1. Flow rate measurements
Bachelor Degree in Chemical Engineering
Course: Process Instrumentation and Control
(Strumentazione e Controllo dei Processi Chimici)
Measuring devices of the main process variables
Flow rate measurements
Rev. 3.2 – March 28, 2019

2. FLOW RATE UNIT OF MEASUREMENT
MASS (m)
(kg/s)
VOLUMETRIC (V)
(L/s)
MOLAR (N)
(kmol/s)
§2.2.1 pag. 9
Magnani, Ferretti and Rocco (2007)
Process Instrumentation and Control - Prof M. Miccio

3. FLOW RATE METERS CLASSIFICATIONS
First classification (by contrast)
Volumetric
Mass
Static
Rotary
Trasducer
Non-Trasducer
Intrusive
Non-Intrusive
Process Instrumentation and Control - Prof M. Miccio

4. FLOW RATE METERS CLASSIFICATIONS
Second Classification
based on
measuring principle
Differential
pressure
Variable
Area
Velocity
Direct Mass
Measurement
Rotary
Process Instrumentation and Control - Prof M. Miccio

5. SECOND CLASSIFICATION (based on principle of measurement)
Differential Pressure
Variable Area
Velocity
Direct Mass Measurement
Positive displacement
Turbine type
Open channel
Process Instrumentation and Control - Prof M. Miccio

6. CONTRACTION-BASED FLOW METERS
HYPOTHESES:
horizontal position
ρ = constant
v # f (r )
Δploc= 0
circular pipe 1 2 d1 d2 A1 A2
From Bernoulli’s principle
(§ page 15 - Magnani, Ferretti and Rocco, 2007):
IDEAL CASE
γ ideal flow coefficient of a contraction
REAL CASE
Velocity is not uniform in cross sectional area (ξ<1, real case)
Local pressure drop
(vortices formation)
where β is the contraction ratio
Process Instrumentation and Control - Prof M. Miccio

7. CONTRACTION-BASED FLOW METERS
Hypotheses:
compressible fluid (Gas or Vapor);
small (P1 - P2);
K = calibration factor [m2]
“PI ON TI” CORRECTION
Process Instrumentation and Control - Prof M. Miccio

8. CONTRACTION-BASED FLOW METERS (orifice plates, flow nozzles, Venturi meter)
from Magnani, Ferretti and Rocco (2007)
Process Instrumentation and Control - Prof M. Miccio

9. ORIFICE PLATE or ORIFICE METERd1 d2
for VOLUMETRIC FLOWRATE MEASUREMENT of GAS or LIQUIDS
sharp restriction of the cross sectional area of the fluid flow;
thin diaphragm thickness;
design and installation meeting to STANDARD REGULATIONS (e.g.: UNI)
orifice can be off-axis;
orifice plate can be shaped as a semicircle;
orifice plate can have a groove interacting with the fluid.
Process Instrumentation and Control - Prof M. Miccio

10. Process Instrumentation and Control - Prof M. Miccio
DIAPHRAGMS Examples
vent (optional)
Φ=2,5mm
C.F.R.
Internal to the pipe
purge (optional)
Process Instrumentation and Control - Prof M. Miccio

11. ORIFICE PLATE INSTALLATION
Re > 500
HORIZONTAL POSITION
Undisturbed and straight pipeline 20D upstream and 5D downstream
d = orifice diameter
D = pipe diameter
β = d/D<1
Exploded view drawing
Process Instrumentation and Control - Prof M. Miccio

12. PRESSURE PROFILE OF A LIQUID IN A CONTRACTION
[(P/ρg)+(v2/2g)]
Friction loss P
Pressure drop due to the orifice
Kinetic energy
Pressure and potential energy
orifice_meter.swf
upstream
vena contracta
downstream
Process Instrumentation and Control - Prof M. Miccio

13. ORIFICE PLATE POSITIONING OF PRESSURE SENSORS
at vena contracta
on the carrier ring
on the pipeline
VENA CONTRACTA TAPS
M =1* PIPE DIA
N VARIES WITH b RATIO
Process Instrumentation and Control - Prof M. Miccio

14. ORIFICE PLATE POSITIONING OF PRESSURE SENSORS
at vena contracta
on the carrier ring
on the pipeline
LINE TAPS
on the pipeline
CORNER TAPS
on the carrier ring
Process Instrumentation and Control - Prof M. Miccio β

15. Process Instrumentation and Control - Prof M. Miccio
FLOW NOZZLE
Installation
Flow Nozzle
It measures the pressure drop before and after a contraction of the cross section of the pipe.
It measure ΔP by means a differential manometer.
It is easy to be replaced in piping with flow nozzles having a more wide range because it can assume different values of β
Process Instrumentation and Control - Prof M. Miccio

16. Process Instrumentation and Control - Prof M. Miccio
VENTURI METER
Venturi meter consists of a converging and a diverging sections.
The decrease in the section of the pipeline, due to the inverse proportionality that links the velocity to the section of the pipeline, determines, at constant flow, an increase in velocity (continuity equation).
Process Instrumentation and Control - Prof M. Miccio

17. Process Instrumentation and Control - Prof M. Miccio
VENTURI METER
The Venturi meter shape allows the homogeneity and the axial symmetry of the vena contracta. In improves the local flow regime of the fluid and the pressure meaurements from which depends the precision of the flow rate measure.
The variation of the inner contour of the Venturi meter, the small imperfection and roughness of the internal surface on the Venturi meter and the installation eccentricity are negligible and they don't have much influence on the measurements.
Venturi meter shows a better repeatability of the measurement with time because of the few scratches produced by the small solid particles transported by fluid do not influence the instrument indications.
With the same contract ratio with the other contraction-based devices Venturi meter has greater accuracy and lower pressure drop than the other contraction flow rate sensors but it is more expensive.
NOTE: It is fundamental to take into account cavitation in the design and the construction of a Venturi meter. The pressure in vena contracta must not be lower the vapor pressure of the liquid. Cavitation can produce considerable damage to the sensor and to the pipeline.
Process Instrumentation and Control - Prof M. Miccio

18. SECOND CLASSIFICATION (based on principle of measurement)
Differential Pressure
Variable Area
Velocity
Direct Mass Measurement
Positive displacement
Turbine type
Open channel
Process Instrumentation and Control - Prof M. Miccio

19. ROTAMETER Variable Area Volumetric Flowmeter
It consists of a transparent tapered pipe, slightly conical, placed vertically with an upward fluid.
A graduated scale is reported externally.
A body (“float”) having a greater density than fluid is located internally.
The float is made on different shapes, as spherical and conical, depending on the application and the fluid.
The flow rate measurement is performed by the observation of the position of the float on the graduated scale. The position is taken on the lowest section flow, corresponding to the section of the diameter for a sphere and of the base for a cone.
A higher volumetric flow rate through a given area increases flow speed and drag force, so the float will be pushed upwards.
The cross section available to the fluid increases when the float is raised, i.e. to increase the flow rate.
A hard-set in placed on the top of the column to avoid severe impact with the upper zone of the rotameter.
A spring is placed at the bottom of the rotameter in order to prevent damage of the instrument for abrupt interruption of the flow.
Pipes made of steel are used for rotameter performing at high pressure. In this case the external indicator is coupled with an electromagnetic float.
Process Instrumentation and Control - Prof M. Miccio

20. Process Instrumentation and Control - Prof M. Miccio
ROTAMETER
When the float is stable on a specified position, an equilibrium of forces occurs.
Readings are directly performed on the graduated scale of the flowrate on the transparent column
Process Instrumentation and Control - Prof M. Miccio

21. Process Instrumentation and Control - Prof M. Miccio
ROTAMETER
Process Instrumentation and Control - Prof M. Miccio

22. ROTAMETER variable area Volumetric FlowMETER
video Rotameter.avi
Process Instrumentation and Control - Prof M. Miccio

23. Process Instrumentation and Control - Prof M. Miccio
ROTAMETER Hypotheses
For a generic float we can indicate:
the bottom position of the float (1), when the sectional area for the fluid flow becomes to reduce
the position of minimum sectional area for the fluid flow (2),
with the subscript “0” the quantity referred to the float.
Spherical float
Steady state
Constant ρ
Section area S2<<S1
z2 - z1  V0/A0; (where: V0 is the volume of the float, A0 is the projected area of the float)
Local and Distributed Pressure drops are negligible
z v ≠ f(r)
Surface for pressure forces = Projected area → A1 = A2= A0
(1)
(2)
Process Instrumentation and Control - Prof M. Miccio

24. ROTAMETER Flow equation
Force balance (scalar) equation on the float
(a) P1A1 - P2A2 - ρ0V0g = 0
where:
P1 : fluid pressure in position (1);
P2: fluid pressure in position (2) (with P2<P1 for the Bernoulli’s principle)
P1A1 = upstream force exerted by the fluid pressure on the float
P2A2 = downstream force exerted by the fluid pressure
ρ0V0g= weight of the float
Since the hypothesis: A1=A2=A0
(b) P1A0 - P2A0 - ρ0V0g = 0
Bernoulli’s equation
For section (1) and (2) and considering a constant density, we have:
(c)
Continuity equation
(d)
where S1>>S2 e v2>>v1
(1)
(2)
Process Instrumentation and Control - Prof M. Miccio

25. ROTAMETER Flow equation
Equation (c) becomes:
(e)
From the force balance eq. (b) we obtain:
(f)
From the previous assumption :
(g)
where V0 is the volume of the float
NOTE:
The assumption (g) is dimensionally correct, but is not properly exact for a sphere.
Process Instrumentation and Control - Prof M. Miccio

26. ROTAMETER Flow equation
Replacing eqs. (f) and (g) in (e) we obtain:
By simplification it becomes:
Considering the continuity equation:
Factorizing in v2:
Process Instrumentation and Control - Prof M. Miccio

27. ROTAMETER Flow equation
and solving for v2 we obtain:
The flow coefficient for a contraction γ is:
And multiplying by S2 the right and the left hand sides we have the final equation:
NOTE:
S2 is a linear function of the position of the float due to the conical shape of the pipe
The mass flow rate can be calculated from the volumetric flow rate as:
Process Instrumentation and Control - Prof M. Miccio

28. ROTAMETER Relationship between Flowrate and Height of the float
The geometric dependence of the surface area of the throttling section S2 on the
height of float lifting H is defined according to the scheme in figure is:
𝑆 2 𝐻 =π 𝐷 𝑡𝑔 θ 𝐻+ 𝑡𝑔 θ 𝐻 2
where θ is the angle of the cone-forming line with relation to the pipe axis.
For pipes with small conicity (from the order of 1:100) and not long float travel, the expression 𝑡𝑔 θ 𝐻 2 gets insignificant values and it can be ignored.
Process Instrumentation and Control - Prof M. Miccio

29. ROTAMETER Relationship between Flowrate and Height of the float
So we can obtain the relationship between the Volumetric Flowrate and on the
height of float lifting H is defined according to the scheme in figure is:
V̇= γπ 𝐷 𝑡𝑔 θ 𝑔 ρ 0 ρ −1 𝑉 0 𝐴 0 𝐻
Multiplying the two sides of this equality by the density of the fluid ρ, we will get the generalized characteristic of the rotameter for measuring the mass
flow ṁ:
ṁ= γπ 𝐷 𝑡𝑔 θ 𝑔ρ ρ 0 −ρ 𝑉 0 𝐴 0 𝐻
Process Instrumentation and Control - Prof M. Miccio

30. ROTAMETER Calibration
The volumetric flow rate of a rotameter is expressed as normal-liters per hour
for the calibration conditions.
If the instrument is used in a different condition than the calibration conditions the measurement needs a correction as:
where:
ρn is the calibration density;
is the corrected measure;
is the actually read flow rate.
Process Instrumentation and Control - Prof M. Miccio

31. ROTAMETER Calibration
Volumetric flow rate:
For an ideal gas:
If P = constant
the correction becomes:
On the other hand, if T = constant
we have:
Process Instrumentation and Control - Prof M. Miccio

32. Process Instrumentation and Control - Prof M. Miccio
ROTAMETER
Accuracy: 1% of the measurement at 100% of the flow rate  (3 10)% of the measurement at 10% of the max flow rate
Measuring range: up to 30 kg/s (H2O), up to 1 kg/s (air)
 Advantages
Linear relation flow rate – float position
Constant pressure drop across the float
Easy to read
Easy to install and to use in laboratories and pilot plants
 Disadvantages
A proper calibration is needed for each fluid at specific temperature and pressure
Correction formulas when it is used in condition different from calibration
It is not an electrical transducer
Only vertical installation
Requires "reinforced" model or non-transparent tube for high working pressures
Process Instrumentation and Control - Prof M. Miccio

33. SECOND CLASSIFICATION (based on principle of measurement)
Differential Pressure
Variable Area
Velocity
Direct Mass Measurement
Positive displacement
Turbine type
Open channel
Process Instrumentation and Control - Prof M. Miccio

34. FLOWMETERS based on measurement of velocity
Name
Principle
Application
Intrusive
Transducer
VORTEX-SHEDDING
frequency of vortices formation
liquids at low viscosity, gas and clean vapors
YES
SWIRL METER
liquids and gases
ELECTRO-MAGNETIC
Faraday-Neumann-Lenz law
liquids (also emulsion or suspension, no gas) with electrical conductivity (C  5S/m) NO
TIME-OF-TRAVEL
ultrasonic wave
liquids
DOPPLER
Liquids with particles or bubbles
Process Instrumentation and Control - Prof M. Miccio

35. SECOND CLASSIFICATION (based on principle of measurement)
Differential Pressure
Variable Area
Velocity
Direct Mass Measurement
Positive displacement
Turbine type
Open channel
Process Instrumentation and Control - Prof M. Miccio

36. CORIOLIS METERS Working principle They use the Coriolis effect.
The measuring element is subjected to a vibration “simulating” the rotation of it;
the Coriolis effect produces a force depending on the mass flow rate.
The measurement is independent from both the flow regime and a possible variation of fluid properties.
TOP VIEW
SIDE VIEW
from Magnani, Ferretti and Rocco (2007)
Process Instrumentation and Control - Prof M. Miccio

37. Process Instrumentation and Control - Prof M. Miccio
CORIOLIS METERS
Process Instrumentation and Control - Prof M. Miccio

38. CORIOLIS MASS FLOWMETER Vibrating tube configuration
Process Instrumentation and Control - Prof M. Miccio

39. CORIOLIS MASS FLOWMETER
Direct measurement of mass flow rate [kg/s]
Recommended to measure flow rate for liquids and fairly dense gases.
Measuring range (liquids) from kg/s to 20 kg/s
Accuracy  0.25% of the measurement
Repeatability 0.15% of the measurement
Rangeability 100:1
Installation No restrictions (vertical installation is better)
 Advantages
Small pressure drop
 Disadvantages
Expensive
Process Instrumentation and Control - Prof M. Miccio

40. ELECTRONIC THERMAL MASS FLOWMETER
Thermal Mass Flow Meters (and Controllers) make use of the heat conductivity of fluids (gases or liquids) to determine mass flow.
Three implementations:
for gases, by-pass principle
for gases, inline principle
for liquids, inline principle
] following the anemometric principle
flowz.flv
Process Instrumentation and Control - Prof M. Miccio

41. ELECTRONIC THERMAL MASS FLOWMETER
for gases, by-pass principle
The sensor is mounted as a by-pass to the main channel, where a patented flow resistance splitter takes care of proportional flow division, also under varying process conditions.
A part of the gas stream flows through the sensor, and is warmed up by heaters RHT1 and RHT2.
Consequently the measured temperatures T1 and T2 drift apart.
The temperature difference is directly proportional to mass flow. Electrically, temperatures T1 and T2 are in fact temperature dependent resistors RHT1 and RHT2.
This laminar flow element consists of a stack of stainless steel disc with high-precision etched flow channels, having similar characteristics as the flow sensor.
Process Instrumentation and Control - Prof M. Miccio

42. ELECTRONIC THERMAL MASS FLOWMETER
Process Instrumentation and Control - Prof M. Miccio

43. ELECTRONIC THERMAL MASS FLOWMETER
Process Instrumentation and Control - Prof M. Miccio

44. ELECTRONIC THERMAL MASS FLOWMETER
Process Instrumentation and Control - Prof M. Miccio

45. ELECTRONIC THERMAL MASS FLOWMETER
for gases, inline principle
Mass Flow Meters with inline sensor (no by-pass) consist of a straight flow channel, into which two stainless steel probes protrude; a heater probe and a temperature sensor probe.
A constant temperature difference (ΔT) is created between the two probes and the energy required to maintain this ΔT is proportional to the mass flow rate (CTA: Constant Temperature Anemometry) .
Mass flow can be measured with low pressure drop.
Compared to traditional thermal MFMs and MFCs with by-pass, they are less sensitive to humidity and contamination.
Process Instrumentation and Control - Prof M. Miccio

46. ELECTRONIC THERMAL MASS FLOWMETER
 Advantages
Direct measurement of mass flow rate [kg/s]
Accuracy up to:
εa =  0.75%
εf =  0.25%
Rangeability from 10:1 to 100:1
Other characteristics
Recommended for “very clean” gas
Adjustable to measurement of flow rate for liquids with special and expensive devices
Process Instrumentation and Control - Prof M. Miccio

47. SECOND CLASSIFICATION (based on principle of measurement)
Differential Pressure
Variable Area
Velocity
Direct Mass Measurement
Positive displacement
Turbine type
Open channel
Process Instrumentation and Control - Prof M. Miccio

48. POSITIVE-DISPLACEMENT METER
DEFINITION
A fluid (liquid or gas) quantity meter that separates and captures definite volumes of the flowing stream one after another and passes them downstream, while counting the number of operations.
Process Instrumentation and Control - Prof M. Miccio

49. Classification ROTARY METERS Positive Displacement Momentum transfer
The axis is normal to the flow direction
The axis is coincident to the flow direction
Process Instrumentation and Control - Prof M. Miccio

50. rotary vane flowmeter Rotation velocity of rotor
from
ISA Certified Control Systems Technician (CCST) program
Rotation velocity of rotor
N. of “units of volume” carried for unit of time
fluid volumetric flow rate
Process Instrumentation and Control - Prof M. Miccio

51. SECOND CLASSIFICATION (based on principle of measurement)
Differential Pressure
Variable Area
Velocity
Direct Mass Measurement
Positive displacement
Turbine type
Open channel
Process Instrumentation and Control - Prof M. Miccio

52. PADDLE WHEEL FLOWMETER (for liquids)
The paddle wheel flow meter is frequently considered as a low cost alternative to the turbine-type flow meter in applications with less demanding accuracy requirements.
The paddle wheel (rotor with blades) is perpendicular to the flow path, not parallel as in the traditional turbine-type flow meter (Tangential rotor)
The rotor's axis is positioned to limit contact between the paddles and the flowing media to less than 50% of the rotational cycle. This imbalance causes the paddle to rotate at a speed proportional to the velocity of the flowing media.
The fluid transfers a small amount of momentum to the impeller
A sensor is used to detect the proximity of micromagnets imbedded in each of the passing paddle wheel blades. The frequency of the output signal is proportional to the fluid velocity and can be transmitted directly to external remote readout/data acquisition.
It is inherently bi-directional.
It is a transducer
Process Instrumentation and Control - Prof M. Miccio

53. TURBINE FLOWMETER (for liquids)
Axial rotor
Rotation speed is detected magnetically (e.g., by a magnet fixed on the rotor)
The fluid transfers a small amount of momentum in the turbine
The sensor relates the volumetric flow rate to the rotation speed of the rotor
It is a transducer
Process Instrumentation and Control - Prof M. Miccio

54. Process Instrumentation and Control - Prof M. Miccio
APPENDICE
Process Instrumentation and Control - Prof M. Miccio

55. SECOND CLASSIFICATION (based on principle of measurement)
Differential Pressure
Variable Area
Velocity
Direct Mass Measurement
Positive displacement
Turbine type
Open channel
Process Instrumentation and Control - Prof M. Miccio

56. VORTEX-SHEDDING FLOWMETER
Vortex sensor
Functioning principle:
Measure the frequency of vortices formation with:
piezo-electric element which detects local pressure variations associated to vortices;
thermistor, heated with a little electric current, which detects resistance temperature variations due to the different cooling transport phenomena occurring between the thermistor and the fluid influenced by vortices formation
Bluff body
Operating equation:
Vortex formation frequency: fv = Kv
Shape of the bluff body 
K constant for different motion condition
Volumetric flor rate:
Bluff body
fv measurement with a thermistor
Process Instrumentation and Control - Prof M. Miccio

57. VORTEX-SHEDDING FLOWMETER
Characteristics:
Recommended for liquids at low viscosity, gas and clean vapors
P/T correction for gas and vapors
Accuracy: 0.75% of the measurement for liquids (1% for gas),
Rangeability: 10:1
Measuring range: 0.2450 kg/s (H2O), 43600 kg/s (air)
Transducer  Intrinsically digital signals (no AC/DC converter)
More modern model  vortex mass flow rate
 Limitation
High turbulent flow regime (Re > 30000)
Installation constraints:
L_ = 15 DN; L+ = 5 DN;
Horizontal position
Process Instrumentation and Control - Prof M. Miccio

58. Process Instrumentation and Control - Prof M. Miccio
SWIRL METER
vortices are caused by specific fins at the entrance of the instrument
it uses a piezo-electric element or a thermistor to “sense” turbulence
it measures the volumetric flow rate of liquids and gases
Measuring range:
0,01 ÷ 500 kg/s liquid
0.3x10-3 ÷ 6.6 kg/s gas
Process Instrumentation and Control - Prof M. Miccio

59. Process Instrumentation and Control - Prof M. Miccio
SWIRL METER vs. VORTEX
COMPARISON WITH A VORTEX-SHEDDING FLOWMETER
horizontal and vertical installation
no upstream and downstream straigth line
Process Instrumentation and Control - Prof M. Miccio

60. ELECTROMAGNETIC FLOWMETER
Functioning principle:
Faraday-Neumann-Lenz law
magnetic field B [weber/m2 = tesla]
 Liquids (also emulsion or suspension, no gas) with electrical conductivity (C  5S/m)
Faraday’s Law (absolute value)
 Advantages
The output signal is linear to the volumetric flow rate.
The flow direction can be inverted.
Not intrusive negligible pressure drop
They are used in all industrial applications, e.g.: food, waste waters, chemicals, etc.
very high accuracy up to <0.5%
rangeability from 50:1 to 100 :1
Measuring range from to kg/s (H2O)
 Limitation/Disadvantages
STRAIGTH LINE constraint (HORIZONTAL and/or VERTICAL installation) with
L_ = 3 DN
L+ = 2 DN
Coil
PIPE
ELECTRODES
OUTPUT SIGNAL
Process Instrumentation and Control - Prof M. Miccio

61. ELECTROMAGNETIC FLOWMETER Technical features
Process Instrumentation and Control - Prof M. Miccio

62. Process Instrumentation and Control - Prof M. Miccio
ULTRASONIC FLOWMETER
2 types:
Time-of-travel
Doppler effect
Process Instrumentation and Control - Prof M. Miccio

63. Time-of-travel ultrasonic meter
Process Instrumentation and Control - Prof M. Miccio

64. Process Instrumentation and Control - Prof M. Miccio
DOPPLER FLOWMETER
Process Instrumentation and Control - Prof M. Miccio

65. DOPPLER FLOWMETER (with clamp-on configuration)
TrANSMITTER, FREQUENCY ft
WEDGE
REFLECTING PARTICLES
flow
RECEIVER, FREQUENCy fr
 Advantages
Non intrusive  negligible pressure drop
Process Instrumentation and Control - Prof M. Miccio