Transcript A Compressed Air System

MER 160 - Design of Thermal Fluid Systems
Flowmeters
Professor Anderson
Winter Term 2005
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Flow Measurement
The choice of a flow meter is influenced
by:
accuracy
range
cost
complication
service life
The simplest cheapest device that gives
the desired accuracy should be chosen
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Flow Measurement Methods
Direct Methods
 Restriction Flow Meters
 Linear Flow Meters
 Others
 Traversing Methods

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Direct Methods

Steady liquid flows


Steady Gas flows


Use a tank and measure the volume/mass
collected during a known interval
Compressibility effects usually make this
impossible
Major Advantage - no calibration is
required
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Restriction Flow Meters
An effective way to
measure flowrate
through a pipe is to
place a restriction in the
pipe and measure
pressure drop from:
(1) High P-Low V upstream to
(2) High V-Low P downstream
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Restriction Flow Meters


Correlation of the pressure difference
with velocity provides a means of
measuring flow rate.
From Bernoulli’s (for ideal flow)
Qideal  A2V2  A2
2( P1  P2 )
 (1   4 )
D2
where  
D1
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Restriction Flow Meters

There is a head loss from point 1 to 2:
V12
V22
P1
P

 2
 hL
g 2 g g 2 g



The ideal situation has hL = 0.
There is no accurate expression for hL.
Need to use empirical coefficients.
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RFM -Orifice Meter
Typical Orifice
meter is
constructed by
inserting a plate
with a hole
between two
flanges of a pipe.
Q  CoQideal  Co Ao
2( P1  P2 )
 (1   4 )
where Ao 
d 2
4
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RFM - Orifice Meter
Co = Orifice Discharge
Coefficient
Value depends on
geometry.
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RFM - Nozzle Meter



Uses a contoured nozzle placed between
flanges of a pipe.
Flow pattern is closer to ideal.
More expensive.
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RFM -Nozzle Meter

Losses are accounted for by a Nozzle
Discharge Coefficient:
Q  CnQideal 
Cn An
An 
2( P1  P2 )
 (1   4 )
d 2
4
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RFM - Venturi Meter




Most precise and most expensive.
Geometry is designed to reduce head losses to
a minimum.
Streamlined contraction and gradual expansion.
Most head loss caused by friction.
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RFM - Venturi Meter

Losses are accounted for by a Venturi
Discharge Coefficient:
Q  CnQideal 
Cv AT
AT 
2( P1  P2 )
 (1   4 )
d 2
4
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RFM - Laminar Flow Meters
The LFE contains small sub passages where
the flow is fully developed and laminar.
Produces a pressure drop directly proportional
to flow rate.
High Range of Flow Rate
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RFM - Example Problem
What is the pressure drop across an 8 in
orifice in a 12 in water pipe for a flow
rate of 5 ft3/s? The water temperature is
60 oF.
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RFM - Example Problem
First calculate Re:
ft 3
(1 ft )(5 )
DQ
s
Re 

 7.8 x105
A ( (1) 2 / 4 ft 2 )(1.22 x105 ft 2 / s )
d 8
  0.667
D 12
From Figure: Co ~ 0.61
What would it be for a nozzle meter (~0.99)?
How about a Venturi Meter (~0.99)
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RFM - Example Problem
Calculate Pressure Drop:
Q  Co Ao
( P1  P2 ) 
2( P1  P2 )
 (1   4 )
Q 2 (1   4 )
2(Co Ao ) 2
 84.5lb / ft 2  0.59 psi

(1.94slugs / ft 3 )(52 ft 6 / s 2 )( 1 - 0.674 )
2(0.61* 0.785) 2 ft 4
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RFM -Summary
Flow Meter
Type
Head Loss
Cost
Orifice
High
Low
Flow Nozzle
Intermediate
Intermediate
Venturi
Low
High
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Linear Flow Meters
Rotameters: A float
rises through the
meter as the fluid
flows. The float
reaches an
equilibrium height as
a function of flow
rate. (net forces add
to zero - buoyancy,
weight, drag)
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Linear Flow Meters
Turbine Meter: Angular
velocity of the freely
rotating turbine is
proportional to fluid
velocity. The angular
velocity is picked up
magnetically.
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Volume Flow Meters
Measure the volume of fluid that has passed
through a pipe during a given time instead
of the instantaneous rate. (i.e. gasoline
pumps)
Nutating Disk Meter:
measures the flow of a
liquid by counting the
number of times a disk
in the path of the liquid
is caused to wobble back and forth.
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Volume Flow Meters
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Volume Flow Meters
Bellows-type Flow
Meter:The bellows
are alternately
filled and emptied
as the gas flows
through the meter,
and their action is
used as a counting
mechanism.
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Others
Electromagnetic - a conductor moving in
a magnetic field produces as
electromagnetic force - this is
proportional to velocity.
Ultrasonic - measures the difference in
travel time for a sound wave to travel
upstream and downstream between 2
measuring stations.
Vortex Flow Meter - Vortex shedding
from a cylinder is detected. The shedding
frequency is proportional to flow rate.
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Traversing Methods
It is sometimes impractical to install
fixed flow meters and instead the flow
rate is found by traversing the pipe with
a velocity probe and integrating the
profile.




Pitot Probe
Hot Wire Anemometer
Laser Doppler Anemometer
Particle Image Velocimeter.
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