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Measurement of flow rate, friction Factor,and velocity Profile in Pipe Flow
57:020 mechanics of Fluids and Transfer Processes
Experimental Laboratory #2
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Purpose
Measure
Flow rate in a pipe (smooth)
Friction factorVelocity profile
Specify the turbulent-flow Reynolds Number
Compare the results with benchmark data
Uncertainty analysis for: Friction factor
Velocity profile
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Test Design
The facility consists of:Closed pipe network
Fan
Reservoir
Instruments used:3 Venturi meters
Simple water ManometerDifferential Water manometer
Pitot Probe
Digital Micrometer (Accurate radial positioning)
Contraction Diameters (mm): 12.7 25.4 52.93
Flow Coefficient, K 0.915 0.937 0.935
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Air Flow Pipe facility
Pressuretaps
Motorcontroller
Floor
6-6
Reservoir
2.0 smooth
0.5 smooth
2.0 rough
Reliefvalves
Blower
D = 2.0D = 1.0
D = 0.5
tt
t
36
Venturi meter gate valves
Thermometer
1 2 3 4
Valve manifold
Simplemanometer
Pitot tubehousings
Valves
Differentialmanometer
Venturi meters
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Test Design(Continue)
Reservoir:To build up pressure and force the air to
flow downstream through any of the threestraight experiment pipes.
Digital Micrometer:Allow the measurement of the position of the
Pitot probe at different locations along thecross section of the pipe tested
Pitot Probe:Located in the glass-wall box
Used to measure the Stagnation pressureand calculate the velocity profile in pipe
Venturi meters:Located on each pipe type
Used to measure flow rate Q along thedifferential water manometer
Pressure Taps:Located along each pipe, they are
connected to the simple water manometer toevaluate the head measurement
They are used to calculate the frictionfactor
Manometers:To measure the head at each pressure Tap
along the pipe and to make the Pitot-tubemeasurements (simple Manometer)
To measure head drops across the venturimeters (differential Manometer)
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Pressure tap manifold and Pitot-tube housing
Pressure tap manifold Pitot-tube housing
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Measurement Systems:
The equipment used in the experiment includes:
Digital thermometerwith a range of40 to 450 F and a smallest reading of
0.1 F for measurement of the environment temperature.
Digital micrometerwith least significant digit 0.01 mm for positioning the
Pitot-tube inside the pipe.
Simple water manometerwith 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 manometerwith a range 3 ft and a least scale division of
0.001ft for measurement of the head drop across the Venturi meters.
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Measurement Systems (continue)
For the flow rate and frictionfactor, the individualmeasurement are performedfor:
Ambient air temperature (A.3)
Pipe air temperature (A.5)
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:
)( oww Tf
)( oairair Tf )( o
airair Tf
air
wDMt ZgKAQ
2
air
e
D
QR
4
ji SMSM
air
w ZZLQ
Dgf
2
52
8
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Measurement Systems (continue)
For the velocity profile, the individual measurement systems are for:
the ambient temperature
pipe air temperature
pitot stagnation and static pressure heads.
The experimental results are for: manometer water density (A.3)
Air density (A.5)
Velocity profile (below)
Data reduction equation: (using the Bernoulli equation along the manometer equation)
staticstag SMSM
a
w ZrZgru )(2)(
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Flow rate, Friction factor and velocity profilemeasurement systems
Block diagram of the experimentaldetermination of the Friction
Block diagram of the Velocitymeasurement
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
zSM
z
zB , P
DM
DM zDM
= 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 , P
SM
B , Pu u
u
= F(T )
u = F( , , z , z ) 2( ) g
=
TEMPERATUREWATER
TEMPERATUREAIR
w
a stag
a
T
TB T, P a z
w
w
w
SMstag
zSM
stag
z
B , P
SMstat
zSM
stat
zSM
stat
= F(T )a
aa SM
stagSM
stat
zSM
stag
- zSM
stat
w
a
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Data Acquisition and reduction
The procedures for data acquisition and reduction are described as follow:
1. Use the appropriate Venturi meter, (2 smooth pipe) measure the headdrop
2. Take reading for ambient air (manometer water) and pipe air
temperatures.3. To obtain velocity data, measure in the appropriate Pitot-tube box, the
ambient head and stagnation heads across the full diameter. Measure thestagnation heads at radial intervals. The recommended radial spacing forone half of the diameter is 0, 5, 10, 15, 20, 23, and 24 mm.
4. Maintaining the discharge, measure the head along the pipe by means ofthe simple water manometer connected to the pressure taps located alongthe pipe being studied (10 times for uncertainty analysis)
5. Repeat step 2
6. Execute data reduction for data analysis and uncertainty analysis usingequation above
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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, Bfand the precision limit, Pf, for the result are given by:
),,,,,,,(ji SMSMaw
ZZQLDgFf
222
fff PBU
2222
1
222
jSMSMjiSMiSM ZZZZ
j
iiif BBBB
M
tSP
f
f
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Uncertainty Analysis (continue)
Data Reduction equation for the velocity profile is as follow:
222
uuu PBU
2222
1
222
statSMstatSMSMstagnstagnSM ZZZZ
j
i
iiu BBBB
M
tSP uu
),,,,(staticstagnation SMSMaw
ZZgFf
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Moody Chart for pipe friction with smoothand rough walls
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
Reynolds Number, Re = VD
FrictionFactorf=
h
f
(L/D)V
/(2
g)
2
0.00001
0.00005
0.0001
0.0002
0.00040.0006
0.00080.001
0.05
0.04
0.03
0.02
0.01
0.015
0.008
0.006
0.004
0.002
RelativeRoughness,
/D
LaminarFlow
CriticalZone
TransitionZone
LaminarF
lowf=
64/R
e
/D = 0.000005
/D = 0.000001
Complete Turbulence, Hydraulically Rough
Hydraulically Smooth
k
k
k
