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11. Flow 11. Flow MeasurementsMeasurements
1. Flow rate measurement1. Flow rate measurement
A primitive (but fairly accurate) way of measuring the flow rate
of water through a garden hose involves collecting water in a
bucket and recording the collection time.
TimeVolume
=Q
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2. Velocity measurement2. Velocity measurement
(1) Pitot probe (or Pitot tube) 皮托管
Stagnation pressure headg
Vh2
2
=
h
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(2) Pitot-static probe (皮托靜壓管)
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Pitot formula:
ρ)(2 21 PPV −=
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(3) Current meter (流速儀)
where(rpm) rotation
(m/s) velocitycurrent ==
+=
NV
bNaV
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(4) Obstruction flowmeters (阻流式流速儀)
Mass balance: 22
21212211 )/()/( VDdVAAVVAVA ==→= (1)
Bernoulli equation )( 21 zz = : gV
gP
gV
gP
22
222
211 +=+
ρρ (2)
Combining Eqs. (1) and (2) and solving for velocity 2V gives
Obstruction (with no loss): )1()(2
421
2 βρ −−
=PPV
where Dd /=β
22
22 )4/( VdVAQ π==
Flow through a constriction in a pipe
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真實流量孔口儀
噴嘴儀
文德利管
22 VCAQ d=
流量係數=dCwhere
30,000ReFor >
meter) (Venturi 98.0(Orifice) 061(Nozzle) 96.0
=
=
=
d
d
d
CCC
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(5) Sonic (or Acoustic) flowmeter (聲波式流速儀)
• Transit time sonic flowmeter (傳遞時差式)
tKLV ∆=
where =K a constant =L distance between transducers =∆t travel
time difference
The operation of a transit time ultrasonic flowmeter equipped
with two transducers,www.flocat.com.
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• Doppler-effect (Frequency shift) sonic flowmeter (杜卜勒效應式)
The operation of a Doppler-effectultrasonic flowmeter equipped
with a transducer pressed on the outer surface of a pipe.
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(6) Thermal (Hot-wire and Hot-film) Anemometer (熱感式流速儀)
Schematic of a thermal anemometer system.
The electrically heated sensor and itssupport of a hot-wire
probe.
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King’s law: nbVaE +=2
where =E voltage =nba , , constants to be calibrated
Thermal anemometer probes with single, double, and triple
sensors to measure (a) one-, (b) two-, and (c) three-dimensional
velocitycomponents simultaneously.
1D 2D 3D
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(7) Laser Doppler Velocimetry (LDV)
or Laser Doppler Anemometry (LDA) (雷射杜卜勒流速儀)
A non-intrusive method (利用光學原理 非浸入式流速儀)
A dual-beam LDV system in forward scatter mode
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)]2/sin(2[ αλ=s
where =s spacing between fringe lines =wavelength of fringes =λ
wavelength of laser beam =α angle between two laser beams
⇒ LDV equation
λα )2/sin(2V
sVf ==
where =f frequency of scattered fringe lines =V velocity of a
particle traversing
fringe lines Fringes that form as a result ofthe interference at
theintersection of two laser beamsof an LDV system (linesrepresent
peaks of waves). Thetop diagram is a close-up viewof two fringe
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(8) Particle Image Velocimetry (PIV) 顆粒影像流速儀
A PIV system to study flame stabilization. Courtesy of TSI
Incorporated (www.tsi.com). Used by permission.
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wake region of a car as measured by a PIV system in a wind
tunnel. Thevelocity vectors are superimposed on a contour plot of
pressure. The interface between two adjacent grayscale levels is an
isobar.
Courtesy Dantec Dynamics, Inc. www.dantecmt.com.
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3D PIV system
A three-dimensional PIV system set up to study the mixing of an
air jet with cross duct flow. Courtesy TSI Incorporated
(www.tsi.com). Used by permission
