Measurement of flow rate, friction Factor, and velocity
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Transcript Measurement of flow rate, friction Factor, and velocity
Measurement of flow rate, friction Factor,
and velocity Profile in Pipe Flow
57:020 mechanics of Fluids and Transfer Processes
Experimental Laboratory #2
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
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)
Air Flow Pipe facility
Simple
manometer
Pitot tube
housings
Valve manifold
2.0” smooth
Reservoir
6’-6”
Motor
controller
Pressure
taps
Valves
1
2
3
4
0.5” smooth
2.0” rough
Relief
valves
Floor
Venturi meters
D t = 1.0”
D t = 2.0”
D t = 0.5”
Blower
36’
Venturi meter gate valves
Thermometer
Differential
manometer
Test Design
(Continue)
Reservoir:
Digital Micrometer:
To build up pressure and force the air to
flow downstream through any of the three
straight experiment pipes.
Allow 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)
Pressure tap manifold and Pitot-tube housing
Pressure tap manifold
Pitot-tube housing
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.
Measurement Systems
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
(continue)
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
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)
2 g w
u (r )
Z SM stag (r ) Z SM static
a
Flow rate, Friction factor and velocity profile
measurement systems
Block diagram of the experimental
determination of the Friction
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) =
gD
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
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
Uncertainty Analysis
The data reduction equation for the friction factor is:
f F ( g, D, L, Q, w , a , ZSMi , ZSM j )
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 2f i2 Bi2 Z2SM BZ2SM Z2SMj BZ2SM
i 1
Pf
tS f
M
i
i
j
Uncertainty Analysis
(continue)
Data Reduction equation for the velocity profile is as follow:
f F ( g, w , a , ZSM sta g n a tio n, ZSM sta tic )
U B P
2
u
2
u
j
Bu2 i2 Bi2 Z2SM
i 1
stagn
2
u
BZ2SMstagn Z2SM BZ2SM
Pu
stat
tSu
M
stat
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
0.02
0.015
0.01
0.008
0.006
0.004
/ Re
= 64
Friction Factor f =
0.040
f
Fl o w
in a r
0.050
Lam
0.060
0.030
0.025
0.002
0.020
0.001
0.0008
0.0006
0.0004
Hydraulically Smooth
0.015
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
Reynolds Number, Re =
10
VD
6
0.00001
10
7
10
8
Relative Roughness,
k /D
0.05
0.04
0.03
0.070