Flowmeter

Flow Measurement and Control
Orifice Meter
The orifice meter consists of an accurately machined and
drilled plate concentrically mounted between two flanges.
The position of the pressure taps is somewhat arbitrary.
Orifice Meter
The orifice meter has several practical advantages
when compared to venturi meters.
Lower cost
Smaller physical size
Flexibility to change throat to pipe diameter
ratio to measure a larger range of flow rates
Disadvantage:
Large power consumption in the form of
irrecoverable pressure loss
Orifice Meter
The development of the orifice meter equation is similar to
that of the venturi meter and gives:
( )
0
4
0
2
1
S V q
p p C
V
b a
=
|
where:
| = ratio of orifice diameter to pipe diameter 0.5 usually
S
0
= cross sectional area of orifice
V = bulk velocity through the orifice
C
0
= orifice coefficient 0.61 for Re > 30,000

There is a large pressure drop much of which is not
recoverable. This can be a severe limitation when
considering use of an orifice meter.
Pressure Loss in
Orifice Meters
ASME Design Standards
Fluid Meters: Their Theory and Applications, 6
th

ed., American Society of Mechanical Engineers,
New York, 1971 pp. 58-65.
Rotameters
Rotameters fall into the category of flow
measurement devices called variable area
meters. These devices have nearly constant
pressure and depend on changing cross
sectional area to indicate flow rate. Rotameters
are extremely simple, robust devices that can
measure flow rates of both liquids and gasses.
Fluid flows up through the tapered tube and
suspends a float in the column of fluid. The
position of the float indicates the flow rate on a
marked scale.
Rotameters
Three types of forces must be
accounted for when analyzing
rotameter performance:
Flow
Gravity
Buoyancy
Flow
Buoyancy
Gravity
For our analysis neglect drag effect
Rotameter
Mass Balance
Assume Gradual Taper
S
Q
V V
S V S V
= =
=
2 1
2 1
Flow Between Float and Tube
( )
3
1 3
S
S
V
S S
Q
V
f
=
=
S
3
is annular flow area at plane 3
Rotameter
Momentum Balance
Note:
p
3
= p
2
Must account for force due to float
( ) ( ) | |
f f f
gV V zS g S p p V V Q A =
2 1 1 3
( )
|
|
.
|
\
|
|
.
|
\
|
= A +
A
b
f
S
gV
S
S
S
Q
z g
p
3
2
1
Rotameter
Mechanical Energy Balance

( )
f
h
p
z g V V W +
A
+ A + =
2
1
2
3
2
1
0
2
2
3
V
K h
R f
=
Assume:
(Base velocity head on
smallest flow area)
(
(
|
|
.
|
\
|
|
|
.
|
\
|
= A +
A
2
3
2
1
2
3
2
1
2
1
2
1
S
S
V K
S
S
V V z g
p
R
Rotameter
( )
( )
(
(
|
|
.
|
\
|
+
|
.
|
\
|
=
|
|
.
|
\
|
|
.
|
\
|
2
3
2
3
2
1 1
2
1
1
S
S
K
S
Q
S
gV
S
S
S
Q
R
b
f

Combining Momentum and Mechanical Energy Balance
After Some Manipulation
( )

+
=
f
f
f
f R
f
S
gV
S S K
S S
S Q
2
1
2
3
Rotameter
Assuming S
f
S a discharge coefficient can be
defined
( )
2 1
1

+ ~
R R
K C
C
R
must be determined experimentally. As Q increases the float rides
higher, the assumption that Sf = S is poorer, and the previous expression
is more nearly correct.

=
f
f
f
R
S
gV
C S Q
2
3
Other Flow Meters
Turbine Meter
Measure by determining RPM of turbine (3) via sensor (6).
Turbine meters are accurate but fragile.
Coriolis Meters
When fluid is passed through a U-bend, it imposes a force on the tube
wall perpendicular to the flow direction (Coriolis force). The
deformation of the U-tube is proportional to the flow rate. Coriolis
meters are expensive but highly accurate.
Pneumatic Control Valves
Orifice Meter Example
A 2 in. Schedule 40 pipe carries 35
API distillate at 50
F (SG=0.85). The flow

rate is measured by an orifice meter which has a diameter of 1.5 in. The
pressure drop across the orifice plate is measured by a water manometer
connected to the flange taps. If the manometer reading is 20 in. of H
2
O, what
is the flow rate of the oil in GPM ?
s
f t
f t
lb
s f t
lb
U
s f t
lb
f t
s
f t
f t
lb
P
N C Assume
P P h g P
in
in
d
d
P P C
U
m
m
o
m m
o
b a
p
o
b a o
o
120 . 3
04 . 53
3 . 502 2
) 726 . 0 ( 1
61 . 0
3 . 502
12
20
2 . 32 4 . 62 ) 85 . 0 1 (
000 , 30 61 . 0 :
) (
726 . 0
067 . 2
5 . 1
) ( 2
1
3
2
4
2 2 3
Re
4
=
|
|
.
|
\
|
-
=
= |
.
|
\
|
- |
.
|
\
|
- - = A
> =
= A A = A
= = =
|
( )
000 , 30 6840
10 7197 . 6
5 . 4
3
04 . 53 120 . 3
12
5 . 1
2 . 17
min
60 48 . 7
120 . 3
4
12
5 . 1
4
4
3
.
2
.
2
< =
|
|
|
|
.
|
\
|

-
|
|
.
|
\
|
-
|
.
|
\
|
-
|
.
|
\
|
=
- -
=
= - - -
|
.
|
\
|
= - =
cP
s f t
lb
cP
f t
lb
s
f t
f t
U d
N
GPM
s
f t
gal
s
f t
f t
U
d
Q
m
m
o o
RE
o
o

t
t
Now what ???

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Flow Measurement and Control

F (SG=0.85). The flow

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