flow measurement part iii

FLOW MEASUREMENT

PART III

ER. FARUK BIN POYEN, Asst. Professor

DEPT. OF AEIE, UIT, BU, BURDWAN, WB, INDIA

[email protected]

Contents:

Variable Area Meter

Rotameter

Cylinder and Piston Type Flow Meter

Magnetic Meter

Turbine Meter

Target Meter

Thermal Meter

Vortex Meter

Ultrasonic Flow Meter

2

Variable Area Meter

Operation

Variable Area flowmeters work with low viscous liquids at high velocities.

The principle of operation is that the flow stream displaces a float placed in the stream.

The rate of flow is related to the area produced by forcing the float up or down, andvarying the area.

In this type of flow meter, the area of the restriction can be altered to maintain a steadypressure difference.

It is because of the low viscosity and high velocity that the frictional resistance of theflow is negligible compared to the resistance of the obstruction (float) placed in theflow stream.

The float in the early stages of development was slotted which caused the floats torotate. This provided stability and centring of the float, and is where the designation ofrotameter came from.

3

Variable Area Meter

The force balance equation of the variable area flow meter is

𝐹𝑑𝑟𝑎𝑔 + 𝐹𝑏𝑢𝑜𝑦𝑎𝑛𝑐𝑦 = 𝐹𝑤𝑒𝑖𝑔ℎ𝑡

𝐴𝑓 𝑝𝑑 − 𝑝𝑢 + 𝜌𝑓𝑓𝑔𝑉𝑓 = 𝜌𝑓𝑔𝑉𝑓

𝑝𝑑 − 𝑝𝑢 =𝑉𝑓

𝐴𝑓𝑔(𝜌𝑓 − 𝜌𝑓𝑓)

𝜌𝑓 & 𝜌𝑓𝑓 are the densities of the float and the flowing fluid respectively

𝑉𝑓 is the volume of the float

𝑝𝑑 & 𝑝𝑢 are the pressures at the downward and upward faces of the float respectively.

𝑄𝑎𝑐𝑡𝑢𝑎𝑙 = 𝐶𝑑𝐴1𝐴2

𝐴12−𝐴2

22𝑔 ∆ℎ =

𝐶𝑑(𝐴𝑡−𝐴𝑓)

1− 𝐴𝑡−𝐴𝑓2/𝐴𝑡

22𝑔

𝑉𝑓

𝐴𝑓

(𝜌𝑓−𝜌𝑓𝑓)

𝜌𝑓𝑓

4

Variable Area Meter

𝑄𝑎𝑐𝑡𝑢𝑎𝑙 = 𝐾(𝐴𝑡 − 𝐴𝑓)

Where 𝐾 is the constant of the rotameter, Cd = discharge coefficient, At = area of

tube at float level, Af = Area of float, (At - Af) = minimum annular area between tube

and float.

If the angle of taper is θ (which is very small), then

𝐴𝑡 =𝜋

4(𝐷𝑖 + 𝑦𝑡𝑎𝑛𝜃)2=

𝜋

4𝐷𝑖2 +

𝜋

2𝑦𝐷𝑖𝑡𝑎𝑛𝜃

where 𝑦 is the float position w.r.t inlet, 𝐷𝑖 is the diameter at the inlet

𝑄𝑎𝑐𝑡𝑢𝑎𝑙 = 𝐾𝜋

4𝐷𝑖𝑦𝑡𝑎𝑛𝜃 + 𝐾

𝜋

4𝐷𝑖2 − 𝐴𝑓 = 𝐾1𝑦 + 𝐾2

5

Rotameter The rotameter consists of a tapered measuring tube and a float.

This arrangement produces a resistance value (coefficient of resistance) for the float,which depends on its position in the measuring tube.

A balance is achieved between the force of the flow stream and the weight of the float.

The float positions itself vertically within the measuring tube such that the resistancevalue is balanced.

The inside of the measuring tube is conical and has guide strips for the float.

For physical indication, there is a scale on the outside to indicate the flow rate.

Metal versions are available that have a means of transmitting the float position.

The measuring tube can be made from steel, stainless steel, plastics (polypropylene,teflon), glass or hard rubber.

Also a number of various floats are available.

6

Rotameter

The rotating float is used for direct control.

Another type that is available is unaffected by viscosity, and a modification of this is

available that magnifies the sensitivity of the operating range by 30%, but is more

sensitive to viscosity.

7


The cylinder and piston type variable area flow meter is most often used for measuringflow of fuel oils, tar chemicals and other super viscous liquids.

It works on similar principle of rotameter and consists of a cylinder and a piston fittedto it. A series of reamed holes are provided in the wall of the cylinder to providepassage for fluid flow.

Holes are helically spaced to offer continuous area variation at various heights of thepiston.

As weight of the piston is constant, differential pressure is also constant.

The flow reading is transmitted by using reluctance type transducers.

When fluid enters the cylinder, the piston exerts a constant downward force and the DPbetween the two sides places the piston in a fixed position.

As the downstream flow is increased, the pressure on the load side of the piston isreduced.

The increased DP then forces the piston up, thereby increasing the area of the openinguntil DP is again balanced.

8


The linear piston movement is sensed by a LVDT which converts it into voltage signalproportional to the flow rate.

Oscillating piston flow meters typically are used in viscous fluid services such as oilmetering on engine test stands where turndown is not critical.

These meters also can be used on residential water service and can pass limited quantitiesof dirt, such as pipe scale and fine (viz,-200 mesh or -74 micron) sand, but not large particlesize or abrasive solids.

The measurement chamber is cylindrical with a partition plate separating its inlet port fromits outlet.

The piston is also cylindrical and is punctured by numerous openings to allow free flow onboth sides of the piston and the post.

The piston is guided by a control roller within the measuring chamber, and the motion ofthe piston is transferred to a follower magnet which is external to the flow stream.

The follower magnet can be used to drive either a transmitter, a register, or both.

The motion of the piston is oscillatory (not rotary) since it is constrained to move in oneplane.

The rate of flow is proportional to the rate of oscillation of the piston.

9


The internals of this flow meter can be removed without disconnection of the meter

from the pipeline.

As because of the close tolerances required to seal the piston and to reduce slippage,

these meters require regular maintenance.

Oscillating piston flow meters are available in 1/2-in to 3-in sizes, and can generally be

used between 100 and 150 psig.

Some industrial versions are rated to 1,500 psig.

They can meter flow rates from 1 gpm to 65 gpm in continuous service with

intermittent excursions to 100 gpm. Meters are sized so that pressure drop is below 35

psid at maximum flow rate.

Accuracy ranges from ±0.5 % AR for viscous fluids to ±2% AR for non-viscous

applications.

Upper limit on viscosity is 10,000 centipoise.

10


Reciprocating piston meters are probably the oldest PD meter designs.

They are available with multiple pistons, double-acting pistons, or rotary pistons.

As in a reciprocating piston engine, fluid is drawn into one piston chamber as it is

discharged from the opposed piston in the meter.

Typically, either a crankshaft or a horizontal slide is used to control the opening and

closing of the proper orifices in the meter.

These meters are usually smaller (available in sizes down to 1/10-in diameter) and are

used for measuring very low flows of viscous liquids.

11

Cylinder and Piston Type Flow Meter 12


Advantages

- Inexpensive

- Wide range of applications

- Very basic operation

- Easy installation and simple to replace

Disadvantages

- Limited accuracy

- Subject to density, viscosity and temperature

- Fluid must be clean, no solids content

- Erosion of device (wear and tear)

- Can be expensive for large diameters

- Operate in vertical position only

- Viscosity > 200 cP

13

Magnetic Flow Meter

The typical lining materials are neoprene, polyterafluroethylene (PTFE) andpolyurethane. The materials used for electrodes are stainless steel, platinum iridiumalloys, titanium and tantalum.

Faradays law states that moving a conductive material at right angles through amagnetic field induces a voltage proportional to the velocity of the conductivematerial.

The conductive material in the case of a magmeter is the conductive fluid.

The fluid therefore must be electrically conductive, but not magnetic.

The operation of magnetic flow meter is based on Faraday’s well-known law ofelectromagnetic induction.

The voltage (E) induced in a conductor moving in a magnetic field at a right angle tothe field is directly proportional to the number of conductors, or, as in this case, thedistance between the probes (l), the intensity of magnetic field (B) and the velocity ofthe motion of the conductor (v) .

𝐸 = 𝐵𝑙𝑣 × 10−8 𝑣𝑜𝑙𝑡𝑠

14

Magnetic Flow Meter

The volume flow rate for a circular pipe is given by

𝑄 = ( 𝜋 4)𝑑2𝑣

Therefore,

𝐸 =4𝐵

𝜋𝑑𝑄 × 10−8 𝑣𝑜𝑙𝑡𝑠

15

Magnetic Flow Meter

Advantages

- No restrictions to flow.

- No pressure loss.

- No moving parts.

- Good resistance to erosion.

- Independent of viscosity, density, pressure and turbulence.

- Good accuracy.

- Bi-directional.

- Large range of flow rates and diameters.

Disadvantages

- Expensive.

- Most require a full pipeline.

- Limited to conductive liquids.

- Not suitable for gas and liquid hydrocarbons

16

Turbine Flow Meter

The blades of a turbine flow meter are made of ferromagnetic material. the magnetic

pickup coils wound are wound on a permanent magnet.

A voltage pulse is obtained at the pickup output whenever a tooth passes the pickup

coil and flow is measured by counting the number of pulses.

The rotational speed of the turbine is proportional to the velocity of the fluid.

𝑄 = 𝑘𝑛 𝑤ℎ𝑒𝑟𝑒 𝑛 = 𝑛𝑜. 𝑜𝑓 𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑙𝑎𝑑𝑒

Different methods are used to convey rotational speed information.

The usual method is by electrical means where a magnetic pick-up or inductive

proximity switch detects the rotor blades as they turn.

As each blade tip on the rotor passes the coil it changes the flux and produces a pulse.

Pulse rate is directly proportional to the flow rate.

17

Turbine Flow Meter

As the rotation of the turbine is measured by means of non-contact, no tapping points

are required in the pipe.

Pressure is therefore not a problem, and in fact pressures of up to 9300psi can be

applied without any problem, but this of course does depend on pipe diameter and

materials of construction.

Temperature limitations are only imposed by the limitations of the materials of

construction.

To reduce losses or changes in process temperature, turbine flow meters are available

which can be subjected to wide temperature variations.

Turbine meters require a good laminar flow.

In fact 10 pipe diameters of straight line upstream and no less than 5 pipe diameters

downstream from the meter are required.

They are therefore not accurate with swirling flows.

18

Turbine Flow Meter

They are not recommended for use with high viscosity fluids due to the high friction of

the fluid which causes excessive losses as the turbine becomes too much of an

obstruction.

The viscosity of the liquid must be known for use of this type of meter.

They are also subject to erosion and damage. Each meter must be calibrated for its

application.

The flow rates range from 0.5 to 150000/min for liquids and 5 to 100000/min for air.

19

Target Flow Meter

The insertion of a suitable shaped body (obstruction) into the flow stream can serve as

a flow meter.

The drag force on the body becomes the measure of the flow rate.

The drag force Fd acting on the body immersed in a flowing fluid is given by

𝐹𝑑 =1

2𝐶𝑑𝜌𝑔𝑉

2𝐴

For a sufficiently high Reynold’s number, the drag coefficient 𝐶𝑑 is reasonably

constant.

The drag force 𝐹𝑑 is proportional to 𝑉2.

The drag force of a body can be measured by attaching the drag body to a suitable

force measuring device.

Cantilever beam arrangement with bonded strain gauges is one such arrangement.

The overall accuracy and repeatability are ±0.5% and within ±0.1% respectively.

20

Target Flow Meter

Common examples of flows measured by it are highly viscous flows of hot asphalt, tar,

oils or slurries at high pressure of the order of 100 bars.

21

Thermal Flow Meter

Thermal flow meters measure mass flow rate by means of measuring the heat

conducted from a heated surface to the flowing fluid.

Relying on the principle that a fluid flowing past a heated temperature sensor removes

a known quantity of heat as it passes, thermal flow meters measure either how much

electrical power is required to maintain the temperature of the heated sensor or the

temperature difference between the heated sensor and the flow stream.

Either of those values is directly proportional to the mass flow rate.

Thermal flow meters are used almost entirely for gas flow applications.

Their design and construction make them popular for a number of reasons.

They feature no moving parts, have nearly unobstructed flow path, require no

temperature or pressure corrections, and retain accuracy over a wide range of flow

rates.

22

Thermal Flow Meter

Straight pipe runs can be reduced by using dual-plate flow conditioning elements and

installation is very simple with minimal pipe intrusions.

Thermal mass flow meters are gas flow meters based on the relationship between

convection heat transfer and mass flow.

There are two types of thermal flow meters: rate of heat loss flowmeters and

temperature rise flowmeters.

23

Thermal Flow Meter

Rate of Loss Flow meter – Hot Wire Flow meter

Rate of heat loss thermal flow meters measure the rate of heat loss to the flow stream from

a heated element such as a resistance wire, thermistor, thermocouple, or thin film sensor.

Governing Equation:

𝑞𝑡 = ∆𝑇 𝐾 + 2 𝑘𝐶𝑣𝜌𝜋𝑑𝑉𝑎𝑣𝑔 1 2

qt = rate of heat loss per unit time; ΔT = mean temperature elevation of wire; d = wire

diameter; k = thermal conductivity of fluid stream; ρ = density of fluid stream;

C v = specific heat of fluid stream; V avg = average velocity of fluid stream;

In this equation, ρ, Vavg, qt, and ΔT are the unknowns, because they change with time

while the other variables are known.

However, qt and T can be obtained through measuring devices, leaving in the product

of and Vavg and cross section area of the pipe.

24

Thermal Flow Meter 25

Rate of Loss Flow meter – Hot Wire Flow meter

Thermal Flow Meter

Temperature Rise Thermal Flow Meter – Heat Transfer Flow meter

Temperature Rise thermal flow meters measure the temperature changes of the flow as itpasses through a heat source.

Governing Equation:

𝑾 =𝑯

∆𝑻𝑪𝒑

W = mass flow; H = Heat (power) input; ΔT = Temperature change; CP = Specific heat;

W and ΔT are unknowns in this equation. ΔT can be measured. W can therefore becalculated.

Thermal flow meters are gas flow meters only and can be used as liquid flow switchbut cannot be used as liquid flow meter due to the sudden drop in ΔT because of thehigher cooling rate of liquids compared to gases.

The higher cooling rate of liquids prevents the transmitter from calculating an adequateflow range in liquids.

26

Thermal Flow Meter

Temperature Rise Thermal Flow Meter – Heat Transfer Flow meter

27

Thermal Flow Meter

Hot Wire Anemometer

Hot-Wire Anemometer is the most well-known thermal anemometer, and measures a

fluid velocity by noting the heat convection away by the fluid.

The core of the anemometer is an exposed hot wire either heated up by a constant

current or maintained at a constant temperature (refer to the schematic below).

In either case, the heat lost to fluid convection is a function of the fluid velocity.

By measuring the change in wire temperature under constant current or the current

required to maintain a constant wire temperature, the heat lost can be obtained.

The heat lost can then be converted into a fluid velocity in accordance with convective

theory.

Typically, the anemometer wire is made of nickel, platinum or tungsten and is 4 ~ 10

µm (158 ~ 393 µin) in diameter and 1 mm (0.04 in) in length.

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Thermal Flow Meter

Hot Wire Anemometer Typical commercially available hot-wire anemometers have a flat frequency response (< 3

dB) up to 17 kHz at the average velocity of 9.1 m/s (30 ft/s), 30 kHz at 30.5 m/s (100 ft/s),or 50 kHz at 91 m/s (300 ft/s).

Due to the tiny size of the wire, it is fragile and thus suitable only for clean gas flows. Inliquid flow or rugged gas flow, a platinum hot-film coated on a 25 ~ 150 mm (1 ~ 6 in)diameter quartz fiber or hollow glass tube can be used instead.

The basic governing equation of the hot wire operation is based on the King’s Law for theconvection heat transfer from the heated wire which is expressed as

ℎ𝐷

𝑘= 0.30 + 0.5

𝜌𝑉𝐷

𝜇

For 𝜌𝑉𝐷

𝜇> 102

h = convective film coefficient of heat transfer; k = thermal conductivity of the hot wire; ρ = density of the fluid; V = velocity of the fluid stream; μ = coefficient of viscosity of the fluid;

D = diameter of the hot wire;

29

Thermal Flow Meter

Hot Wire Anemometer

Advantages:

-Excellent spatial resolution.

-High frequency response, > 10 kHz (up to 400 kHz).

Disadvantages

- Fragile, can be used only in clean gas flows.

-Needs to be recalibrated frequently due to dust accumulation (unless the flow is very

clean).

-High cost.

30

Vortex Flow Meter

The vortex flow meter is used for measuring the flow velocity of gases and liquids

in pipelines flowing full.

The measuring principle is based on the development of a Karman vortex shedding

street in the wake of a body built into the pipeline.

The obstruction is referred to as a bluff body and causes the formation of swirls,

called vortices, downstream from the body.

The periodic shedding of eddies occurs first from one side and then from the other

side of a bluff body (vortex-shedding body) installed perpendicular to the pipe axis.

Vortex shedding generates a so-called "Karman vortex street" with alternating

pressure conditions whose frequency is proportional to the flow velocity.

31

Vortex Flow Meter

Differential pressure changes occur as the vortices are formed and shed.

This pressure variation is used to actuate the sealed sensor at a frequency proportional

to the vortex shedding.

For continuous flow, a series of vortices generates electrical pulses with a frequency

that is also proportional to the flow velocity.

The velocity can then be converted to volumetric flow rate.

The output of a vortex flow meter depends on the K-factor.

The K-factor relates to the frequency of generated vortices to the fluid velocity.

Velocity Fluid = Vortex frequency / k-Factor

32

Vortex Flow Meter

The fluid parameter which governs the operation of the vortex – shedding flow meter

is a non – dimensional number, Strouhal number S which is expressed as

𝑆 =𝑓𝑠𝐷

𝑉

Where f s = vortex shedding frequency; D = diameter of the bluff body;

V = average velocity of the flow

The flow rate Q in the vortex flow meter can be evaluated as follows

𝑄 =𝜋

4𝐷2𝑉𝑢 =

𝜋

4𝐷2 − ℎ𝐷 𝑉𝑑 ,

𝑤ℎ𝑒𝑟𝑒 𝑉𝑢 = 𝑢𝑝𝑠𝑡𝑟𝑒𝑎𝑚 𝑓𝑙𝑜𝑤 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦, 𝑉𝑑 = 𝑑𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚 𝑓𝑙𝑜𝑤 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦

The K-factor varies with the Reynolds number, however it is virtually constant over a

broad range of flows.

Vortex flow meters provide very linear flow rates when operated within the flat range.

33

Vortex Flow Meter

There are three types of vortex flow meter.

They are

1. Swirlmeter

2. Vortex Shedding Meter

3. Fluidic Meter

34

Vortex Flow Meter - Swirlmeter

It operates on the principle of vortex precession.

It gives an output in the form of pulses whose frequency is proportional to fluid flow

rate.

It consists of a fixed set of swirl blades, usually made of stainless steel, which

introduces a spinning or swirling motion to the fluid at the inlet.

At the downstream of the swirl blades, venturi like contraction and expansion is

provided with a temperature sensor.

At the exit, there are deswirl blades employed to straighten out the flow leaving the

meter.

As fluid passes through the fixed set of swirl blades at the inlet, a swirling motion is

imparted to it.

35

Vortex Flow Meter - Swirlmeter 36

In the area where expansion occurs, the swirling flow precedes or oscillates at a

frequency proportional to the fluid flow rate.

This precession causes variations in temperature sensed by thermistors. The amount of

heat extracted is a function of fluid velocity.

Vortex Flow Meter – Vortex Shedding Meter

An object viz. bluff body is introduced in the flow path.

When the fluid flows past the obstacle, boundary layers of slow moving fluid are

formed along the outer surfaces of the obstacle and the flow is unable to follow

contours of the obstacle on its downstream side.

Thus the flow layers are separated from the surface of the object and a low pressure

area is formed behind the object which causes the separated layers to get detached

from the main stream of the fluid and roll themselves into eddies or vortices in the

low pressure area.

Each eddy or vortex first grows and gets detached or shed from alternate sides of the

object. The frequency at which the vortices are formed is directly proportional to the

fluid velocity.

37

Vortex Flow Meter – Vortex Shedding Meter

As a vortex is shed from one side of the bluff body, the fluid velocity on that side

increases and the pressure decreases and at the same time the velocity on the

opposite side decreases and pressure increases, thus causing a net pressure change

across the bluff body.

The change in pressure of velocity is sensed by a flow sensitive detector which can

be either a thermistor or a spherical magnetic shuttle.

38

Vortex Flow Meter – Fluidic Meter

Fluidic meter operates on the principle of Coanda Effect.

It consists of a turbulent jet which can be deflected from its central position due to the

internal geometry of the meter body and it is initially attached to one of the side walls

of the meter.

As the fluid enters the meter, it is entertained into the jet from its surroundings, which

causes a reduction in pressure.

The jet curvature is sustained by the pressure differential across the jet.

If sufficient volume of fluid is introduced into the control port, it causes the jet to

switch from the initial position to the opposite side wall.

This is known as Coanda Effect.

39


The jet can be made to oscillate in two ways.

In the first method, the two ports are connected together and fluid is sucked from the

high pressure side to the low pressure side causing the jet to switch to the other wall.

The jet thus continues to oscillate as the fluid is sucked alternately from one side to the

other.

The second method is the feedback oscillator system in which the deflected jet causes

low pressure area at the control port.

At the upstream feedback passage the pressure is higher due to a combination of the jet

expanding and stagnation pressure.

Thus a small portion of the main stream of fluid is diverted through the feedback

passage to the control port.

40


The feedback flow intersects the main flow and diverts it to the opposite side wall.

The whole feedback operation is then repeated which results in a continuous self –

induced oscillation of the flow between the side walls of the flow meter.

The frequency of oscillation is proportional to the volumetric flow rate. The frequency

is detected by means of a thermistor.

41

Vortex Flow Meter

Secondary Elements of Vortex Flow Meter:

A number of devices can be used to measure the vortex frequency. The choice depends

on the application, and more particularly the operating conditions.

- Thermistors

- Pressure sensors

- Magnetic pick-up

- Strain gauge

- Piezoelectric

- Capacitive

42

Vortex Flow Meter Advantages

- Suitable for liquid, gas or steam.

- Used with non-conductive fluids.

- No moving parts, low maintenance.

- Sensors available to measure both gas and liquid.

- Not affected by viscosity, density, pressure or temperature.

- Low installation cost.

- Good accuracy.

- Linear response

Disadvantages

- Unidirectional measurement only.

- Clean fluids only.

- Not suitable with partial phase change.

- Not suitable for viscous liquids.

- Large unrecoverable pressure drop.

- Straight pipe runs required for installation.

43


Ultrasonic flow meters utilize sound waves to measure the velocity of a fluid from

which the volumetric flow rate can be calculated.

Unlike most flow meters, ultrasonic meters do not include any moving parts and thus

are more reliable, accurate and provide maintenance free operation.

Since ultrasonic signals can also penetrate solid materials, the transducers can be

mounted onto the outside of the pipe offering completely non-invasive measurement

eliminating chemical compatibility issues, pressure restrictions, and pressure loss.

Ultrasonic flow meters are affected by the acoustic properties of the fluid and can be

impacted by temperature, density, viscosity and suspended particulates depending on

the exact flow meter.

44


There are two types of ultrasonic flow meters:

1. Transit Time

2. Doppler Shift

45

Ultrasonic Flow Meter – Transit Time

Transit time flow meters measure the travel time of two sound waves.

One wave travels the same direction as the flow while the other travels against the

flow.

At zero flow, sensors receive both waves at the same time, i.e., without transit time

delay.

As the fluid moves, it takes an increasingly longer time for the downstream wave to

reach the upstream sensor.

This measured "transit time difference" is directly proportional to the flow velocity

and therefore to flow volume.

Transit time flow meters require the fluid to be free from suspended solids or gas

bubbles and in a closed and full piping system.

46

Ultrasonic Flow Meter – Transit Time

With zero flow velocity, the transit time to of the pulse from the transmitter to the

receiver is given by: 𝒕𝟎 =𝒍

𝑽𝒔

With a velocity V, the transit time to becomes

𝑡 =𝑙

𝑉𝑠 + 𝑉=𝑙(𝑉𝑠 − 𝑉)

𝑉𝑠2 − 𝑉2

∆𝑡 = 𝑡2 − 𝑡1 =𝑙

𝑉𝑠 − 𝑉−

𝑙

𝑉𝑠 + 𝑉=

2𝑙𝑉

𝑉𝑠2 (∵ 𝑉 ≪ 𝑉𝑠)

47

Ultrasonic Flow Meter – Doppler Shift

Doppler-shift flow meters operate on the principle that the wavelength of an

approaching sound source is shorter than the wavelength of that same source as it is

moving away.

A transducer emits a sound wave which reflects off entrained particles or bubbles

back to the transducer.

The measured difference in the wavelengths of the transmitted signal versus the

reflected signal is proportional to the process' velocity.

Doppler flow meters are used for slurries, liquids with bubbles, or gases with sound-

reflecting particles.

They can also be adapted for use in open channels by integrating with level

transmitters.

48

Ultrasonic Flow Meter – Doppler Shift

The velocity of the fluid is given by

𝑉 =∆𝑓𝐶𝑡

2𝑓0𝑐𝑜𝑠𝜃= ∆𝑓𝐾,

𝑤ℎ𝑒𝑟𝑒 ∆𝑓 = 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑 𝑎𝑛𝑑 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑑 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦,𝐶𝑡 = 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑠𝑜𝑢𝑛𝑑 𝑖𝑛 𝑡𝑟𝑎𝑛𝑠𝑑𝑢𝑐𝑒𝑟𝑓𝑜 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑜𝑛

𝜃 = 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑟 𝑎𝑛𝑑 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟 𝑐𝑟𝑦𝑠𝑡𝑎𝑙 𝑤. 𝑟. 𝑡 𝑡ℎ𝑒 𝑝𝑖𝑝𝑒𝑟 𝑎𝑥𝑖𝑠𝐾 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

49

References:

Chapter 11: Flow Measurement, “Industrial Instrumentation and

Control” by S K Singh. Tata McGraw Hill, 3rd Edition. 2009, New

Delhi. ISBN-13: 978-0-07-026222-5.

Chapter 12: Flow Measurement, “Instrumentation, Measurement and

Analysis”. 2nd Edition, B C Nakra, K K Chaudhry, Tata McGraw-Hill,

New Delhi, 2005. ISBN: 0-07-048296-9.

Chapter 7: Flowmeter, “Fundamentals of Industrial Instrumentation”,

1st Edition, Alok Barua, Wiley India Pvt. Ltd. New Delhi, 2011. ISBN:

978-81-265-2882-0.

Chapter 5: Flow Measurement, “Principles of Industrial

Instrumentation”, 2nd Edition. D. Patranabis, Tata McGaw-Hill, New

Delhi, 2004. ISBN: 0-07-462334-6.

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flow measurement part iii

Engineering