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11-1 Flow *
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Measures of Fluid Flow
- Flow velocity.
Speed of material flowing past a plane.
- Volumetric flow.
Volume of material passing a plane per unit time.
- Mass flow.
Mass of material passing a plane per unit time.
When fluid incompressible : : :
: : :flow velocity, volumetric, and mass flow are proportional.
Types of Flowing Fluids to be Measured
- Liquid in closed conduit. (E.g., water in a pipe.)
- Liquid in an open conduit. (E.g., water in a canal.)
- Gas in an closed conduit.
- Slurry (solids suspended in liquids) in a closed conduit.
Different transducers may be required for each situation.
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Some Major Types of Sensors
- Rotation.
Fluid forces an object placed in flow to rotate. Speed of rotation
is measured.
- Obstruction.
Fluid flow is partially obstructed. Pressure is measured on both
sides of obstruction, flow rate deduced.
- Heat dissipation.
A heating element is placed in the flow. Flow rate deduced by
amount of heat removed.
- Head.
Measure fluid level flowing into a drop.
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11-3 Rotation Sensors *
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Force of flow causes some object to rotate. Two types will be dis-
cussed, turbine and paddle wheel.
Turbine Type
Used to measure volumetric flow in a closed conduit.
Typical Construction.
Turbine placed in flow in a plastic section of pipe.
Turbine blades made of metal.
Magnetic reluctance transducers placed outside pipe near blades.
Flow causes turbine to spin.
Rate of spin measured by magnetic reluctance sensor.
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11-4 *
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Model Function
This includes the turbine, the magnetic reluctance sensor, a conditioning
circuit, and a frequency counter.
Ht1 (x) = k x, where k is a constant called the k factor, having units of
one over volume.
Paddle Wheel
Used to measure volumetric flow in an open conduit.
Consists of a wheel partially immersed in the flow.
Flow causes wheel to turn.
Same model function as turbine flow meter.
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11-5 Paddle Wheel/Speed Measurement Example *
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Design a system to convert process variable x 2 [0; 80 ml__s], flow in a
pipe, into a floating-point number H (x) to be written into variable
paddleFlow, where H (x) = x _s__ml. The value must have a precision
of 0:1 ml__s. Use an FP-2502 paddle-wheel flow sensor.
Solution Overview
Flow sensor generates a voltage pulse train.
Digital comparator converts to logic level.
Counter counts pulses.
At regular intervals count transfered to register, and counter reset.
At irregular intervals interface routine reads register and completes condi-
tioning.
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The FP-2502 Flow Sensor
Output pulse minimum 2 V.
For each ml flow there are 8.5 pulses.
Measurable range, 50 _ml___min; 6000 _ml___min.
Cost, $530.
Design Decisions
Threshold for digital comparator.
Number of bits in counter and register.
Amount of time between samplings of counter.
Interface routine.
Digital Comparator Threshold
Set negative input to slightly less than 2 V.
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Counter Contents
Let Hctr(x; t) give the counter value t time after being reset, where x is
the flow rate.
Then, Hctr(x; t) = x k t, where k = 8:5_ml. (This assumes that x is constant
while the counter is counting.)
Let tc denote the amount of time that the counter counts before its con-
tents are transfered to the register.
Let Hr(x) give the value clocked into the register.
Then r = Hr(x) = Hctr(x; tc) = x 8:5_mltc.
This value will be read by the interface routine.
Solving for x yields x = r ml__8:51_t.
c
To obtain Hf :
Hf(Hr(x)) = H(x)
Hf(r) = H r ml__8:51_t
c
= __s_mlr ml__8:51_t
c
= r __1____8:5ts
c
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To complete the solution choose tc and the number of bits in the counter
and register.
Precision goal is 0:1 ml__s.
Smallest change in r is 1.
Therefore constraint Hf(r) Hf(r 1) 0:1 must hold.
Applying Hf, _1__8:51_ts(r (r 1)) 0:1.
c
As a safety margin, solve _1__8:51_ts = 0:025.
c
tc = 4:706 s.
Then, Hr(80 ml__s) = 3200. Therefore a 12-bit counter is needed.
Interface routine code:
r = readInterface();
paddleFlow = r * 0.025;
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11-9 Obstruction Flow Meters *
* 11-9
Used to measure volumetric flow in closed conduits.
Typical Construction
An obstruction placed in pipe.
Obstruction might be:
a plate with hole in center (called an orifice plate) or
a carefully shaped venturi tube.
Obstruction causes a pressure difference.
Pressure difference measured with a differential pressure sensor.
Flow rate deduced from differential pressure.
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11-10 *
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Model Function
Consider an obstruction flow meter in which:
the pipe is in a horizontal position,
the fluid is incompressible and of density ffi,
the area at point 1 is A1 , the area at point 2 is A2 ,
and the pressure at point 1 is P1 and the pressure at point 2 is P2 .
The model function for such a transducer is
2 )
Ht1 (x) = x2 ffi(1__(A1_=A2_)______2C2= 2P2 P1 ,
d A1
where Cd is a constant called the discharge coefficient.
In an ideal transducer, Cd = 1.
For a typical venturi tube, Cd = :97 and for a typical orifice plate, Cd =
:6.
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11-11 *
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Example Problem
Convert the process variable x 2 0 __l__min; 1000 __l__min, volumetric flow
of water in a 50 mm diameter pipe, to a floating point number H (x)
stored in variable vflow where H (x) = x min__l. Use an Omega brand
PX 820-070DV differential pressure sensor and an ADC with re-
sponse HADC(10 V ;10) .
Solution Diagram:
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Solution Overview:
- Use an orifice plate flow transducer. Call area of orifice A1 .
Call response and output of flow transducer
2 )
y = Ht1 (x) = x2 ffi(1__(A1_=A2_)______2C2: 2
d A1
- Use the differential pressure transducer to convert pressure differ-
ence to voltage.
Response of Omega brand PX 820-070DV differential pressure
sensor is
z = Hp (y) = ___y___p100 mV
max
for a 5 V excitation and for y 2 [0; pmax ] where pmax = 5 bar .
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Solution Overview:
- Use an instrumentation amplifier to amplify the voltage for the
ADC. Response is w = Hc (z) = gz. (Symbol g is being used for
gain instead of A.)
- Use the ADC and an interface circuit to prepare the data for the
computer.
w
Response is r = HADC(10 V;10) (w) = _______1023.
10 V
- Write an interface routine, Hf, to produce the desired output:
Hf(HADC(10 V;10) (Hc(Hp (Ht1 (x))))) = H(x) = x min___l:
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Constraints and Solution Plan:
- Choose orifice diameter so that differential pressure is in range
[0; pmax ]:
0 Ht1 (x) pmax = 5 bar for x 2 0 __l___min; 1000 __l___min
- Choose amplifier gain, g, so that ADC input is in range [0; 10 V]:
0 Hc(Hp (Ht1 (x))) 10 V for x 2 0 __l___min; 1000 __l___min
- Write interface routine to get desired output.
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Orifice Plate Diameter
To make full use of the pressure sensor's dynamic range : : :
: : :choose A1 so that:
0 Ht1 (x) pmax = 5 bar
2 )
0 x2 ffi(1__(A1_=A2_)______2C2 p2max = 5 bar ;
d A1
where ffi = 1 __g___cm3, A2 = ss(25 mm )2 and Cd = :6.
Solve Ht1 (xmax ) = pmax for A1 :
0 1 1_2
1 pmax C 2
A1 = B@ _____2 _______________ij2A = 0:0008018 m
A2 ffi_xmax__
2 Cd
Or, orifice diameter is 31:95 mm .
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Amplifier Gain
To avoid confusion with A1 and A2 : : :
: : :let g denote amplifier gain.
Choose amplifier gain so that:
0 Hc(Hp (Ht1 (x))) 10 V
Since each function is monotonic and has a positive slope:
Hc(Hp (Ht1 (xmax ))) = 10 V
Substituting pmax for Ht1 (xmax ):
Hc(Hp (pmax )) = 10 V
Applying functions: g pmax___p100 mV = 10 V, so
max
g = 100.
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Interface Routine
Output of ADC:
r = HADC(10 V;10) (Hc(Hp (Ht1 (x))))
10 1) 100 mV ffi x 2 1 1
= (2__________10gV___________5_bar2___C ____2 ____2
d A1 A2
Solving for x yields
s _____________________________________________________
1
x = _10_V_____2101_g15_bar_1002mV_ffiC2d _1__A2 _1__2 r
r ________________________ 1 A2
6
= 2:718 107 m____s2r
Need to find Hf such that:
Hf(HADC(10 V;10) (Hc(Hp (Ht1 (x))))) = H(x) = x min___l
Substituting,
r ________________________! r _________________________
6 m6 min
Hf(r) = H 2:718 107 m____s2r = 2:718 107 _____s2r ______l
3 min p __ p __
= 0:0005212 m____s_____l r = 31:27 r
Interface routine:
r = readInterface();
vflow = 31.27 * sqrt( r );
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11-18 Other Flow Transducers *
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Hot-Wire Anemometer
Used to measure mass flow in a closed or open conduit.
Construction:
A thermistor, RTD, or other self-heating temp. transducer placed in
flow.
Fluid carries heat away from temperature transducer.
Transducer is maintained at a constant temperature by a feedback cir-
cuit.
Current is related to flow rate.
No model function or circuit will be given.
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11-19 *
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Two-Temperature Transducer Flow Meter
Used to measure mass flow in a closed or open conduit.
Construction:
Two temperature transducers placed in fluid.
One is exposed to flow.
The other is exposed to stationary fluid.
Transducers are connected in a bridge configuration.
No model function or circuit will be given.
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Weir Flow Meter
Used to measure volumetric flow in open conduits.
Construction:
Water flows in an open conduit (like an aqueduct), over a drop.
Shape of cut over which water falls is specially chosen.
Flow rate determined by height of water.
Model Function
For a rectangular cut, Ht1 (x) = k x2=3 .
For a V-notch cut, Ht1 (x) = k x2=5 .
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Slurry Flow Measurement Methods
Flow contains a suspension of particles.
For example, coal mixed with water,
water with air bubbles, etc.
- Sonar. Measures flow velocity.
Sound injected nearly parallel to the direction of flow.
Microphones pick up reflected sound.
Speed determined by Doppler shift.
- Cross correlation. Measures flow velocity.
Some property is measured at two points in the flow, for example
electrical resistance.
Let the two points be separated by a distance d.
Let p1 (t) be the property measured at point 1 and time t.
Let p2 (t) be the property measured at point 2 and time t.
The interface routine finds a t such that p1 (t) ss p2 (t + t) for
some range t 2 [t1 ; t2 ].
The flow velocity is then d=t.
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| David M. Koppelman - koppel@ee.lsu.edu | Modified 24 Feb 1999 8:21 (14:21 UTC) |