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 MeterThe development of the orifice meter equation is similar to that of the venturi meter and gives:

0

4

0 2

1

SVq

ppCV ba

where: = ratio of orifice diameter to pipe diameter ≈ 0.5 usuallyS0 = cross sectional area of orificeV = bulk velocity through the orificeC0 = 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 inOrifice Meters

ASME Design Standards

Fluid Meters: Their Theory and Applications, 6th ed., American Society of Mechanical Engineers, New York, 1971 pp. 58-65.

RotametersRotameters 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

RotameterMass Balance

Assume Gradual Taper

S

QVV

SVSV

21

21

Flow Between Float and Tube

313 S

SV

SS

QV

f

S3 is annular flow area at plane 3

Rotameter

Momentum BalanceNote:• p3 = p2

• Must account for force due to float

fff gVVzSgSppVVQ 2113

bf

S

gV

S

S

S

Qzg

p

3

2

1

Rotameter

Mechanical Energy Balance

fhp

zgVVW

21

232

1ˆ

0

2

23VKh Rf Assume: (Base velocity head on

smallest flow area)

2

3

21

2

3

21

212

1

S

SVK

S

SVVzg

pR

Rotameter

2

3

2

3

2

112

11

S

SK

S

Q

S

gV

S

S

S

QR

bf

Combining Momentum and Mechanical Energy Balance

After Some Manipulation

f

f

f

fR

f

S

gV

SSK

SSSQ

2

1 23

Rotameter

Assuming Sf ≈ S a discharge coefficient can be defined 211 RR KC

CR 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

fR S

gVCSQ

23

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 35º 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 H2O, what is the flow rate of the oil in GPM ?

s

ft

ftlbsftlb

U

sft

lbft

s

ft

ft

lbP

NCAssume

PPhgP

in

in

d

d

PPCU

m

m

o

mm

o

ba

p

o

baoo

120.304.53

3.5022

)726.0(1

61.0

3.50212

202.324.62)85.01(

000,3061.0:

)(

726.0067.2

5.1

)(2

1

3

2

4

223

Re

4

000,306840107197.6

5.4

3

04.53120.312

5.1

2.17min

6048.7120.3

412

5.1

4

4

3

.2

.2

cPsft

lb

cP

ft

lb

sft

ftUd

N

GPMs

ft

gal

s

ftft

Ud

Q

m

m

ooRE

oo

Now what ???