This article provides a brief yet concise idea about flow meters and the pertinent terms related to them. This article classifies the different types of flowmeters and cites the different devices for measurement under these categories. Also, this article speaks about the major five classes of flowmeters viz. differential pressure, velocity, positive displacement, mass, and open channel.

1. Flowmeter - Brief
ER. FARUK BIN POYEN
FARUK.POYEN@GMAIL.COM

2. Overview:
 Flowrate (Flow) is defined as any quantity of fluid (gas, liquid or vapour)
that passes per unit time, expressed as below
𝐹𝑙𝑜𝑤 𝐹 = ∆𝑄 =
𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 (𝑄)
𝑇𝑖𝑚𝑒 (𝑡)
 For flow to occur, there must be a pressure difference (ΔP) between the
ends of a tube, and it can be demonstrated that ΔQ is directly proportional
to ΔP.
 In other words the greater the pressure difference, the greater the flow.
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3. Physical Characteristics affecting Flow:
 Flow is affected by a number of physical characteristics viz.:
 Tube diameter: If the diameter (d) of the tube is halved the flow through it
reduces to 1/16. This means that flow is directly proportional to 𝑑4
 Length: If the length is doubled the flow is halved, therefore flow is
inversely proportional to the length of the tube.
 Viscosity: This is a measure of the frictional forces within the ‘layers’ of
the fluid and the adjacent surface. As the viscosity increases the flow
decreases proportionally, therefore flow and viscosity are inversely
proportional.
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4. Hagen – Poiseuille Equation:
 The Hagan-Poiseuille equation (for laminar flow) brings together all of the
variables that determine flow along with a constant (π⁄128 that is derived
theoretically).
∆𝑄 =
𝜋 ∗ 𝑑𝑃 ∗ 𝑑4
128 ∗ 𝜖 ∗ 𝑙
∆𝑄 = 𝐹𝑙𝑜𝑤𝑟𝑎𝑡𝑒; 𝑑𝑃 = 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑑𝑖𝑓𝑓. ; 𝑑 = 𝑝𝑖𝑝𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟; 𝜖
= 𝑓𝑙𝑢𝑖𝑑 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦; 𝑙 = 𝑙𝑒𝑛𝑔𝑡𝑕;
 In turbulent flow, the flow rate is proportional to the square root of the
pressure gradient, whereas in laminar flow, flow rate is directly
proportional to the pressure gradient.
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5. Selection Considerations for Flowmeters:
 Important factors when selecting flow metering devices are:
• accuracy
• cost
• legal constraints
• flow rate range
• head loss
• operating requirements
• maintenance
• life time
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6. Terminologies related to Flow Measurement:
 Newtonian Fluid: In continuum mechanics, a Newtonian fluid is a fluid in
which the viscous stresses arising from its flow, at every point, are linearly
proportional to the local strain rate—the rate of change of its deformation
over time.
 Example: Water, oil, gasoline, alcohol, glycerine, ethyl alcohol et cetera.
 When held at a constant temperature, the viscosity of a Newtonian fluid
will not change regardless of the size of the shear force.
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7. Terminologies related to Flow Measurement:
 Non – Newtonian Fluid: A non-Newtonian fluid is a fluid that does not
follow Newton's law of viscosity. Most commonly, the viscosity (the
gradual deformation by shear or tensile stresses) of non-Newtonian fluids
is dependent on shear rate or shear rate history. Therefore, a constant
coefficient of viscosity cannot be defined.
 Examples: Blood, Ketchup, Toothpaste, Shampoo, Honey, Custard, Paint
et cetera.
 When held at a constant temperature, the viscosity of a Non-Newtonian
fluid will change with relation to the size of the shear force, or will change
over time under a constant shear force.
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8. Terminologies related to Flow Measurement:
 Reynolds Number (Re): It is the ratio of inertial forces to viscous forces of
fluid flow within a pipe and is used to determine whether a flow will be
laminar or turbulent.
𝑅𝑒 =
𝑉𝑑𝜌
𝜖
 Re = Reynolds number; V = average velocity; d = inside pipe diameter; ρ
= density of flowing fluid; ϵ = absolute viscosity
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9. Terminologies related to Flow Measurement:
 Measurements in tubes have shown that when:
 Reynolds number < 2000 there is laminar flow.
 Reynolds number 2000-4000 there is transitional flow i.e. a mixture of
laminar and turbulent flow.
 Reynolds number >4000 flow will be turbulent.
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10. Terminologies related to Flow Measurement:
 For a given fluid, in a given tube, once a critical velocity is reached flow
will become turbulent.
 If critical velocity is not exceeded, flow through a tube is laminar and
hence dependent on viscosity, whereas if it is through an orifice it is
turbulent and dependent on density.
 For Rotameter, as flowrate increases, the flow changes from being
directly proportional to pressure to proportional to the square root of
pressure and hence the graduations on the flowmeters are not uniform.
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11. Terminologies related to Flow Measurement:
 Rotameter under Low (Laminar) & High (Turbulent) Flow
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12. Terminologies related to Flow Measurement:
 Laminar Flow: In laminar flow the molecules of the fluid can be imagined
to be moving in numerous ‘layers’ or laminae as shown below.
 If the mean velocity of the flow is v, then the molecules at the centre of
the tube are moving at approximately 2v (twice the mean), whilst the
molecules at the side of the tube are almost stationary.
 Flow is usually considered to be laminar when a fluid flows through a
tube and the flow rate is low.
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13. Terminologies related to Flow Measurement:
 Turbulent Flow: In turbulent flow, instead of the fluid moving in
seemingly ordered layers, the molecules become more disorganised and
begin to swirl with the formation of eddy currents, as shown below.
 Turbulent flow occurs when fluids flow at high velocity, in large diameter
tubes and when the fluids are relatively dense.
 Also, decreasing the viscosity of a fluid leads to turbulent flow.
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14. Terminologies related to Flow Measurement:
 Vena Contracta is the minimum jet area that appears just downstream of
the restriction.
 The viscous effect is usually expressed in terms of the non-dimensional
parameter Reynolds Number - Re.
 Due to the Benoulli and the Continuity Equation the velocity of the fluid
will be at its highest and the pressure at the lowest in "Vena Contracta".
 After the metering device the velocity will decrease to the same level as
before the obstruction.
 The pressure recover to a pressure level lower than the pressure before the
obstruction and adds a head loss to the flow.
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15. Terminologies related to Flow Measurement:
 •Drag Force or Resistance (R): As fluid flows through tubes there is
resistance, between the fluid and vessel wall that opposes the flow.
 For any given system, this resistance is constant and can be expressed as:
𝑅 =
∆𝑃
∆𝑄
(This can be compared with V=IR in electrical physics).
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16. Terminologies related to Flow Measurement:
 •Bernoulli’s Principle: Bernoulli's principle says that a rise (fall) in
pressure in a flowing fluid must always be accompanied by a decrease
(increase) in the speed, and conversely, i.e. an increase (decrease) in the
speed of the fluid results in a decrease (increase) in the pressure.
𝑝 +
1
2
𝜌𝑉2 + 𝜌𝑔𝑕 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
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17. Terminologies related to Flow Measurement:
 Valve Flow Coefficient 𝐶 𝑉 : It is a number which represents a valve’s
ability to pass flow.
 The bigger the Valve Flow Coefficient, 𝐶 𝑉, the more flow a valve can pass
with a given pressure drop. A 𝐶 𝑉 of 1 means a valve will pass 1 gallon per
minute (gpm) of 60 °F water with a pressure drop (ΔP) of 1 (PSI) across
the valve. A 𝐶 𝑉 of 350 means a valve will pass 350 gpm of 60 °F water
with a (ΔP) of 1 PSI.
𝐶 𝑉 = 𝛥𝑄
𝑆𝑄
62.34 ∆𝑃
; 𝐾 = 𝑑
29.9
𝐶 𝑉
𝛥𝑄 = 𝐹𝑙𝑜𝑤𝑟𝑎𝑡𝑒; 𝑑 = 𝑖𝑛𝑛𝑒𝑟 𝑝𝑖𝑝𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟; 𝐾
= 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡;
𝑆𝑄 = 𝑤𝑒𝑖𝑔𝑕𝑡 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑓𝑙𝑢𝑖𝑑; 𝛥𝑃 = 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒
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18. Flowmeter Classification:
 Flowmeters are principally classified into five categories:
 Differential Pressure Flow meters – (Variable Head & Variable Area)
 Velocity Flow meters
 Positive Displacement Flow meters
 Mass Flow meters
 For Open Channel Flow meters - weirs, flumes, submerged orifices,
current meters, acoustic flow meters and et cetera.
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19. Flowmeter Classification:
 Flowmeters can be divided into two types:
 New Technology Flowmeters
 Traditional Technology Flowmeters
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New Technology Flowmeters Traditional Technology Flowmeters
Coriolis Differential Pressure (DP)
Magnetic Positive Displacement
Ultrasonic Turbine
Vortex Open Channel
Multivariable Differential Pressure (DP) Variable Area
Thermal

20. Flowmeter Classification:
Differential
Pressure
Positive
Displacement
Velocity Mass Open-
Channel
Orifice Plate;
Venturi Tube;
Flow Tube;
Flow Nozzle;
Pitot Tube;
Elbow Tap;
Target;
Variable-Area;
(Rotameter)
Reciprocating
Piston;
Oval Gear;
Nutating Disk;
Rotary Vane;
Turbine;
Vortex Shedding;
Swirl;
Coanda Effect &
Momentum Exchange;
Electromagnetic;
Ultrasonic, Doppler
Ultrasonic, Transit-Time
Coriolis;
Thermal;
Weir;
Flume;
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21. Differential Pressure (DP) Flow meters :
 A differential pressure transmitter is used to measure pressure differential
between the two ports.
 This indication of velocity combined with the cross-sectional area of the
pipe provides an indication of flow rate.
 These flow meters use Bernoulli's equation to measure the flow of fluid in
a pipe.
 DP flow meters introduce a constriction in the pipe that creates a pressure
drop across the flow meter.
 When the flow increases, more pressure drop is created.
 Impulse piping routes the upstream and downstream pressures of the flow
meter to the transmitter that measures the differential pressure to
determine the fluid flow.
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22. Velocity Flow meters:
 In a velocity flow meter, the flow is calculated by measuring the speed in
one or more points in the flow, and integrating the flow speed over the
flow area.
 These flow meters are among the most sensitive to process conditions.
 The flow rate is directly proportional to the velocity of the fluid.
 This linear relationship between flow and velocity enables velocity type
flow meters to measure flow over a wide range.
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23. Positive Displacement (PD) Flow meters:
 It is the only flow measurement technology that directly measures the
volume of the fluid passing through the flow meter.
 These flow meters achieve this by repeatedly entrapping fluid in order to
measure its flow.
 PD Flow meters feature two precisely machined rotating members inside a
measuring chamber of known volume.
 This process can be thought of as repeatedly filling a bucket with fluid
before dumping the contents downstream.
 The number of times that the bucket is filled and emptied is indicative of
the flow through the flow meter.
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24. Positive Displacement (PD) Flow meters:
 Many positive displacement flow meter geometries are available.
 Entrapment is usually accomplished using rotating parts that form moving
seals between each other and/or the flow meter body.
 In most designs, the rotating parts have tight tolerances so these seals can
prevent fluid from going through the flow meter without being measured
(slippage).
 In some designs, bearings are used to support the rotating parts.
 Rotation can be sensed mechanically or by detecting the movement of a
rotating part.
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25. Positive Displacement (PD) Flow meters:
 When more fluid is flowing, the rotating parts turn proportionally faster.
 The transmitter processes the signal generated by the rotation to
determine the flow of the fluid.
 Some PD flow meters have mechanical registers that show the total flow
on a local display.
 Other PD flow meters output pulses that can be used by a secondary
electronic device to determine the flow rate.
 PD flow meters can be applied to clean, sanitary, and corrosive liquids,
such as water and foods, and some gases.
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26. Mass Flow meters:
 A mass flow meter, also known as an inertial flow meter is a device that
measures mass flow rate of a fluid traveling through a tube.
 The mass flow rate is the mass of the fluid traveling past a fixed point per
unit time.
 For liquid fluid media, the density value changes with temperature; for
gas media the density changes with both temperature and pressure. The
changing density leads to inaccuracy.
 Mass flow meters are immune to temperature and pressure changes.
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27. Mass Flow meters:
 A Mass Flow Meter operating on the "Coriolis principle" contains a
vibrating tube in which a fluid flow causes changes in frequency, phase
shift or amplitude.
 The sensor signal is fed into the integrally mounted pc-board.
 The resulting output signal is strictly proportional to the real mass flow
rate, whereas thermal mass flow meters are dependent of the physical
properties of the fluid.
 Coriolis mass flow measurement is fast and very accurate.
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28. Open Channel Flow meters:
 Open channel flow meters perform flow measurement of liquids that are
open to the atmosphere at some point in the flow measurement path.
 The liquid may be entirely open to the atmosphere, or may be contained
within a closed pipe that is not full of liquid and only open to the
atmosphere at the installation point of the flow meter itself.
 Level measurement must be used in combination with velocity
measurement.
 Open channel flow meters consist of a primary device, transducer, and
flow transmitter.
 The wetted primary device restricts the liquid flow stream.
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29. Open Channel Flow meters:
 Under flowing conditions, this restriction causes a rise in liquid level at a
location either upstream or within the flow meter.
 When the flow increases, the level rises higher.
 A transducer is mounted on or near the primary device to sense the level.
 The electronic flow transmitter uses the signal from the transducer to
measure the level and determine liquid flow.
 The principal problem is sedimentation, dirt, and other debris often times
accumulate on the bottom of these devices, making level measurement
highly inaccurate.
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30. References:
 http://www.flowmeters.com/positive-displacement-technology
 https://www.smartmeasurement.com/flow-meters/positive-displacement
 https://www.forbesmarshall.com/fm_micro/news_room.aspx?Id=seg&nid
=134
 https://www.bronkhorst.com/service-support/technologies/coriolis-mass-
flow-measuring-principle/
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