g. Thevapor in air having a relative hu m id ity less than 100% is effectively superheatedsteam and so the po int will lie in the vapor regio n.Point A represents the actual condit ion of the vapor in the air and it wil l beseen that it is in the superheated steam region . On the saturation line for the vapor,at the same temperature (point B), the pressure is/?y .


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Io >P.< L >II

Liquid

Region

Constant Pressure LinesP2

Liquidplus

Vapor

SaturatedLiquid Line Region

/ D r y BulbTemperature

RegionBulb Temperature

D ew PointSaturatedVapor Line

Entropy - sFigure 5.21 Temperature vs. entropy plot for H 2O.

If the air is cooled from point A it will follow the/?? curve to the saturationline at C, which is the dew point at this pressure. From Figure 5.21 the relativehumidity is given as:

< p =

The pressures/)/ and/> 2 can be obtained from Figure 5.16, knowing the cor-responding saturation temperatures TK and Tc.6.1.3 Psychrometric ChartThe above expression, in terms of pressures, and other equations that can be de-rived from the Ideal Gas Law, however, are of little practical use in the process ofdetermining relative humidity. For this we generally use wet- and dry-bulb ther-mometers or a hygrometer. The actual, or dry-bulb temperature, of the air is repre-sented by point B on Figure 5.21 and point D represents the approximate locationof the wet-bulb temperature fo r unsaturated air.

Since this method depends upon eq u i l i b r i u m between heat and mass transferrates, the equations are rather complicated, and so data is given in charts and ta-bles. The information is usually presented in a psychrometric chart. Such a chart,fo r air at atmospheric pressure, is shown inFigure 5.22. This is a graph of specifichumidity plotted against dry-bulb temperature.


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176 Chapter 5

0-025

0-020Xl2i. 0-015X 0-010

0-005

030 1100 50 60 70 80 90

Dry Bulb Temperature - FFigure 5.22 Psychrom etric chart for air at atmospheric pressure.

The saturation line is presented on this chart and this represents a relativehumidity of 100%. This is the same line as that drawn on Figure 5.17. D ry air, orair with a relative humidity below 100%, is represented in the area to the right ofth e saturation line. Lines of both constant wet-bulb temperature and relative hu-midity are superimposed on the chart. Thus, if the wet- and dry-bulb temperaturesare known, for a given sample of air, both relativ e humid i ty and specific hum iditycan be determined quite simply. On some psychrometric charts lines of constantspecific enthalpy and specific volume are also superimposed so that this data canalso be obtained quickly if required.6.1.4 Universal ModelB y comb ining Equ at ions 5.25 an d 5.26 an equat ion is obtained in which both rela-t ive hum idity and specific humid i ty appear. This is:

C O =0 - 6 2 2 < p PgP - < P P K (27)

Thus, with relative humidity, (p, obtained from a hygrometer, the pressure,p, obtained from a barometer or pressure gauge, and the saturation pressure, pK ,obtained from Figure 5.16 or an appropriate set of tables, th e specific humidity ofany sample of air can be readily evaluated.


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Air Requirements 177N O M E N C L A T U R EACCpdmmMPRR O

StTVV

Pipe section areaVelocitySpecific heatPipe boreMassMass flow rateMolecular weightPressureCharacteristic gas constantUniversal gas constantSpecific entropyActual temperatureAbsolute temperatureVolumeVolumetric flow rate

. 7in"ft/minBtu/lb Ri nI bIb/h-l b f / i n 2

Btu/lb RBtu/lb-mol R= l - 986 B tu / l b -mo lRBtu/lb RopR= t + 460f t 3ftVmin

SIm 2m /skJ/kg Kmkgkg/s, tonne/h(1 tonne = 1000kg)-k N / m , bar(1 bar =100kN/m 2)kJ/kg KkJ/kg-mol K= 8 -314kJ /kg -mo lKkJ/kg KCK= t + 273m 3m 3/s

Greekp Density I b / f t 3

< / > Solids loading ratio= mplma

( p Relative Humidity %co Specific Humidity lb v/lb a

kg/m3

Subscriptsa AirffggPssat

Saturated liquidChange of phase (evaporation) (= g - f)Saturated vaporConveyed material or productSuspensionSaturation value or con ditio nsWater vaporR eference cond itions (free air)= 14-7 l b f / i n 2 absolutePo

Tn = 5 1 9 R= 1 0 1 - 3 k N / m 2 abs= 2 8 8 K

1 ,2 Actual conditions - usually inlet an d outlet


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178 Chapters

REFERENCE1. D. Mil ls . Opt imiz ing p neumat ic conveying. Chemical Engineer ing . V ol 107. N o 13. pp

74-80. Dec 2000.

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