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1. Admissions in India 2015
By:
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2. 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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3. Purpose
Measure
Flow rate in a pipe (smooth)
Friction factor
Velocity profile
Specify the turbulent-flow Reynolds Number
Compare the results with benchmark data
Uncertainty analysis for:
 Friction factor
 Velocity profile
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4. Test Design
The facility consists of:
Closed pipe network
Fan
Reservoir
Instruments used:
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)
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5. Air Flow Pipe facility
P r e s s u r e
t a p s
M o t o r
c o n t r o l l e r
6 ’ - 6 ”
F l o o r
R e s e r v o i r
2 . 0 ” s m o o t h
0 . 5 ” s m o o t h
2 . 0 ” r o u g h
R e l i e f
v a l v e s
B l o w e r
1 2 3 4
D = 2 . 0 ” D = 1 . 0 ”
D = 0 . 5 ”
t
t
t
3 6 ’
V e n t u r i m e t e r g a t e v a l v e s
T h e r m o m e t e r
V a l v e m a n i f o l d
S i m p l e
m a n o m e t e r
P i t o t t u b e
h o u s i n g s
V a l v e s
D i f f e r e n t i a l
m a n o m e t e r
V e n t u r i m e t e r s
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6. Test Design (Continue)
Reservoir:
To build up pressure and force the air to
flow downstream through any of the three
straight experiment pipes.
Digital Micrometer:
Allow 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 box
Used to measure the Stagnation pressure
and calculate the velocity profile in pipe
Venturi meters:
Located on each pipe type
Used 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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7. Pressure tap manifold and Pitot-tube housing
Pressure tap manifold Pitot-tube housing
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8. Measurement Systems:
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.
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9. Measurement Systems (continue)
For the flow rate and friction
factor, the individual
measurement are performed
for:
 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:
( o )
w w r = f T
( o )
r = f T n = f ( T
o )
air air air air = 2 D r
w
air
t DM Q KA g Z
r
R Q
air
= 4
e D
p n
( ) SMi SM j
2 5
8
f = g p D r
-
w Z Z
air
LQ
r
2
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10. 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)
[ ]úû
ù
é
u(r) 2g r
w Z (r) Z
= - SMstag SMstatic
êë
r
a
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11. Flow rate, Friction factor and velocity profile
measurement systems
Block diagram of the experimental
determination of the Friction
Block diagram of the Velocity
measurement
E X P E R I M E N T A L
R E S U L T S
E X P E R I M E N T A L E R R O R S O U R C E S
I N D I V I D U A L
M E A S U R E M E N T
S Y S T E M S
M E A S U R E M E N T
O F I N D I V I D U A L
V A R I A B L E S
D A T A R E D U C T I O N
E Q U A T I O N S
T E M P E R A T U R E
W A T E R
T E M P E R A T U R E
A I R
r
r
g p D w
8 L Q
f
B , P
V E N T U R I
P R E S S U R E
P I P E
P R E S S U R E
w
Q = F ( D z )
f = F ( r , r , z , Q ) = w
a a
T
B T , P T
z
B z , P
f f
S M
w w S M
D M
S M
2
2
5
T a
B T , P T
a a z S M
z
D M
B z , P
D M z D M
r = F ( T )
r
( )
w
= F ( T a )
z S M i
- z S M j
w
a
E X P E R I M E N T A L
R E S U L T
T
w
B T , P T
w
S T A G N A T I O N
P R E S S U R E
S T A T I C
P R E S S U R E
E X P E R I M E N T A L E R R O R S O U R C E S
I N D I V I D U A L
M E A S U R E M E N T
S Y S T E M S
M E A S U R E M E N T
O F I N D I V I D U A L
V A R I A B L E S
D A T A R E D U C T I O N
E Q U A T I O N S
z
S M
B , P
u
T
B T , P T
r = F ( T )
r
u = F ( r , r , z , z )
B u , P u
2 ( ) r g
r
S M s t a t
½
=
T E M P E R A T U R E
W A T E R
T E M P E R A T U R E
A I R
w
a s t a g
a
a z
w
w
w
S M s t a g
z S M s t a g
z
B , P
z S M s t a t
z S M s t a t
= F ( T a )
a
a S M s t a g S M s t a t
z S M s t a g
- z S M s t a t
w
a
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12. 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 head
drop
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 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, measure the head along the pipe by means of
the simple water manometer connected to the pressure taps located along
the pipe being studied (10 times for uncertainty analysis)
5. Repeat step 2
6. Execute data reduction for data analysis and uncertainty analysis using
equation above
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13. Uncertainty Analysis
The data reduction equation for the friction factor is:
( , , , , , , , ) w a SMi SM j f = F g D L Q r r Z Z
However here we will only consider bias limits for ZSM i and ZSM j . The total uncertainty
for the friction is:
2 2 2
f f f U = B + P
The Bias Limit, Bf and the precision limit, Pf, for the result are given by:
f i i B B B B q q q + = =å=
2 2 2 2
2 2 2
1
ZSMi ZSMi ZSMj ZSM j
j
i
tS
P f
f =
M
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14. Uncertainty Analysis (continue)
Data Reduction equation for the velocity profile is as follow:
( , , , , ) w a SMstagnation SMstatic f = F g r r Z Z
2 2 2
u u u U = B + P
u i i B B B B q q q + = =å=
2 2 2 2
2 2 2
1
ZSMstagn ZSMstagn ZSMstat ZSMstat
j
i
P tSu
u =
M
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15. Moody Chart for pipe friction with smooth
and rough walls
C o m p l e t e T u r b u l e n c e , H y d r a u l i c a l l y R o u g h
1 0 3 1 0 4 1 0 5 1 0 6 1 0 7 1 0 8
0 . 1 0
0 . 0 9 0
0 . 0 8 0
0 . 0 7 0
0 . 0 6 0
0 . 0 5 0
0 . 0 4 0
0 . 0 3 0
0 . 0 2 5
0 . 0 2 0
0 . 0 1 5
0 . 0 1 0
0 . 0 0 9
0 . 0 0 8
R e y n o l d s N u m b e r , R e = V D
h f
( L / D ) V 2 / ( 2 g )
F r i c t i o n F a c t o r f =
0 . 0 5
0 . 0 4
0 . 0 3
0 . 0 2
0 . 0 1 5
0 . 0 1
0 . 0 0 8
0 . 0 0 6
0 . 0 0 4
0 . 0 0 2
0 . 0 0 1
0 . 0 0 0 8
0 . 0 0 0 6
0 . 0 0 0 4
0 . 0 0 0 2
0 . 0 0 0 1
0 . 0 0 0 0 5
0 . 0 0 0 0 1
R e l a t i v e R o u g h n e s s , / D
L a m i n a r
F l o w
C r i t i c a l
Z o n e
T r a n s i t i o n
Z o n e
L a m in a r F l o w f = 6 4 / R e
/ D = 0 . 0 0 0 0 0 5
/ D = 0 . 0 0 0 0 0 1
H y d r a u l i c a l l y S m o o t h
k
n
k
k
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