FLUID FLOW MEASUREMENT

FLOWMETER

• Flowmeter adalah alat untuk mengukur jumlah ataulaju aliran dari suatu fluida yang mengalir dalam pipaatau sambungan terbuka.

• Flowmeter umumnya terdiri dari dua bagian, yaitu alatutama dan alat bantu sekunder. Alat utamamenghasilkan suatu signal yang merespons terhadapaliran karena laju aliran tersebut telah terganggu. Alatutamanya merupakan sebuah orifis yang mengganggulaju aliran, yaitu menyebabkan terjadinya penurunantekanan.

• Alat bantu sekunder menerima sinyal dari alat utama lalumenampilkan, merekam, dan/ataumentrasmisikannya sebagai hasil pengukuran dari lajualiran.

Water Flow Rate Units

• Volume / Time• Cubic Feet Per Second (CFS)• Gallons / Minute (GPM)

• Acre-inch / hour• Miners Inch - used in the western US

The Bernoulli equation can be applied to several commonly occurring situations in which useful relations involving pressures, velocities and elevations may be obtained.

A very important application in engineering is fluid flow measurement

�Measurement of velocity : Pitot-static tube�Measurement of flow rate: Venturi meter

Orifice meter

Applications : Flow Measurement

Flow Measurement Devices

• Pitot static tube

• Orifice Meter• Nozzle Meter

• Venturi Meter• Rotameter

• Turbine Meter• Coriolis Meter

The Pitot-Static Tube

P1,V1 Stagnation Point V2=0

1 2

�P1 is a Static pressure: It is

measured by a device (static

tube) that causes no velocity

change to the flow. This is

usually accomplished by drilling

a small hole normal to a wall

along which the fluid is flowing.

�P2 is a Stagnation pressure:

It is the pressure measured by

an open-ended tube facing the

flow direction. Such a device is

called a Pitot tube.

P2

Pitot-Static tubeBernoulli equation between 1 and 2: 0

2

)VV()PP( 21

2212 =−+

ρ−

(Recall that position 2 is a stagnation point: V2= 0)

2/1

121

)PP(2V

ρ−=

We can measure pressures P1 and P2 using hydrostatics:

P1=Patm + ρgh1, P2=Patm + ρgh2

or using a Pressure Gauge

2112 V

2

1PP ρ+=

�Stagnation Pressure is higher than Static Pressure

Example: Measurement of VelocityAn airplane flies at an elevation of 10,000 ft in standard atmosphere. The pressure difference indicated by the Pitot-static probe attached to the fuselage is 0.1313 psi. What is the velocity of the airplane? (The density of air at this altitude is 0.056 lbm/ft3)

ORIFICE METER

• Fluid is accelerated by forcing it to flow through a constriction, thereby increasing kinetic energy and decreasing pressure energy. The flow rate is determined by measuring the pressure difference between the meter inlet and a point of reduced pressure.

• Desirable characteristics of flow meters:

– Reliable, repeatable calibration

– Introduction of small energy loss into the system

– Inexpensive

– Minimum space requirements

Basic principle: Increase in velocity causes a decrease in pressure.

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.

Generalized flow obstruction in a pipe

P1 P2

V1

1 2

Bernoulli equation between 1 and 2:

Continuity equation between 1 and 2: 2211 VAVAQ ==

])A/(A-[1

)PP(2 V

212

21ideal,2 ρ

−=

02

)VV()PP( 21

2212 =−+

ρ−

Generalized flow obstruction in a pipe

• In eq. frictional losses have not been taken into account• To account for frictional losses we use a “discharge”

coefficient, Cυ:

])A/(A-[1

)PP(2C V

VCV

212

212

ideal,22

ρ−=

=

υ

υ

22AVQ =

• The volumetric flow rate can be easily calculated:

Orifice MeterThis type of meter consists of a thin flat plate with a circular hole drilled in its center. It is very simple, inexpensive and easy to install, but it can cause significant pressure drops.

P1 P2

V1

1 2

Front view of orifice plate

])A/(A-[1

)PP(2C V

212

212 ρ

−= υ

Where the discharge coefficient,

Cυ =f(Re, D2/D1), can be found

in textbook

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

=

−−

=ρβ

where:β = 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.

Nozzle Meter

P1 P2

The nozzle meter uses a contoured nozzle. The resulting flow pattern for the nozzle meter is closer to ideal.

])A/(A-[1

)PP(2C V

212

212 ρ

−= υ

Where the nozzle discharge

coefficient, Cυ =f(Re, D2/D1),

can be found in textbooks and

is higher than the orifice

discharge coefficient.

Venturi MeterThis device consists of a conical contraction, a short cylindrical throat and a conical expansion. The fluid is accelerated by being passed through the converging cone. The velocity at the “throat” is assumed to be constant and an average velocity is used. The venturi tube is a reliable flow measuring device that causes little pressure drop. It is used widely particularly for large liquid and gas flows.

P1 P2

])A/(A-[1

)PP(2C V

212

212 ρ

−= υ

Where the discharge

coefficient, Cυ =f(Re), can

be found in textbook

Example 1: Flow through an orifice meterA lubricating oil flows through a 5” Schedule 40 steel pipe (which corresponds to 5.047in ID) at 300 gal/min. A sharp-edged orifice is inserted into this pipe and attached to a mercury manometer. At the flow temperature the oil has a specific gravity of 0.87 and a viscosity of 15cp. What manometer reading is expected if the manometer is positioned vertically and the orifice diameter is 3.5 in?

Example 1

Example 2: Flow through an orifice meter

An orifice meter like that shown in the previous page is used to monitor the water flow rate in a 10 cm diameter pipe. Determine the volumetric flow rate if the orifice has a diameter of 2 cm and the manometer shows a 30 cm difference in mercury.

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. Rotametersare 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 ρρρ −−∆−−=− 2113

( )ρ

ρρρ

−−

−

=∆+∆ bf

S

gV

S

S

S

Qzg

p

3

2

1

Rotameter

Mechanical Energy Balance

( ) fhp

zgVVW +∆+∆+−=ρ

21

232

1ˆ

0

2

23V

Kh Rf =Assume: (Base velocity head on smallest flow area)

−

−=∆+∆

2

3

21

2

3

21

212

1

S

SVK

S

SVVzg

pRρ

Rotameter

( ) ( )

+−

=−−

−

2

3

2

3

2

112

11

S

SK

S

Q

S

gV

S

S

S

QR

bf

ρρρ

Combining Momentum and Mechanical Energy Balance

After Some Manipulation

( ) ρρρ −

+= f

f

f

fR

f

S

gV

SSK

SSSQ

2

1 23

RotameterAssuming 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.

ρρρ −

= 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. Coriolismeters 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

ft

lbsft

lb

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

=

∗

−=

=

∗

∗∗−=∆

>→=

−=∆∆=∆

===

−−

=

ρ

β

ρβ

( )

000,306840107197.6

5.4

304.53120.3

125.1

2.17min

6048.7120.3

412

5.1

4

4

3

.2

.2

<=

×∗

∗

∗

=∗∗=

=∗∗∗

=∗=

−

cPsft

lb

cP

ft

lb

s

ftft

UdN

GPMs

ft

gal

s

ftft

Ud

Q

m

m

ooRE

oo

µρ

ππ