Flow Measurement
• Direct Method
• Restriction Flow Meter
– Orifice Plate
– Flow Nozzle
– Venturi
• Linear Flow Meters
• Traversing Methods
Flow Measurement
• Direct Method
• Restriction Flow Meter
– Orifice Plate
– Flow Nozzle
– Venturi
• Linear Flow Meters
• Traversing Methods
Direct Method
Liquid
Gas
Restriction Flow
Meters
1
2
V
1
V
2
D
1
D
2
D
t
Vena contracta
Assumptions:
(1)
Steady flow
(2)
Incompressible flow
(3)
Flow along a streamline
(4)
No friction
(5)
Uniform velocity at 1
and 2
(6)
Uniform pressure at 1
and 2
(7)
z
1
=z
2
Theoretical Flow Rate
Basic equations:
2
2
2
2
2
2
1
1
V
p
V
p
CS
CV
A
d
V
V
d
t
0
= 0
1
2
V
1
V
2
D
1
D
2
D
t
Vena contracta
2
2
2
2
2
2
1
1
V
p
V
p
CS
CV
A
d
V
V
d
t
0
= 0
2
2
1
1
A
V
A
V
2
2
1
2
2
2
1
2
2
2
1
1
2
2
V
V
V
V
V
p
p
2
1
2
2
2
1
or
A
A
V
V
2
1
2
2
2
2
1
1
2
A
A
V
p
p
Theoretical Flow Rate
]
1
[
2
2
1
2
2
1
2
A
A
p
p
V
2
1
2
1
2
1
2
2
2
2
l
theoretica
2
]
1
[
p
p
A
A
A
A
V
m
Theoretical Flow Rate vs(versus) Actual Flow Rate
2
1
2
1
2
1
2
2
l
theoretica
2
]
1
[
p
p
A
A
A
m
2
1
2
1
2
1
actual
2
]
1
[
p
p
A
A
CA
m
t
t
C: discharge coefficient
Let = D
t
/D
1
,
then (A
t
/ A
1
)
2
= (D
t
/D
1
)
4
=
4
2
1
2
1
4
actual
2
]
1
[
p
p
CA
m
t
factor
-approach
elocity-of
:
1
1
4
2
1
actual
2
p
p
KA
m
t
2
1
4
]
1
[
C
K
C: discharge coefficient
For the turbulent flow regime,
n
D
b
C
C
1
Re
Flow-coefficient equation has the form of
n
D
b
K
K
1
Re
1
1
4
Subscript denotes the coefficient at infinite Reynolds number.
Flow Meter Installation
• Flow meter coefficients are measured
with fully developed turbulent velocity
distributions at the meter inlet.
• If installed downstream from a valve, a
fitting, or other disturbance, a straight
section pipe must be placed in front of the
meter.
– For venturi meters, L
straight pipe
10 D
– For orifice-plate or flow nozzle meters,
L
straight pipe
40 D
Flow Meter Type
Head Loss
Cost
D
1
D
t
Orifice
High
Low
D
1
D
t
Flow Nozzle
IntermediateIntermediate
D
1
D
t
Venturi
Low
High
Characteristics of Restriction Flow Meters
The Orifice Plate
D
2
D
''
1
''
1
Flow
D and D/2 taps
Corner taps
Flange taps
75
.
0
5
.
2
8
1
.
2
1
Re
71
.
91
184
.
0
0312
.
0
5959
.
0
D
C
7
4
10
Re
10
and
75
.
0
2
.
0
For
1
D
For corner taps
The Flow Nozzle
Nozzle
2
D
1
p
0
1
V
Flow
Plenum chamber
Flow
2
D
1
D
1
V
1
p
2
p
5
.
0
5
.
0
1
Re
53
.
6
9975
.
0
D
C
7
4
10
Re
10
and
75
.
0
2
.
0
For
1
D
ASME long-radius nozzle
The Venturi
• Discharge coefficients range from 0.98
to 0.995 at high Reynolds numbers.
• All restriction flow meters produce
pressure differentials proportional to
the square of the flow rate.
• A meter must be chosen to
accommodate the highest expected
flow rate.
Linear Flow Meters
• Flow meters produce outputs that
are directly proportional to flow
rate.
• Examples of linear flow meter
– Float meter (rotameter), turbine flow
meter, vortex flow meter,
electromagnetic flow meter,
ultrasonic flow meter.
Traversing Methods
• The duct cross section is subdivided
into segments of equal area; the
velocity is measured at the center of
each area segment using a pitot tube
or a suitable anemometer.
• Flow meter can be used for traversing
method
– Pitot tube, thermal anemometer, Laser
Doppler anemometer.
Homework: 8.88, 8.145, 8.159, 8.167