University of Ottawa Chemical Engineering Faculty of Engineering

Universit dOttawa Gnie Chimique Facult de Gnie

Air Flow Measurements Chemical Engineering Practice

By

David Carey (7195956) Shail Joshi (7282674)

CHG3122

Jan 29 2016

1

CoverletterTo: Dr. Lan

From: David Carey & Shail Joshi, Group 4

Date: Jan 29, 2015

Subject: CHG 3122, Air Flow Measurements

This investigation was designed for students to apply their fundamental

knowledge of fluid mechanics and chemical process to measure accurate pressure drop

values in a 30-foot long pipe. These values were then used to calculate local velocities

using fluid mechanics concepts. These local velocities were in turn used to calculate

appropriate Reynolds numbers and friction factors in the pipes. The relationship between

friction factor and Reynolds number was analyzed by measuring the pressure drop in the

pipe and an orifice meter. Thus the velocity profiles were determined and analyzed at

varying Reynolds number.

In order to determine the velocity profile, it was necessary to calculate traverse

points in order to ensure that equal area was maintained. The traverse points were as

follows: 0.6, 1, 1.5, 2.1, 3, 4.2, 5.4, 6.3, 6.7, 7.2, 7.8. The pressure drop was recorded at

each of these traverse points, and was used to estimate the velocity profile at varying

airflow.

Airflow under contracted conditions was also investigated using the orifice meter.

The differential pressure was measured across the orifce and these values were used to

calculate the discharge coeffients at varying flow rates of air. All the measurements were

made with the aid of an electronic pressure transducer

The local velocities yielded turbulent flow regime in the pipe and the friction

factors suggested that the inside of the pipe was rough. Furthermore the discharge

coefficients calculated in orifice matched literature values.

TableofContents

Coverletter.................................................................................................................1

Equipment..................................................................................................................3

Procedure...................................................................................................................4

SummaryOfResults....................................................................................................5

Discussion...................................................................................................................7

ConclusionsAndRecommendations..........................................................................10

Appendix...................................................................................................................11Tables...........................................................................................................................................................................11SupportingFigures.................................................................................................................................................14SampleCalculations...............................................................................................................................................16References..................................................................................................................................................................19

EquipmentFigure 1: Experimental Setup. Not to scale

The experiment consists of 4 critical

components. The first of which is the

long cylindrical pipe through which the

air flows. The pipe has an internal

diameter of 3 inches. At the bottom of

the pipe a blower fitted with a

dampener. By restricting the amount of

air that is let into the pipe, the

dampeners serves as an airflow

controller. The flow rate of air within

the cylinder can be calculated using

local velocity measurements taken from the second component the Pitot tube. The

position of the Pitot tube can also be varied and it can be placed anywhere along the

diameter of the pipe. With both these apparatus it will be possible to observe the

different velocities in the pipe and where the airflow is greatest. An orifice meter with

inner diameter of 1.8 inches is placed above the Pitot tube. The orifice meter installed

with Vena contracta taps will measure the pressure drop. Furthermore several other

pressure taps are installed the length of the pipe to measure pressures at various critical

locations. Along with the orifice meter these taps will measure electronically the majority

of the data for this investigation.

Procedure1. AmbientConditionsLaboratoryconditionswererecorded2. Thepositionsforthe10-pointtraverseofthePitottubewerecalculatedandtheappropriatepencilmarksweremadeonthePitottuberuler.3. Themotorandblowerwereturnedontostartdeliveringairtothepipe4. Thedampenerwasopenedsoastoletthemaximumairflowintothepipe5. The bulk air pressure just above the blower, the pressure drop across the orifice

and the pressure drop along the pipe were all recorded.

6. The pressure drop across the Pitot tube was measured along the 10 point traverse. 7. ThedampenerwasclosedprogressivelyuntilthereadingonthePitottubewas80%oftheoriginalmaximumvalue.8. Step6isnowrepeatedandthepressuredropismeasurealongthetraverse.9. Thedampenerisnowclosedtillthereadingreaches60percentofthemaximumvalue.10. Theabovestepsarethenrepeateduntilthedampenerisfullyclosed.

SummaryOfResults1. Apitottubeoperatesbymeasuringthestagnationpressureattheentranceofthetubeandcomparingittothestaticpressurethatsurroundsthetubeintheflowstream.Advantages:-costeffectivepressuremeasurements-nomovingparts-simpletouseandinstall-lowpressuredrop-worksinhightemperaturesDisadvantages:-canbecloggediftheflowstreamincludesparticulates-iftheflowrateistoolowortoohighthemeasurementsonthetransducercouldbeincorrect2. TheaveragesvelocityandReynoldsnumberscalculationscanbefoundontheExcelsheetandintheAppendix.Thecentrepointmeasurementwasnotincluded,asthevelocitymeasurementsarefoundinbetweentheradiiofequalareacirlces.Thismakeseachmeasuredvelocityanaverageofthethevelocityfoundateachradius,meaningthatthevelocityoneithersideofthecentrepointincludesthecentrepointvelocityinitscalculation.Includingthecentrepointinatotalaveragecalculationwouldraisethevelocitytoalargervaluethanitshouldbe.3. Ifequalareaswerenotusedtofindthetransversepoints,thenanydistancesusedwouldhavetobereferencedtothecentretocreateanaveragevelocityprofile.Otherwisetheweightingofthevelocitiesintheaverageequationwouldbeincorrect.

4. OurresultsaccuratelyrepresentliteraturepublishedchartsofdischargecoefficientagainstReynoldsNumber.Theonlycauseofnon-conformitywasourfinaltwopoints,at10%and20%ofthetotalflowrate.Thedischargecoefficientforthesevalueswasabove1,whichgenerallyrepresentsanerrorinthecalculationorflaweddata.Theflaweddataismostlikelyagoodassumptioninthiscase,asforthesetwoflowrates,thedampenerfortheblowerwaseitheralmostcompletelyclosedorclosedentirely,whichcouldresultinverystrangereadingsfromtheorificeplate.5. Forthegraphofeq.11frictionfactorsandthesmoothpipefrictionfactorsvs.ReynoldsNumbers,thedatadoesnotfollowthesmoothpipecurve.Itincreasesmuchmorerapidlythanthecalculatedsmoothpipedatadoes.Thismostlikelymeansthattheinnersurfaceofthepipeisrough,causingalargerslowdownoftheairthanasmoothpipewould.6. K1isequalto-1.4andk2isequalto14.35.Ineq.13,k1isequalto2.5andk2isequalto1.75.Thedifferenceismostlikelyattributedtotheassumedroughnessofthepipe,aseq.13isonlyapplicabletosmoothpipes.Thiswouldgenerateasignificantdifference,asroughnesscannotbeaccountedforeasilyinanempiricalequationlikethefrictionfactorequationsare.

Discussion The experiment began by determining the locations that would be needed for an

equal-area ten point traverse of the tube. With these 5 circles extending from the center,

the locations could be determined for the points of measurement. The radii of these

circles on either side of center became the target points where the Pitot tube was set to

record the pressure drop across the pipe. Since these velocities are actually the average of

velocity at the radii on either side of it, the center point velocity can be ignored for the

calculation of average velocity as it is included in the measurement on either side of it.

These was held true for each of the flow rates throughout the experiment. The largest

change made to the procedure was that the blower was unable to reach 10% of its

pressure drop before the dampener was fully closed. This made the final step closer to

18% instead of 10%.

While making measurements of the pressure differences recorded by the Pitot

tube during the experiment, it was often very difficult to get a constant readout from the

pressure transducer. Quite often, guesswork and approximated averaging was used to

determine the value to be recorded. This lead to a good deal of potential error in the final

data points and calculated velocities. A way to improve this may be to have software

recording the fluctuations at each point. Once a desired time is reached, the operators can

take the mean and standard deviation to find a far more accurate value than what is taken

by guessing where the display is most constant.

When all the pressure differences were recorded, the local velocities could be

determined by using equation 1 in the lab manual, which assumes the fluid is isothermal

and incompressible. The velocities were also calculated using equation 2, which is used

when the fluid is compressible and adiabatic, gave nearly identical results to equation 1,

with an error on the scale of 0.0006% and 0.005%. This verified the assumption that the

gas was incompressible and isothermal. This assumption also lead to density being

assumed to be constant throughout the pipe at 1.225kg/m3, based on the conditions. The

Reynolds numbers were calculated from these assumptions, with the average velocities

coming from equation 1, and the density being assumed to be constant. The numbers

varied from 1.3*104 to 2.9*104, making the flow regime at all flow rates turbulent. This

turbulence was very important for the other calculations, and may be a slight source of

error for other aspects.

The orifice plate installed in the pipe plays an important role in determining

velocity of the air when it is contracted. This velocity was determined by examining the

incoming velocity and adjusting according to the size of the contraction of the orifice

plate. The Reynolds numbers for these new velocities were also calculated, using the

diameter of the orifice to determine the values instead of the diameter of the pipe. For this

case, the discharge coefficient was calculated and plotted on a graph against the

Reynolds numbers for each flow percentage. Compared to literature values and charts of

the same type (figure 4), the results matched almost perfectly, apart from the points from

the 20% and 18% flow rate trials, which are believed to be outliers. They may be

explained by low velocity having a skewing effect on the transducer readout from the

orifice plate, but the other data points follow the established literature very well, and

approach the ideal value, which is around 0.62, as the flow rate increases.

The friction factors of this system were calculated in a number of different ways,

resulting in different numbers each time. This is most likely due to the difference in how

the equations were created analytically, and what different variables they depend on. The

main friction factor was calculated using equation 11 in the lab handout, which, unlike

the other methods, does not use the Reynolds number to calculate friction factor. By

analyzing the pressure drop across the entire length of the tube, an approximation for

friction can be found. This method was compared to equation 15, which is based on the

assumption of smooth piping and a Reynolds number in the range of 3*103 to 3*106,

which fit the previously calculated Reynolds numbers of the average velocities perfectly.

The smooth pipe approximations vary from the calculated friction factors by an average

of 97.64%, which is incredibly significant. This would mean that the inside of the pipe

cannot be assumed to be smooth, as roughness causes the friction factor to become much

larger. This is also shown on a log friction factor vs. log Reynolds number graph, on

which both calculations are present. The expected smooth straight line is seen by the

smooth pipe approximation, but as the flow rates increase as used in equation 11, the

friction factors increase as well, indicating more surface disruption.

When the friction factor data was analyzed, it was then modeled in the form of the

Van Karman equation, using a y-axis of 2/

1f

and an x-axis of )8/ln(Re f . This

resulted in a much different form, with a slope of -1.419 and a y-intercept of 14.475. The

difference from the Van Karman equation shown in equation 13 of the lab handout and

this empirically found equation is most likely explained again by the surface roughness of

the pipe, bringing about much different friction factors than were used to originally find

the given equation.

ConclusionsAndRecommendationsIn Conclusion the investigation was a success to an extent. The pressure drops at

different traverse points were successfully recorded using the Pitot tube. Although the

readings fluctuated a lot due to the instrumentation. Thus a suitable solution to this

problem would be to install a more sensitive instrument, or incorporate recording

software, which measures the fluctuation of the values and calculates the appropriate

average pressure drop.

Using the pressure drop values the local velocities were using equation 1 in the

lab manual which assumes air is an incompressible and isothermal fluid. This assumption

was verified using equation 2 which calculates local velocities for compressible fluids

such as air. It was found that the both equations yielded nearly identical results with

minimal error.

These average velocities were used to calculate The Reynolds numbers. The flow

regime was found to be turbulent since the lowest Reynolds number calculated was

1.3*104 which falls under the turbulent flow criteria. These Reynolds number

calculations were all done under the assumption that the density of air stays constant at

1.225kg/m3 . This value was verified by literature, however instead of relying on literature

values, the density of air could have been measured using an aerometer.

The friction factors within the pipe were calculated using numerous equations and

methods. However the main friction factor was calculated by analyzing the pipe as

whole and using the pressure drop from the bottom to the top. This method relied

primarily on the assumption that the inside of the pipe was smooth and did not affect the

calculations. However when this assumption was compared with friction factors

calculated using equation 15 it was found that the both values varied considerably. This

meant that the inside of the pipe was rough and the smooth pipe assumption was false.

Thus in order to generate better friction factor values the roughness of the pipe could be

estimated using moody diagrams.

In depth analysis of the system was done and appropriate charts and figures were

plotted; thus the investigation was a success and generated acceptable data.

Appendix

Tables

Table 1 - Operation Parameters

Parameters

Patm (Pa) Tatm (K) air (Pas)* Do (m) Dc (m) L (m)

103591.48 295.95 0.000018 0.04572 0.0762 6.26

*Evaluated at 20 oC

Table 2 - Local pressure at each radial position and percentage flow rate

%

maximum

flow rate

r, radial position of Pitot Tube from centre (cm)

0.6 1 1.5 2.1 3.0 4.2 5.4 6.3 6.7 7.2 7.8

Kpa gauge

100% 0.0135 0.018 0.02 0.024 0.026 0.028 0.026 0.023 0.021 0.02 0.016

80% 0.012 0.015 0.017 0.019 0.021 0.022 0.022 0.019 0.018 0.016 0.013

60% 0.009 0.011 0.013 0.014 0.016 0.017 0.016 0.015 0.014 0.012 0.01

40% 0.006 0.008 0.009 0.009 0.010 0.011 0.011 0.010 0.009 0.0085 0.0075

20% 0.004 0.0045 .0055 .0055 .0055 0.0055 0.005 0.005 0.005 0.045 0.004

10% 0.0035 0.004 0.004 0.0045 0.0045 0.005 0.005 0.0045 0.0045 0.004 0.004

Table 3- Local Velocity Calculations by equation 1 (air incompressible fluid)

Table 4- Local Velocity Calculations by equation 2 (air compressible fluid)

Table 5- Percent Error Between Velocities at Equation 1 and 2

Table 6- Pressures of air in Bulk, Discharge, and Orifice

% Maximum flow rate P gauge (KPa)

(bulk)

P Top (KPa)

Discharge

Orifice

(Torr)

100 .21kpa 0.04 2.1

80 0.165 0.031 1.7

60 0.122 0.023 1.1

40 0.066 0.015 06

20 0.017 0.006 0.2

18 0.015 0.004 0.1

Table 7 - Average velocity result summary

%

Maximum

flow rate

(m/s) Re

Re (orifice)

(m/s)

(Orifice)

100 5.880925638 29673.24344 49455.40574 16.33590455

80 5.342121779 26954.61392 44924.35653 14.83922716

60 4.649622728 23460.4883 39100.81383 12.91561869

40 3.820459847 19276.80132 32128.0022 10.61238846

20 2.790784806 14081.39501 23468.99168 7.752180016

18 2.651714801 13379.69287 22299.48811 7.365874446

Table 8- Discharge Coefficients

DischargeCo.100 0.730627883

80 0.71986854860 0.77889542340 0.86659278320 1.09651241718 1.473428326

Table 9- Summary of Friction Factors

%ofDampenerOpen FrictionFactor(equation11) FrictionFactor(equation12) SmoothPipeFrictionFactor100 4.705481137 0.000539206 0.00603183680 3.009136796 0.00059359 0.00617647460 1.691281649 0.000681998 0.00639346740 0.744689461 0.000830013 0.00671739420 0.158948568 0.001136251 0.00727954118 0.09566791 0.001195842 0.007376504

SupportingFigures

Figure1- Discharge Coefficients Against Reynolds Number

Figure 2- Friction Factors of Smooth and Rough Pipes

00.20.40.60.811.21.41.6

0 10000 20000 30000 40000 50000 60000

Disch

arge

Coe

f.icent

ReynoldsNumber

DischargeCoefXicientAgainstReynoldsNumber

-6-4-2029.4 9.5 9.6 9.7 9.8 9.9 10 10.1 10.2 10.3 10.4

LogFrictionF

actors

LogReynold'sNumbers

FrictionFactorsofSmoothandRoughPipes

logf logsmooth

Figure 3- Comparison to Von Karman Equation

Figure 4: Typical Orifice Plate vs. C Relationship

y=-1.4187x+14.475012345

0 2 4 6 8 10 12

ComaprisontoVonKarmanEquation

SampleCalculations

Any parameters dependent on flow profile were calculated using the centre point

maximum flow rate and 100% flow rate.

Local velocity at the traverse points

smumkg

kPaPakPa

u

Pu P

/76.6/225.1

1000*028.0*2

2

3

=

=

=

u is the local velocity

Pp is the pressure difference measured by the Pitot tube

Average velocity through pipe

smusmsmsm

smsmsmsmsmsmsmu

un

un

ii

/79.5)/11.5/71.5/86.5

/13.6/52.6/52.6/26.6/71.5/42.5/69.4(*101

11

=

+++

++++++=

= =

u is the average velocity

Reynolds numbers of the pipe average velocities

07.29229Re/10*8.1

/79.5*0762.0*/225.1Re

Re

25

3

=

=

=

smsmmmkg

uDP

Re is the Reynolds number

DP is the inner diameter of the pipe

Velocity and Reynolds number through orifice plate

11.48715Re/10*8.1

/09.16*04572.0*/225.1Re

/09.16

)04572.00762.0(*/79.5

)(

25

3

2

2

=

=

=

=

=

=

o

o

o

o

o

Po

oop

smsmmmkg

smummsmu

DDuu

AuAu

ou is the average velocity of the orifice

Reo is the Reynolds number of the orifice

Ap and Ao are the cross sectional area of the pipe and orifice

Do is the diameter of the orifice

Orifice discharge coefficient

72.065.266*2/225.16.01/09.16

21

2

1

34

4

4

=

=

=

=

o

o

ooo

ooo

CPamkgsmC

PuC

PCu

Co is the discharge coefficient of the orifice plate

is the ratio of orifice diameter to pipe diameter

Po is the pressure drop across the orifice

Friction Factor of flow in pipe (equation 11)

57.4/79.5*/225.1*144.9*2

0762.0*402

3

2

=

=

=

fsmmkgm

mPaf

uLDP

f ps

f is the friction factor

Ps is the pressure drop due to skin friction

L is the length of the pipe

Dp is the inner diameter of the pipe

Smooth pipe friction factor approximation

006.007.29229125.00014.0

Re125.00014.0

32.0

32.0

=

+=

+=

f

f

f

Comparison of velocities calculated using equation 1 and equation 2

is the ratio of the pressure and volumetric heat capacities, in this case of an ideal gas

Po is the bulk pressure through the pipe

Ps is the stagnation pressure as measured by the Pitot tube

smuPaPaPa

mkgPau

PPPu

smu

eq

eq

o

s

o

oeq

eq

/76.6

]1)10153510153528)[(

/225.1101535(

14.14.1*2

]1))[((1

2

/76.6

2

4.114.1

32

1

2

1

=

+

=

=

=

References

Lan, C., Air Flow Measurements Chemical Engineering Practice, Ottawa ON. (2016)

McCabe, W.L., Smith, J.C. and Harriott, P., Unit Operations of Chemical Engineering

Sixth ed., McGraw-Hill, New York NY, 2001.

Nevers, N. d. Fluid Mechanics for Chemical Engineers, McGraw-Hill.(2004)

Holinsgard, C., Discharge Coefficient Performance of Venturi, Standard Concentric Orifice Plate, V-Cone, and Wedge Flow Meters at Small Reynolds Numbers (2011)