Measurement of flow rate, velocity profile and friction factor in Pipe Flow S.
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Transcript Measurement of flow rate, velocity profile and friction factor in Pipe Flow S.
Measurement of flow rate, velocity profile
and friction factor in Pipe Flow
S. Ghosh, M. Muste, M. Marquardt, F. Stern
Overview
Purpose
Experimental design
Experimental Process
Test Set-up
Data acquisition
Data reduction
Uncertainty analysis
Data analysis
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
Experimental Design
The facility consists of:
Closed pipe network
Fan
Reservoir
Instrumentation:
3 Venturi meters
Contraction Diameters (mm):
12.7
25.4
52.93
Flow Coefficient, K
0.915
0.937
0.935
Simple water Manometer
Differential Water manometer
Pitot Probe
Digital Micrometer (Accurate radial positioning)
Pressure transducer
Computer based Automated Data Acquisition System (DA)
Experimental process
Test
Set-up
Data
Acquisition
Facility &
conditions
Prepare
experimental
procedures
Airflow pipe
system
Install
model
Data
Reduction
Statistical
analysis
Uncertainty
Analysis
Estimate bias
limits
Data
Analysis
Compare results
with benchmark
data, CFD, and
/or AFD
Remove outliers
Set blower
speed
Set valves in
proper
positions
N/A
Data reduction
equations
Evaluate Eq. 3
Table 1
Estimate
precision limits
Evaluate Eq. 4
Calibration
Use Fig 8 as
reference value
for velocity
profile
Use Fig 9 as
reference value
for friction factor
Evaluate Eq. 5
Plot experimental
velocity profile
and friction
factor on
reference data
Evaluate Eq. 6
N/A
Prepare
measurement
systems
Initialize data
acquisition
software
Evaluate Eq. 9
Evaluate Eq. 13
Open Labview
program
Venturimeter
Enter hardware
settings
Pressure
transducer
Valve
manifold
Run tests &
acquire data
Pitot tube
Micrometer
Estimate total
uncertainty
Measure total
discharge
Measure pressure
drop in pipe
Measure velocity
profile
Repeat discharge
measurement
Store data
Write results to
output file
Evaluate fluid
physics, EFD
process and UA
Evaluate Eq. 7
Evaluate Eq. 11
Measure room
and pipe
temperature
Report difference
between
experimental and
reference data
Answer
questions in
section 4
Prepare report
Test set-up
Test Set-up: Venturi meter and Pitot-tube
housing
Venturimeter
Pitot-tube housing
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
Test set-up: Instrumentation
Reservoir:
Digital Micrometer:
To build up pressure and force the air to
flow downstream through any of the three
straight experiment pipes.
Allows the measurement of the position of
the Pitot probe at different locations along the
cross section of the pipe tested
Pitot Probe:
Venturi meters:
Located in the glass-wall box
Used to measure the Stagnation pressure
and calculate the velocity profile in pipe
Located on each pipe type
Used to measure flow rate Q along the
differential water manometer
Pressure Taps:
Manometers:
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
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)
Data acquisition
The procedures for data acquisition and reduction are described as follow:
1.
2.
3.
4.
5.
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.
Take reading for ambient air (manometer water) and pipe air temperatures.
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.
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
Repeat step 2
Automated Data Acquisition System
Pitot-Tube
Housing
Tested Pipe
Static Pressure from Pressure Taps
To
Atmosphere
To
Atmosphere
DA 2
DA 1
Differential
Manometer
Static
Pressure
Stagnation
Pressure
Pressure
Transducer
Valve
Manifold
Simple
Manometer
Venturi Meter
Return Pipe
(a)
(b)
Layout of the data acquisition systems: a) photo; b)
schematic
LEGEND
Tygon Tubing
Connections
Introduction to ADAS Software - Labview
Front panel on Data Acquisition program
Initial settings
Flow rate measurement
Friction factor measurement
Velocity profile measurement
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
Data reduction equations are:
w f (Two )
air f (Tairo ) air f (Tairo )
Q KAt 2 gZ DM
The experimental Results are:
Manometer water density
Air density
Kinematic viscosity
Flow rate
Reynolds number
Friction factor
w
air
4Q
Re
D air
g 2 D5 w
f
Z SM i Z SM j
2
8LQ air
Data reduction equations: Flow rate
pa Va2 pb Vb2
( Bernoulli)
g 2 g g 2 g
Va Aa Vb Ab (Continuity)
Volumetric flow rate
Q AbVb
Q CD
K CD
Equation (1), lab handout
Q KAt 2 gz DM
Aa Ab
2 gh(
Aa2 Ab2
Aa Ab
Aa2 Ab2
w
a
,
w
1) ,
a
Friction factor
Pitot-Tube
Housing
Tested Pipe
Static Pressure from Pressure Taps
To
Atmosphere
To
Atmosphere
DA 2
DA 1
Differential
Manometer
Static
Pressure
Stagnation
Pressure
Pressure
Transducer
Valve
Manifold
Simple
Manometer
Venturi Meter
Return Pipe
LEGEND
Tygon Tubing
Connections
Friction factor (contd.)
g 2 D 5 w
f
z SM i z SM j
8LQ 2 a
Equation 2 is a form of Darcy Weisbach equation
in terms of flow rate Q and pressure drop where,
and A is the pipe cross sectional area.
Velocity profile
p0 pstat
1
V 2 , Bernoulli
2
V 2( p0 pstat ) /
2 g w
u (r )
z SM Stagnation r z SM Static
a
Equation 3, Exercise notes
pstag pstat w g ( z SM stag z SM stat );
p0 pstag
1/ 2
Appendix C:
Spreadsheet for data acquisition, data reduction and uncertainty analysis for
Measurement of Velocity profile and friction factor in pipe flows (smooth pipe)
Table of Contents
Data reduction:
Spreadsheet
Color code:
Sections
Comments
Enter student data
Constants
Calculated or output values
1. Experimental Summary
2. Data reduction equations
3. Data Acquisition and Reduction
3.1 Input variables
3.2 Measured variables
4. Uncertainty Analysis
4.1 Bias Limits
4.2 Precision Limits
4.3 Total Uncertainty
1. Experiment summary
Statement of Purpose:
To measure velocity profile and friction factor
in rough pipe and determine the uncertainties
and compare results with benchmark data.
Air-flow unit (WTA)
Air flows through a pipe system
Lab2 Handout: http://css.engineering.uiowa.edu/~fluids/Lab/EFDLab2.PDF
Facility:
Test Design:
References:
2. Data Reduction Equations
2 g w
u (r )
z SM Stagnation r z SM Static
a
1/ 2
f
Eqn. (3)
g 2 D 5 w
z SM i z SM j
8LQ2 a
Eqn. (4)
3. Data acquisition and reduction for multiple test UA approach
3.1 Input variables
Table A1.
Table A2.
Quantity
Gravity
Number of test
Coverage factor for standard deviation
Symbol
g
M
K
Value
9.8031
10
2
Units
m/s^2
---------
3.2 Measured variables
Target Conditions
Target Reynolds #
Re= 100,000
Target Headdrop (ft water)
ZDM= 0.59
Date
Temperature(deg C)
Room
Pipe
Initial
Final
Average ###### #DIV/0!
Actual Flow rate
Venturi Head Drop z DM (ft water)
Initial
Final
Average #DIV/0!
FRICTION FACTOR
TAP #
Smooth Pipe
z SM
fij
(ft water)
1
2
f 12 = #DIV/0!
3
f 23 = #DIV/0!
4
f 34 = #DIV/0!
Constant
Discharge Coeff.
Cross-sectionArea
Symbol
K
At
Gravity
Pipe Diameter
Pipe Length
g
D
L
VELOCITY PROFILE
z SM stagnatio z SM static
r
(m)
(ft
n (ft
0.026
0.024
0.023
0.020
0.015
0.010
0.005
0.000
-0.005
-0.010
-0.015
-0.020
-0.023
-0.024
-0.026
Location
(ft)
5
10
15
20
Value
Units
0.935
0.002154 m2
9.8031 m/s2
0.05238 m
9.144 m
u
(m/s)
0.000
#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!
0.0000
Time
Fluid Property
w (kg/m3) =
a (kg/m3) =
m a (kg/m.s) =
Reynolds Number (Re)
Flow Rate Q (m 3/s)
from integration of velocity Initial
profile Final
Average
Avera
#IV/0!
ge
Repeated Measurements
Smooth Pipe
z SM3
z SM4
f 34
Measur..
#
(ft water)
(ft water)
1
#DIV/0!
2
#DIV/0!
3
#DIV/0!
4
#DIV/0!
5
#DIV/0!
6
#DIV/0!
7
#DIV/0!
8
#DIV/0!
The following example illustrates the procedure for calculating Q using velocity
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.
The following example illustrates the procedure for calculating Q using velocity
integration method. Note: The x axis on the following plot is cell A85 - A91. The
Y axis is cell D85 - D91. Once the velocity profile is plotted, fit a 2nd order polynomial
curve to the points and display the equation on the chart, as shown below. The y in the
equation 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.
Also Rmax is the radius of the pipe.
Q 2
Rmas
0
(2733x2 287.11x 41.434) xdx
9
10
#DIV/0!
#DIV/0!
Average f 34 #DIV/0!
St. Deviation Sf34 #DIV/0!
Repeated Measurements (near wall)
z SM stagnation
z SM static
Measur. #
u
(m/s)
(ft water)
(Ft water)
1
#DIV/0!
2
#DIV/0!
3
#DIV/0!
4
#DIV/0!
5
#DIV/0!
6
#DIV/0!
7
#DIV/0!
8
#DIV/0!
9
#DIV/0!
10
#DIV/0!
Average
#DIV/0!
#DIV/0!
#DIV/0!
Std. Dev
#DIV/0!
#DIV/0!
#DIV/0!
Alternate measurements at various radial positions with repeated
measurements.
Note: The value in cell G 66 for the flow rate should be approximately
0.07 m3/s. Check your flow rate calculation of your value deviates
too much from the recommended value.
Conversion of pressure head from ft of water to pascals
Tap #
1
2
3
4
ZSM(ft water)
0.0000
0.0000
0.0000
0.0000
ZSM pas
0
0
0
0
Uncertainty analysis
Block diagram of the experimental
determination of the Friction factor
Block diagram of the Velocity
measurement
EXPERIMENTAL ERROR SOURCES
EXPERIMENTAL ERROR SOURCES
TEMPERATURE
WATER
Tw
Ta
B T , PT
B T , PT
w
PIPE
PRESSURE
TEMPERATURE
AIR
a
w
Bz
a
z SM
, Pz
SM
SM
VENTURI
PRESSURE
Bz
z DM
, Pz
DM
= F(T )
w
w
a = F(Ta )
Q = F(z DM )
f = F( , , z
w
a
2
SM
, Q) =
g D
8LQ
f
B f , Pf
5
2
w
(z - z )
a SM i SM j
DM
INDIVIDUAL
MEASUREMENT
SYSTEMS
TEMPERATURE
WATER
TEMPERATURE
AIR
MEASUREMENT
OF INDIVIDUAL
VARIABLES
Tw
Ta
DATA REDUCTION
EQUATIONS
B T , PT
w
w
z
a
SM
2( z
a
SM
,z
stag
SM
) =
stat
u
EXPERIMENTAL
RESULTS
, Pz
stag
= F(T )
w
w
= F(Ta )
w
z
SM stag
Bz
B T , PT
a
a
u = F( , , z
STATIC
PRESSURE
STAGNATION
PRESSURE
Bu, Pu
Bz
SM
stag
-z
SM stag
SM stat
SM stat
SM
, Pz
stat
) g
w
SM
stat
½
INDIVIDUAL
MEASUREMENT
SYSTEMS
MEASUREMENT
OF INDIVIDUAL
VARIABLES
DATA REDUCTION
EQUATIONS
a
EXPERIMENTAL
RESULT
Uncertainty Analysis
The data reduction equation for the friction factor is:
g 2 D 5 w
f
z SM i z SM j
2
8LQ a
However here we will only consider bias limits for ZSM i and ZSM j . The total
uncertainty for the friction is:
U 2f B2f Pf2
The Bias Limit, Bf and the precision limit, Pf, for the result are given by:
j
B i2 Bi2 Z2SM BZ2SM Z2SMj BZ2SM
2
f
i
i 1
Pf
tS f
M
i
j
Uncertainty Analysis
(continue)
Data Reduction equation for the velocity profile is as follow:
2 g w
u (r )
zSM Stag r zSM Stat
a
1/ 2
Uu2 Bu2 Pu2
j
Bu2 i2 Bi2 Z2SM
i 1
stagn
BZ2SMstagn Z2SM BZ2SM
tSu
Pu
M
stat
stat
Data Analysis: Results and discussions
Moody Chart for pipe friction with smooth and rough walls
Laminar
Flow
Critical
Zone
Transition
Zone
0.10
0.090
0.080
Complete Turbulence, Hydraulically Rough
2
(L/D)V /(2g)
hf
0.01
0.008
0.006
0.004
/R
= 64
0.030
e
Friction Factor f =
0.02
0.015
f
Flo w
0.040
in a r
0.050
Lam
0.060
0.025
0.002
0.020
0.001
0.0008
0.0006
0.0004
Hydraulically Smooth
0.015
Relative Roughness,
k /D
0.05
0.04
0.03
0.070
Low speed = 44 m/s
Smooth Pipe (2”) low speed
Rough Pipe (2”) low speed
0.0002
0.0001
k /D = 0.000005
0.010
0.009
0.008
0.00005
k /D = 0.000001
10
3
10
4
10
5
10
Reynolds Number, Re =
6
0.00001
10
7
10
8
VD
Benchmark data for Friction Factor
07/10/03
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)
Low speed = 44 m/s
High speed = 62 m/s
PIV-Particle Image Velocimetry
•
PIV Process
1.
2.
3.
4.
•
Inject flow with Particles
Illuminate particles with Light
Take snapshots of the particles with a
Camera
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
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
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
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
PIV-Continued
•
PIV equations
Stream wise velocity component
Average flow rate
The End