fluid flow measurement - laskarteknik.co.id · • flowmeter adalah alat untuk mengukur jumlah atau...
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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