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Measurement of flow rate, velocity profile and friction factor in Pipe
Flow
S. Ghosh, M. Muste, M. Marquardt, F. Stern
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Overview
Purpose Experimental design Experimental Process Test Set-up Data acquisition Data reduction Uncertainty analysis Data analysis
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Purpose Provide hands-on experience with pipe stand facility and modern measurement systems including pressure transducers, pitot probes and computer data acquisition and data reduction.
Comparison between automated and manual data acquisition systems.
Measure flow rate, velocity profiles and friction factor in smooth and rough pipes.
Determine experimental uncertainties.
Compare results with benchmark data
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Experimental DesignThe facility consists of:Closed pipe networkFanReservoir
Instrumentation:3 Venturi meters
Simple water ManometerDifferential Water manometerPitot ProbeDigital Micrometer (Accurate radial positioning)
Pressure transducer
Computer based Automated Data Acquisition System (DA)
Contraction Diameters (mm):
12.7 25.4 52.93
Flow Coefficient, K 0.915 0.937
0.935
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Experimental process Data
Analysis
Compare results with benchmark data, CFD, and
/or AFD
Use Fig 8 as reference value
for velocity profile
Plot experimental velocity profile
and friction factor on
reference data
Use Fig 9 as reference value
for friction factor
Evaluate fluid physics, EFD
process and UA
Answer questions in
section 4
Report difference between
experimental and reference data
Prepare report
Data Reduction
Statistical analysis
Data reduction equations
Remove outliers
Evaluate Eq. 3
Evaluate Eq. 4
Uncertainty Analysis
Estimate bias limits
Table 1
Estimate precision limits
Evaluate Eq. 9
Evaluate Eq. 13
Estimate total uncertainty
Evaluate Eq. 7
Evaluate Eq. 11
Test Set-up
Facility & conditions
Prepare measurement
systems
Venturimeter
Pressure transducer
Valve manifold
Pitot tube
Micrometer
Install model
N/A
Calibration
N/A
Data Acquisition
Prepare experimental procedures
Run tests & acquire data
Store data
Write results to output file
Measure room and pipe
temperature
Initialize data acquisition software
Open Labview program
Set blower speed
Set valves in proper
positions
Airflow pipe system
Enter hardware settings
Measure total discharge
Measure velocity profile
Measure pressure drop in pipe
Repeat discharge measurement
Evaluate Eq. 5
Evaluate Eq. 6
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Test set-up
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Test Set-up: Venturi meter and Pitot-tube housing
Venturimeter Pitot-tube housing
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Test set-up: Instrumentation
The equipment used in the experiment includes:
Digital thermometer with a range of – 40 to 450 F and a smallest reading of 0.1 F for measurement of the environment temperature.
Digital micrometer with least significant digit 0.01 mm for positioning the Pitot-tube inside the pipe.
Simple water manometer with a range of 2.5 ft and a least scale division of 0.001 ft for measurement of the head at each pressure tap along the pipes and for measurement of velocities using the Pitot-tube arrangement .
Differential water manometer with a range 3 ft and a least scale division of 0.001ft for measurement of the head drop across the Venturi meters. Pressure transducer calibrated with ft of water
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Test set-up: Instrumentation
Reservoir:To build up pressure and force the air
to flow downstream through any of the three straight experiment pipes.
Digital Micrometer:Allows the measurement of the
position of the Pitot probe at different locations along the cross section of the pipe tested
Pitot Probe:Located in the glass-wall boxUsed to measure the Stagnation
pressure and calculate the velocity profile in pipe
Venturi meters:Located on each pipe typeUsed to measure flow rate Q along the
differential water manometer
Pressure Taps:Located along each pipe, they are
connected to the simple water manometer to evaluate the head measurement
They are used to calculate the friction factor
Manometers:To measure the head at each pressure
Tap along the pipe and to make the Pitot-tube measurements (simple Manometer)
To measure head drops across the venturi meters (differential Manometer)
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Data acquisitionThe procedures for data acquisition and reduction are described as follow:
1. Use the appropriate Venturi meter, (2” contraction diameter) to measure the total discharge. Increase blower setting from 15% to 35% with 5% increments and measure flow rate using both manometer and pressure transducer.
2. Take reading for ambient air (manometer water) and pipe air temperatures.
3. To obtain velocity data, use the Pitot-tube box to measure the ambient head and stagnation heads across the pipe. Measure the stagnation heads at radial intervals. The recommended radial spacing for one half of the diameter is 0, 5, 10, 15, 20, 23, and 24 mm.
4. Maintaining the discharge at 35%, measure the head along the pipe by
means of the ADAS the pressure heads at pressure taps 1, 2, 3, and 4
5. Repeat step 2
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Automated Data Acquisition System
Layout of the data acquisition systems: a) photo; b)
schematic
(a) (b)
D A 2 D A 1
Tes te d P ipe
P ito t-Tu beH o us in g
S ta ticP ressu re
S ta gn a tio nP ressu re
S ta tic P re ssure from P ressu re Ta ps
Ve ntur i M eter
P ressu reTran sd uce r
Va lveM a nifo ld
R e tu rn P ip e
S im pleM a no m ete r
D iffe ren tia lM a no m ete r
Tyg on Tu b in gC o nn ec tion s
LEGEND
ToAtmosphereTo
Atmosphere
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Introduction to ADAS Software - Labview
Front panel on Data Acquisition program
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Initial settings
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Flow rate measurement
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Friction factor measurement
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Velocity profile measurement
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Data reduction
For the flow rate and friction factor, the individual measurements are performed for:
Ambient air temperature Pipe air temperature Pipe pressure head Venturi meter pressure head
drop
The experimental Results are:
Manometer water density Air density Kinematic viscosity Flow rate Reynolds number Friction factor
Data reduction equations are: )( o
ww Tf)( o
airair Tf )( oairair Tf
air
wDMt ZgKAQ
2
aire D
QR
4
ji SMSM
air
w ZZLQ
Dgf
2
52
8
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Data reduction equations: Flow rate
)(22
22
Bernoullig
V
g
p
g
V
g
p bbaa
)(ContinuityAVAV bbaa
Volumetric flow rate bbVAQ
,
,)1(2
22
22
ba
baD
a
w
ba
baD
AA
AACK
ghAA
AACQ
a
wDMt zgKAQ
2Equation (1), lab handout
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Friction factor
D A 2 D A 1
Tes te d P ipe
P ito t-Tu beH o us in g
S ta ticP ressu re
S ta gn a tio nP ressu re
S ta tic P re ssure from P ressu re Ta ps
Ve ntur i M eter
P ressu reTran sd uce r
Va lveM a nifo ld
R e tu rn P ip e
S im pleM a no m ete r
D iffe ren tia lM a no m ete r
Tyg on Tu b in gC o nn ec tion s
LEGEND
ToAtmosphereTo
Atmosphere
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Friction factor (contd.)
jSMiSMa
w zzLQ
Dgf
2
52
8
Equation 2 is a form of Darcy Weisbach equationin terms of flow rate Q and pressure drop where, and A is the pipe cross sectional area.
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Velocity profile
/)(2
,2
1
0
20
stat
stat
ppV
BernoulliVpp
2/1
2)(
StaticStagnation SMSMa
w zrzg
ru
Equation 3, Exercise notes
stag
SMSMwstatstag
pp
zzgppstatstag
0
);(
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Data reduction: Spreadsheet
Spreadsheet for data acquisition, data reduction and uncertainty analysis for Measurement of Velocity profile and friction factor in pipe flows (smooth pipe)
Table of ContentsColor code:
1. Experimental Summary Sections2. Data reduction equations Comments3. Data Acquisition and Reduction Enter student data 3.1 Input variables Constants 3.2 Measured variables Calculated or output values4. Uncertainty Analysis 4.1 Bias Limits 4.2 Precision Limits 4.3 Total Uncertainty
1. Experiment summaryStatement of Purpose: To measure velocity profile and friction factor
in rough pipe and determine the uncertainties and compare results with benchmark data.
Facility: Air-flow unit (WTA)Test Design: Air flows through a pipe systemReferences: Lab2 Handout: http://css.engineering.uiowa-
.edu/~fluids/Lab/EFDLab2.PDF
2. Data Reduction Equations
3. Data acquisition and reduction for multiple test UA approach3.1 Input variables
Quantity Symbol Value UnitsGravity g 9.8031 m/s^2Number of test M 10 -----Coverage factor for standard deviation K 2 -----
3.2 Measured variablesThe following example illustrates the procedure for calculating Q using velocity
Date Time For calculating the flow rate Q (Cell no. G66) first obtain the velocity profile with respect to radial distance. Cells D84-D98 calculates the velocity profile.
Re= Room Pipe The following example illustrates the procedure for calculating Q using velocityInitial integration method. Note: The x axis on the following plot is cell A85 - A91. The
ZDM= Final Y axis is cell D85 - D91. Once the velocity profile is plotted, fit a 2nd order polynomial
Average ###### #DIV/0! curve to the points and display the equation on the chart, as shown below. The y in theequation is velocity and the x is radial distance r. Finally the flow rate Q is given by the following formula. Note that the variable x in the integral equation is actually radius.
Initial Also Rmax is the radius of the pipe.
FinalAverage Avera
ge
TAP # Locationz SM
(ft water)
(ft) z SM4
(ft water)f 34
1 5 #DIV/0!2 f 12 = #DIV/0! 10 #DIV/0!3 f 23 = #DIV/0! 15 #DIV/0!4 f 34 = #DIV/0! 20 #DIV/0!
#DIV/0!Symbol Value Units #DIV/0!
K 0.935 #DIV/0!At 0.002154 m2 #DIV/0!
g 9.8031 m/s2 #DIV/0!D 0.05238 m #DIV/0!L 9.144 m #DIV/0!
#DIV/0!
r (m)
z SM stagnatio
n (ft z SM static
(ft
u (m/s)
Measur. #
0.026 0.000 10.024 #DIV/0! 20.023 #DIV/0! 30.020 #DIV/0! 40.015 #DIV/0! 50.010 #DIV/0! 60.005 #DIV/0! 70.000 #DIV/0! 8 Note: The value in cell G 66 for the flow rate should be approximately-0.005 #DIV/0! 9 0.07 m3/s. Check your flow rate calculation of your value deviates-0.010 #DIV/0! 10 too much from the recommended value.-0.015 #DIV/0! Average -0.020 #DIV/0! Std. Dev Conversion of pressure head from ft of water to pascals-0.023 #DIV/0!-0.024 #DIV/0! Tap # ZSM(ft water) ZSM pas-0.026 0.0000 1 0.0000 0
2 0.0000 03 0.0000 04 0.0000 0
Alternate measurements at various radial positions with repeated measurements.
#DIV/0! #DIV/0! #DIV/0!#DIV/0! #DIV/0! #DIV/0!
#DIV/0!#DIV/0!
#DIV/0!#DIV/0!
#DIV/0!#DIV/0!
#DIV/0!#DIV/0!
#DIV/0!#DIV/0!
VELOCITY PROFILE Repeated Measurements (near wall)z SM stagnation
(ft water)z SM static
(Ft water)u
(m/s)
Pipe Diameter 10Pipe Length Average f 34
St. Deviation Sf34
Cross-sectionArea 8
Gravity 9
Constant 6Discharge Coeff. 7
4
5
23
f i j Measur.. #
z SM3
(ft water)
1
FRICTION FACTOR Repeated MeasurementsSmooth Pipe Smooth Pipe
Average #DIV/0! #IV/0!
Venturi Head Drop z DM (ft water) Flow Rate Q (m3/s) Reynolds Number (Re)Initial from integration of velocity
profileFinal
0.59 a (kg/m3) =
m a (kg/m.s) =
Actual Flow rate
Temperature(deg C) Fluid Property100,000
Target Headdrop (ft water) w (kg/m3) =
Appendix C:
Target ConditionsTarget Reynolds #
2/1
2)(
StaticStagnation SMSMa
w zrzg
ru jSMiSM
a
w zzLQ
Dgf
2
52
8 Eqn. (3) Eqn. (4)
Table A1.
Table A2.
xdxxxQRmas
)434.4111.2872733(20
2
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Uncertainty analysis
Block diagram of the experimental determination of the Friction factor
Block diagram of the Velocity measurement
EXPERIMENTALRESULTS
EXPERIMENTAL ERROR SOURCES
INDIVIDUALMEASUREMENT
SYSTEMS
MEASUREMENTOF INDIVIDUAL
VARIABLES
DATA REDUCTIONEQUATIONS
TEMPERATUREWATER
TEMPERATUREAIR
fB , P
VENTURIPRESSURE
PIPEPRESSURE
f = F( , , z , Q = )a
a
wg D
8LQ
Q = F( z )
w
w
T
TB T, P
z
zB , P
f f
SM
SMww
DM
SM
2
2
5
aT
TB T, Paa
z SM
z
zB , PDM
DM z DM
= F(T )
( )
w
= F(T )a
zSM i
- zSM j
w
a
EXPERIMENTALRESULT
w
w
T
TB T, P
STAGNATIONPRESSURE
STATICPRESSURE
EXPERIMENTAL ERROR SOURCES
INDIVIDUALMEASUREMENT
SYSTEMS
MEASUREMENTOF INDIVIDUAL
VARIABLES
DATA REDUCTIONEQUATIONS
z
B , PSM
B , Pu u
u
= F(T )
u = F( , , z , z ) 2( ) g
½
=
TEMPERATUREWATER
TEMPERATUREAIR
w
a stag
a
T
TB T, Pa
z
w
w
w
SMstag
zSM
stag
z
B , PSM stat
zSM
stat
zSM
stat
= F(T )a
aa SM
stagSM
stat
zSM stag
- zSM stat
w
a
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Uncertainty Analysis
The data reduction equation for the friction factor is:
However here we will only consider bias limits for ZSM i and ZSM j . The total uncertainty for the friction is:
The Bias Limit, Bf and the precision limit, Pf, for the result are given by:
222fff PBU
2222
1
222
jSMSMjiSMiSM ZZZZ
j
iiif BBBB
M
tSP f
f
jSMiSMa
w zzLQ
Dgf
2
52
8
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Uncertainty Analysis (continue)
Data Reduction equation for the velocity profile is as follow:
222uuu PBU
2222
1
222
statSMstatSMSMstagnstagnSM ZZZZ
j
iiiu BBBB
M
tSP uu
2/1
2)(
StatStag SMSMa
w zrzg
ru
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Data Analysis: Results and discussions
10 104
10 10 10 105 6 7 83
0 .008
0 .009
0 .015
0 .025
0 .020
0 .010
0 .030
0 .040
0 .050
0 .060
0 .070
0 .080
0 .090
0 .10
R eynolds N umber, R e = VD
Fric
tion
Fac
tor
f =h
f
(L/D
)V /
(2g)
2
0 .00001
0 .00005
0 .0001
0 .0002
0 .00040 .00060 .00080 .001
0 .050 .04
0 .03
0 .02
0 .01
0 .015
0 .0080 .006
0 .004
0 .002
Rel
ativ
e R
ough
ness
, /D
Lam ina rF low
Critica lZ one
T rans itionZ one
/D = 0 .000005
/D = 0 .000001
Com p le te T u rbu lence , Hyd rau lica lly Rough
Hyd rau lica lly S m oo th
k
k
k
Smooth Pipe (2”) low speed
Rough Pipe (2”) low speed
07/10/03
Benchmark data for Friction Factor
Moody Chart for pipe friction with smooth and rough walls
Low speed = 44 m/s
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Data Analysis: Results and discussions (contd.)
r/R u/umax
0.0000 1.0000
0.1000 0.9950
0.2000 0.9850
0.3000 0.9750
0.4000 0.9600
0.5000 0.9350
0.6000 0.9000
0.7000 0.8650
0.8000 0.8150
0.9000 0.7400
0.9625 0.6500
0.9820 0.5850
1.0000 0.4300
Benchmark data for velocity profile (Schlichting, 1968)
0
0. 2
0. 4
0. 6
0. 8
1
-1 -0. 8 -0. 6 -0. 4 -0. 2 0 0. 2 0. 4 0. 6 0. 8 1
r / R
Rough pipe - Low Speed
Smooth pipe -Low Speed
Rough P ipe - High Speed
Smooth P ipe - High speed
Schlichting Data
Low speed = 44 m/sHigh speed = 62 m/s
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PIV-Particle Image Velocimetry
• PIV Process 1. Inject flow with Particles2. Illuminate particles with Light3. Take snapshots of the particles with a
Camera4. Process Images with Software
•PIV Equipment• Particles : Very small, neutrally
buoyant, and “reflective”.• Light: Generated using lasers, LEDS,
… and formed into a thin sheet of light
• Camera: Digital camera capable of taking images at a fast rate
• Images: Show movement of particles with stark contrast
• Software: Analyzes patterns of particles, now pixels, and tracks there displacement
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PIV-continued• PIV Fundamentals-abridged
-PIV measures whole velocity fields by taking two images shortly after each other and calculating the distance individual particles travelled within this time. From the known time difference and the measured displacement, the velocity can be calculated
• Benefits of PIV -Pitot tube, thermal anemometers, laser Doppler velocimetry,…only measure velocity at points of the flow→PIV measures entire cross section or volume of flow
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PIV-Continued
• PIV Fundamentals-fine details
•Two camera images are divided in to similar small tiles, called interrogation windows. •A pattern of particles is detected in the interrogation window•The predominant movement of the pattern from the first image to the second is measured •The displacement of the pattern from the first to the second image is measured in pixel dimensions•The spatial dimensions of the image are correlated to the pixel dimensions•The spatial displacement divided by the time interval of images →velocity
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PIV-Continued
• PIV uses for Lab 2•Apply the continuity equation to flow field measurements•Calculate flow rate across a varying cross section orifice
• PIV steps for Lab 2•Take at least two images of the flow•Analyze the images•Extract the raw velocity field measurements•Sample velocity data from two transverse cross sections of the flow•Extract the mean stream wise velocity components from each cross section •Multiply the mean velocity by cross sectional area to find flow rate
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PIV-Continued
• PIV equations
Stream wise velocity component
Average flow rate
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The End