9AEI306.59-60 1

Necessity Of Flow Measurement

• Flow Measurements are important in a number of applications such as

• Drinking purpose

• Agriculture purpose

• Industrial purpose

9AEI306.59-60 2

• Construction purpose etc

• To store the water for proper utilization

• To know volume of liquid and rate of flow

• Laboratory purpose

Necessity Of Flow Measurement

9AEI306.59-60 3

Flow of Water

9AEI306.59-60 4

Domestic Water Meter

Flow Meter

9AEI306.59-60 6

• Classification of flow meters based on

1.Weight / quantity (or) volume

2.Rate of flow

9AEI306.59-60 7

Quantity Meters

• A quantity meter is defined as one in which fluid passing through the primary Element is accurately quantified in terms of weight or volume of the fluid.

• It measures volume in liters.

Eg:- Positive displacement meter

Reciprocating piston

Nutating discs etc

9AEI306.59-60 8

Rate of Flow Meter

• A flow meter can be defined as one the fluid passing through the primary element in a continuous stream.

• Rate of flow means quantity of flow per unit time.

Eg:- Orifice Plate Turbine meter Electromagnetic flow meter

9AEI306.59-60 9

1. Head type flow meters based on differential pressure measurements

a) Orifice plate

b) Venturi tube

c) Flow nozzle

d) Pitot tube

2. Electromagnetic flow meters

3. Rotameters (variable are meters)

Classification of Flow Meters

9AEI306.59-60 10

4. Mechanical flow meters

a) Positive displacement

b) Turbine flow meter

5. Anemometer

a) Cup type anemometer

b) Hot wire anemometer

6. Ultrasonic flow meter

7. Vortex flow meter

9AEI306.59-60 11

Head Type Flow Meter

9AEI306.59-60 12

Principle of Head Type Flow Meter

• In this ,a restriction is placed in fluid path.

• Restriction creates pressure difference

• The pressure difference indicates flow rate.

• The relationship based on Bernoulli's theorem

9AEI306.59-60 13

Head Type Flow Meter

• The Head type flow meters have a common feature in

that they produce a pressure difference when fluid flow

is maintained through them .

• There is a certain linear relationship between the

pressure difference and flow rate of the fluid

• Head type flow meters follows Bernoulli's theorem

9AEI306.59-60 14

Bernoulli’s Theorem

• It states that in a fluid stream, the sum of

• Pressure head,

• Velocity head

• Elevation head

• At a point is equal to their sum at any other point removed in the

direction of flow from the first point plus loses due to the

friction between the two points.

9AEI306.59-60 15

Diagram

Fig 1

9AEI306.59-60 16

• Consider a flow tube of varying cross sectional area and

having a difference in level as shown in fig. 1

• An incompressible fluid density ‘ ρ’ is assumed to

steadily flowing through the pipe

• The flow tube axis inclined above datum line ‘XY’ line

• Applying the Bernoulli’s theorem , the relationship for the

fluid flow under equilibrium conditions can be expressed

as

Description

9AEI306.59-60 17

2 21 1 2 2

1 2 (1)2 2

p v p vh h kg g

Where p1 = Pressure per unit area at BD

p2 = Pressure per unit area at FH

v1 = The fluid velocity at BD

v2 = The fluid velocity at FH

Equation

9AEI306.59-60 18

ρ = Fluid density

g = Acceleration due to gravity

h1 = Height of centre of gravity of volume BCED above datum line

h2 = Height of centre of gravity of volume FGIH above datum line

9AEI306.59-60 19

)2(22

222

211

gvp

gvp

If the level of the pipe line is parallel to the datum line then h1 = h2

If the flow is continuous, then the quantity fluid Qv passing Per second at BD must be equal to that at FH

Qv = A1v1 = A2v2 -------------(3)

2 21 2 2 1

2P P V Ve g

9AEI306.59-60 20

2 22 1 1 2

2 ( ) (4)gV V P Pe

21 2 2

1

(5)Av v mvA

2

1

(5) (4)Am substituting inA

2 2 21 2 1 22 2 2

2 ( ) 2 (( )2(1 )(1 )

g p p g p pgv m v xm

1 22 2

2 ( )1

(1 )

g P Pvm

9AEI306.59-60 21

2 2( )rAV Q

= velocity approach factor

9AEI306.59-60 22

22 d

vgPQ CEAe

v dQ p Since all other parameters are constant

9AEI306.59-60 23

• The orifice plate is basically a thin metal

plate with circular opening

Definition

9AEI306.59-60 24

Classification of Orifice Plate

• Concentric

• Eccentric

• Segmental

• The concentric type is by far the most widely used.

9AEI306.59-60 25

• The materials used for construction of orifice plates are

• Mild steel

• Stain less steel

• Phosphor bronze

Orifice Plate

9AEI306.59-60 26

• The orifice meter is most common type of head

type flow measuring device for medium and large

pipe sizes.

• The office plate inserted in a pipe line causes an

increase in the flow velocity and a corresponding

decrease in pressure.

Orifice Plate

Orifice Plate

9AEI306.59-60 28

Fig-b

Orifice Plate

9AEI306.59-60 29

• The flow pattern shows an effective decrease in the

cross-section of the flow beyond the orifice plate with

maximum velocity and minimum pressure

• The particular position where the velocity is maximum

and static pressure is minimum is called vena

contracta

Working

9AEI306.59-60 30

Functioning of orifice plate

• An orifice plate installed in a pipeline creates a

pressure differential as the fluid flows through it

• This differential pressure is proportional to the

rate of flow

9AEI306.59-60 31

• They offer low cost over other types of flow meters

• Especially in a large line sizes and have proved to

be rugged ,effective and reliable over many years

• It has low installation cost and a turn down of not

more than 4 : 1

Merits of orifice plate

An orifice plate with vena contracta

9AEI306.59-60 33

Working of Orifice Plate

• The orifice plate is inserted in pipe line between two

flanges.

• The fluid flow through orifice causes increase in flow

velocity and decrease in the pressure .

9AEI306.59-60 34

• At a particular position beyond the orifice plate the velocity is maximum and pressure is minimum

• This position is called vena contracta.

• Before the vena contracta the fluid velocity decreases and pressure increases.

• It reaches to a position where the velocity and pressure equal as upstream side.

9AEI306.59-60 35

• The volume of flow can be determined by the equation –

22 d

vgPQ CEAe

9AEI306.59-60 36

Where

Qv = Volume flow rate; m3 / sec

C = Discharge Coefficient

A = Area of the orifice plate; m2

9AEI306.59-60 37

Pd = Differential pressure; pascals,

g = Accelaration due to gravity; m/sec2,

ρ = Density of a fluid; kg/m3,

9AEI306.59-60 38

E = Velocity approach factor

• By knowing the values of Cd, E, A, g, ρ and Pd

the volume flow rate can be determined.

9AEI306.59-60 39

Advantages

• Low cost

• High reliability

• Easy to install.

9AEI306.59-60 40

Disadvantages

• High Pressure loss

• Discharge coefficient is low compared to venturimeter

• Poor accuracy

Venturi Flow Meter

9AEI306.61 429AEI306.61 42

• It is head type flow meter

• It follows Bernoulli's theorem

• It works on the principle that by reducing the cross sectional area of the flow passage a differential pressure is created

• This differential pressure is proportional to the discharge through the pipe

Venture Flow Meter

9AEI306.61 439AEI306.61 43

Fig-2

Venture Flow Meter

9AEI306.61 449AEI306.61 44

• Equation of Bernoulli's theorem

1 22

1

2 ( )g P PQ EAe

9AEI306.61 459AEI306.61 45

Construction

• Converging conical section

• Cylindrical throat

• Diverging Section

• Venturi meter consists of

9AEI306.61 469AEI306.61 46

Flow

Venturi Tube

9AEI306.61 479AEI306.61 47

• Converging Conical section : converging cone converges from diameter D at its upstream side to diameter d at this down side stream.

• As the flows takes place in the convergent cone the velocity increases and pressure decreases.

• The convergent cone has a sharp angle of 21±20.

9AEI306.61 48

Venturi Tube

9AEI306.61 499AEI306.61 49

Throat

• It is a small portion of circular pipe in which

diameter is kept constant .

• In this section the flow velocity neither

increases nor decreases i.e. in steady state

9AEI306.61 50

Venturi Tube

9AEI306.61 519AEI306.61 51

Diverging Section

• The downstream side of the throat examples from

throat d to D is known as divergent cone .

• The angle of divergent cone is 5 to 150

• It results in pressure recovery

9AEI306.61 529AEI306.61 52

Operation

• The pressure at different locations are measured

• By knowing the pressure differences, we can

calculate the flow rate using the equation

1 22

1

2 ( )g P PQ EA

9AEI306.61 539AEI306.61 53

Where Q = Flow rate

ø = Expansion factor E = Velocity approach factor

A2 = Area of cross factor e1 = Density at pressure Pd = P1 – P2 = pressure differences

g = Acceleration due to gravity

9AEI306.61 549AEI306.61 54

9AEI306.61 559AEI306.61 55

9AEI306.61 569AEI306.61 56

• The pressure tapings can be placed at the

upstream entrance to the convergent cone and at

the throat.

• The flow rate or the discharge rate can be

determined by the following equation .

9AEI306.61 579AEI306.61 57

• A1= Cross sectional area at the inlet

• A2= Cross sectional area at the throat

• H = Difference of pressure head in a U-tube

• G = Acceleration due to gravity

1 2

2 21 2

2A A ghQ

A A

9AEI306.61 589AEI306.61 58

Advantages

• Simple in operation

• Low pressure loss

• Good reliability

• No moving parts.

9AEI306.61 59

Venturi Flow Meter

9AEI306.61 609AEI306.61 60

9AEI306.61 619AEI306.61 61

Disadvantages

• The venture tube has high cost

• It is large in size

9AEI306.61 629AEI306.61 62

Applications

• It can measure flow velocity all shapes

(circular, square, rectangular) pipes

Pitot tube

9AEI306.62 649AEI306.62 64

• It was invented by henry pitot in 1732 to measure the

fluid velocity

• It is used in wide range of flow measurement and

applications such as

• Air speed in racing car

• Air force in fighter jets

9AEI306.62 659AEI306.62 65

Industrial Applications of Pitot Tube

PITOT TUBE

9AEI306.62 669AEI306.62 66

Pitot Tube

9AEI306.62 679AEI306.62 67

• It consists of a cylindrical probe is inserted in to the fluid stream

• In this device the velocity head is converted in to an impact pressure

• The difference between the impact pressure and static the pressure is a measure of flow rate

Principle

9AEI306.62 68

Principle

9AEI306.62 699AEI306.62 69

A Blunt Object Is Placed In A Fluid Stream Sa Obstruction To The Flow As Shown In Fig B

9AEI306.62 709AEI306.62 70

• As the fluid approaches the object, the

velocity will decrease until it reaches zero at

the point where it impinges on it.

• This results in increase in the pressure on

downstream side.

9AEI306.62 719AEI306.62 71

Mathematical Expression

• At the point of impact v2 is zero .in other words • The kinetic energy has been converted in to potential

energy ,• the result is reflected in the value of p2 at the impact

point.

gVP

gVP

22

22

2

221

1

1

9AEI306.62 729AEI306.62 72

• where

V1= velocity of the fluid on the upstream

V2= velocity of the fluid on the down stream

ρ1= density of the fluid on the upstream

ρ2= density of the fluid on the downstream

9AEI306.62 739AEI306.62 73

• This new pressure , known as the total pressure, comprises the normal static pressure and pressure

produced as a result of energy conversion when v2 = 0

• For incompressible fluids ρ1=ρ2=ρ

• The equation (1) becomes

2

211

2p

gvp

9AEI306.62 749AEI306.62 74

• v1= 2g(p2-p1)

ρ

• G and ρ are constant for particular fluid• The pressure difference is proportional to the

velocity of fluid

9AEI306.62 75

S-type Pitot Tube

9AEI306.62 769AEI306.62 76

Pitot Tube With Manometer

9AEI306.62 779AEI306.62 77

Pitot Tube

9AEI306.62 789AEI306.62 78

• When the blunt object is replaced with a tube having a small opening ,

• Facing the direction of the fluid flow, connected to a differential pressure gauge as show in the fig B.

• As there is no flow through the tube and since the flow is brought to rest ,

• The new pressure developed and sensed is impact pressure p2

Operation of Pitot Tube

9AEI306.62 799AEI306.62 79

• A static pressure reading p1 is taken upstream a little

away from the tube .

• By measuring the differential pressure ,the velocity can be computed by knowing the density of the fluid

• It is very convenient to measure the static pressure in the close neighborhood of the tube

Operation of Pitot Tube

9AEI306.62 809AEI306.62 80

Advantages

• It is a simple and low cost device

• It does not produce appreciable pressure loss

• It can be easily inserted through a small hole in to the

pipe

• It is very useful for checking the mean velocities of the

flows in venturi, nozzle ,orifice plate

9AEI306.62 819AEI306.62 81

Disadvantages

• It is not suitable for measuring low velocities, bellow 5

m/s

• Is sensitive to misalignment of probe with respect to free

stream velocity

• It is not suitable for the measurement of highly

fluctuating velocities i.e. highly turbulent flows

9AEI306.62 829AEI306.62 82

Industrial Applications

• It is used to measure air flow in pipes ducts and stacks

• It is also used to measure velocity of liquid flow in pipes

and open channels

Rotameter

9AEI306.63TO64 84

Rotameter

• It consists of a vertical tube with a tapered cone in which

float assumes a vertical position corresponding to each

flow rate through the tube.

• It is also called as constant pressure drop, variable area

meter.

9AEI306.63TO64 85

Definition

• A Rotameter is a device that measures the flow rate of liquid or gas in a closed tube.

9AEI306.63TO64 86

The Fundamental Equation For An Incompressible Flow Through A Tube

22 d

vgp

Q CEA

------------------- (A)

C = Discharge coefficient

E = Approach factor

A2= Orifice area

g = Acceleration due to gravity

Pd= Pressure difference

= Density

9AEI306.63TO64 87

• Earlier we have discussed orifice , venturi tube ,pitot tube.

• If C, E, A2 ,g, are constant for particular fluid

• Then the flow rate is proportional to the pressure difference.

• In the case of Rota meter A2 = Area between the vertical

tube and float

• If C, E, Pd ,g, are constant for particular fluid

• Then the flow rate is proportional to the A2.

• That is why it is also called constant pressure drop with variable area type flow meter.

9AEI306.63TO64 88

Operation

• It is a vertical tube of conical shape, the area gradually expanding from bottom to top.

• The fluid allowed to flow in an upward direction in the tube.

• If a disc is placed which is free to move in the fluid path, it acts as a float in the fluid.

• An orifice is setup between the perimeter of the disc and inside surface of the tube with a corresponding pressure drop.

9AEI306.63TO64 89

• Initially when there is no fluid flows through the Rotameter

then float is at equilibrium in a vertical tube.

• When fluid flows through the Rotameter it, will effect the

pressure drop, altering the relation between the inlet and

outlet pressure.

• Thus upsetting the equilibrium for force acting on the disc

(float).

9AEI306.63TO64 90

• The disc (float) will then move up or down the tube there

by creating variable area of the orifice until the pressure

drop is at original value when the forces are again at

equilibrium.

• The position of the float in the tube is then measure of

the rate of flow.

9AEI306.63TO64 91

Analysis of Rotameter

• Consider the forces acting on the float in the vertical

column of liquid as shown in fig. 2

• The effective weight ‘W’ acting on the float

W = Vf (2 - 1) --------------(1)

• Where Vf = Volume of the float

2 = Material density of the float

1 = density of the liquid

9AEI306.63TO64 92

Fig. Force acting on a float in a Rota Meter

9AEI306.63TO64 93

Rotameter

9AEI306.63TO64 94

• Force Fd acting in a down ward direction on the upper

surface of the float

Fd = p2Af -----------------------(2)

p2 = pressure per unit area on the upper surface of

the float.

Af =surface area of the float

9AEI306.63TO64 95

• Force Fu acting in a up ward direction on the Lower

surface of the float

Fu = p1Af --------------(3)

p1 = pressure per unit area on the Lower surface of

the float.

Af =surface area of the float

9AEI306.63TO64 96

• A drag force D tending to pull the float in an upward

direction (in the direction of the flow ) may be represented

by an equation

D = K v lf ή ------------------------------ (4)

k = a constant

v = velocity of the fluid

ή = absolute viscosity of the fluid

lf = a dimensional function equivalent to length

In Balance Condition

9AEI306.63TO64 97

fu +D = W+ fd ---------------------(5)

• if viscous drag force effects are neglected i.e, D = 0

P1Af = vf (ρ 2– ρ1) +p2Af ---------------------(6)

• When the flow increases from an equilibrium value, an

increased differential pressure ( p1-p2)

• The ratio p1/p2 increases from which means that the force

p1Af is now greater than vf (ρ 2– ρ1) +p2Af

9AEI306.63TO64 98

• Then the float is free, it will moved in the direction of flow

• As it moves upward it increases the orifice area due to the

expanding sectional area of the tube and pressure

differential falls proportionally

9AEI306.63TO64 99

• This operation continues until (p1-p2) reaches its original

value then the equation (6) are equilibrium again

• The new float position is the measure of the new flow rate

9AEI306.63TO64 100

• This operation is reversed when the flow rate decreases

• From equation (6) we can write in to

• (p1-p2) Af = vf (ρ1-ρ2 )----------------- (7)

1 2 2 1( ) ( ) (8)f

f

Vp p

A

9AEI306.63TO64 101

• Substituting this in equation (A)

• A2 = The gap area between the float and the tube

• x = Displacement of the float

f 2 1v 2

f 1

V ρ ρQ cEA 2g (9)A ρ

9AEI306.63TO64 102

• The equation (9) can be written as

• Where = Proportionality constant

2 1

1

2 (10)fv

f

VQ KcxE g

A

2AKx

9AEI306.63TO64 103

• In Rota meters the velocity approach factor E is of no

significance. The equation (10) can be written as

• The mass flow rate of fluid is

2 1

1

2 (11)fv

f

VQ Kcx g

A

2 11

1

2 (12)fv

f

VQ Kcx g

A

9AEI306.63TO64 104

Advantages of Rota Meter

• It gives direct visual indication on a linear scale

• Low cost

• It has high accuracy

9AEI306.63TO64 105

Advantages

• A rotameter requires no external power or fuel,

• It uses only the inherent properties of the fluid, along with gravity, to measure flow rate.

• A rotameter is also a relatively simple device

• It can be mass manufactured out of cheap materials, allowing for its widespread use.

9AEI306.63TO64 106

Limitations of Rota Meter

• Due to its use of gravity, a rotameter must always be

vertically oriented and right way up, with the fluid flowing

upward

9AEI306.63TO64 107

Disadvantages

• Graduations on a given rotameter will only be accurate for

a given substance at a given temperature.

• Rotameters normally require the use of glass (or other

transparent material), otherwise the user cannot see the

float. This limits their use in many industries to benign

fluids, such as Water.

• Rotameters are not easily adapted for reading by machine

9AEI306.63TO64 108

Applications of Rota Meter

• Laboratory• Testing and production lines • It can be easily integrated for instrumentation with

1. Alarms

2. Indicators

3. Controllers

4. Recorders

Turbine Flow meter

9AEI306.65 110

Description

• It is non- friction displacement type of mechanical

flow meter

• It consists of two parts

• The rotor with multiple blades

• Variable reluctance tachometer

9AEI306.65 111

Diagram

9AEI306.65 112

• The rotor consists of turbine blades

• It consists of an axially mounted freely rotating turbine

wheel / (rotor). It is placed in the path of a fluid steam.

• When the flowing fluid impinging on the turbine blades

imparts a force on the blade surfaces

• Due to this force the rotor in motion with an angular

velocity “v”.

Operation

9AEI306.65 113

• This angular velocity is proportional to the fluid of

whose velocity to be measured.

• The turbine flow meter with an electrical output suitable

for measuring the flow in the tubes as shown in the

figure 2.

• The turbine flow meter consists of a rotor with multiple

blades. The rotor is supported by ball bearing and is

located centrally in the pipe .

9AEI306.65 114

Fig 2

2

9AEI306.65 115

• A permanent magnet is encased in the rotor body

and pick-up coil is placed on the frame as shown in

the figure 2.

Turbine Type Flow Meter

9AEI306.65 117

• When the flowing fluid impinging on the turbine blades

imparts a force on the blades surfaces

• The angular velocity of the can be sensed by the means

of a proximity type of pick of reluctance type.

• A permanent magnet is encased in the rotor body and

each time the rotating magnet pass the pole of the pickup

coil,

Working Principle of Turbine Flow Meter

9AEI306.65 118

• The change in permeability of the magnetic circuit

produces a voltage pulse at the output terminals

• These voltage pulses are counted by the means of

electronic digital counter

9AEI306.65 119

• The relationship between the volume flow rate and

the angular velocity of the rotor is

Q = kn

Q= The volume flow rate

n = The rotor angular velocity in rad/s

k= Constant for any given meter

9AEI306.65 120

• Alternatively the frequency is converted in to voltage

and is fed to analog/digital voltmeter

• The out put voltage of analog/digital voltmeter is

proportional to the volume flow rate of the fluid.

9AEI306.65 121

Advantages of Turbine Flow Meter

• High accuracy

• Good repeatability

9AEI306.65 122

Disadvantages of Turbine Flow Meter

• Highly expensive

Anemometers

9AEI306.66 124

Definition of Anemometer

• Velocity-measuring devices for obtaining velocity of a

fluid stream

• Such as air flow in a ventilating duct

• Wind tunnel

• Water flow in a closed channel

• Wind speed as in meteorology

9AEI306.66 125

Types of Anemometer

• Cup-type Anemometer

• Hot-wire/Hot-film anemometer

9AEI306.66 126

Hemispherical Cup Anemometer of Cup-type Anemometer

Fig 2

9AEI306.66 127

Cup-type Anemometer With Vertical Axis

9AEI306.66 128

Cup Type Anemometer

9AEI306.66 129

• Vertical spindle rotating freely about the vertical axis

mounted on bearings

• Spindle is coupled to three equally-spaced horizontal arms

• Hemi spherically-shaped cup is mounted at the end of each

arm with the meridian plane vertical

• When placed in an air stream ,a difference of pressure is set

up between the concave and convex sides of the cups

9AEI306.66 130

• Resulting in a rotational torque at the vertical spindle

• The spindle is coupled to a mechanical or electrical

counter calibrated in the units of velocity i.e m/s

• The readings on the counter integrated over a specified

period gives an indication of the wind speed.

9AEI306.66 131

• Three cup anemometers are currently used as the

industry standard for wind resource assessment studies

• They can measure velocities up to 3000 m/s

• Due to frictional losses, the device is not very accurate

and needs calibration periodically

Hotwire or Hot film anemometer

9AEI306.67-68 133

Hot-wire Anemometer

Fig 36.1

9AEI306.67-68 134

Hot-wire Anemometer

Fig 36.2

9AEI306.67-68 135

Principle of Hot-Wire Anemometer

• When a fluid flows over a heated surface

• Heat transferred from surface causes temperature

reduces

• The rate of reduction of temperature indicates velocity

of the fluid stream.

9AEI306.67-68 136

Construction of Hot-Wire Anemometer

Hot wire

9AEI306.67-68 137

Construction of Hot-Wire Anemometer

Fig

9AEI306.67-68 138

Operation Of Hot-wire ANEMOMETER

• Fluid flows over the platinum wire, its temperature

reduces

• Resistance of wire changes ,bridge unbalanced

• The bridge is balanced by adjusting the current

through wire

• Temperature remains constant

9AEI306.67-68 139

• Current measured due to voltage drop across resistance

• Heat generated=I2R

• Heat loss from the surface due to fluid flow=a (v ρ + b)1/2

• Under equilibrium condition

• Heat generated=Heat loss

9AEI306.67-68 140

• I2R= a (vρ +b)1/2

• V=[I4R2/a2 –b] / ρ

• Temperature and resistance of a wire kept constant

• Velocity measured by measuring current (i), through

the heated wire

9AEI306.67-68 141

Hot-Film Anemometer

• It is commonly used to measure the mean and

fluctuating velocity in fluid flow

• The flow sensing element is a platinum tungsten wire

• It is welded between two prongs of the probe

• It is placed in one arm of the Wheat stone's bridge

• It is heated electrically

9AEI306.67-68 142

Hot-Film Anemometer

• The probe is introduced in the fluid stream

• Then it tends to get cooled by the instantaneous velocity

• Consequently its resistance decreases

9AEI306.67-68 143

Hot-Film Anemometer

• The rate of cooling depends on

1. Shape, size and physical properties of the wire

2. Temperature difference between the heated hot

wire and the fluid stream

3. Physical properties of flowing fluid

4. Velocity of fluid stream

9AEI306.67-68 144

Hot-Film Anemometer

• The first three conditions are generally constant

• So the instrument response is direct measurement of

the velocity

• There are two ways to measure the velocity using the

H. W. Anemometer

1. Constant current mode

2. Constant temperature mode

9AEI306.67-68 145

Hot-Film Anemometer

• In both modes the bridge is initially balanced

• When there is a fluid flow the hot wire/film resistance

changes

• This unbalances the bridge and some output voltage is

generated

• That voltage is proportional to the velocity of fluid flow

9AEI306.67-68 146

Fig 6

Fig 7

Hot Film Anemometer

9AEI306.67-68 147

Hot-Film Anemometer-Range

Hot-Film probes are used for measurements in liquids

for flow-rates up to 25m/s.

Frequency response extending up to about 150kHz

9AEI306.67-68 148

Fig 8

Thin Platinum Hot-Film

9AEI306.67-68 149

Fig 37.4

Circuit Diagram

9AEI306.67-68 150

Operation of Hot-Film Anemometer

• Hot-Wire Anemometer is another version of Hot-Film

transducer.

• Sensor is the thin film of platinum deposited in a

glass or quartz substrate.

• The film replaces the Hot –wire , remaining circuit is

same as Hot-wire

• The film transducers gives mechanical strength .

9AEI306.67-68 151

• It can also be used at very high temperatures , using

cooling arrangements

• The directional sensitivity of the probe, maximum ay

right angles to the flow

• In the angle 450 <θ 1350 effective velocity , u rms =u

sinθ.

9AEI306.67-68 152

• This property directly utilized in flow- direction

measurements.

• In steady-flow conditions by rotating probe, until

sharply-defined null is obtained.

9AEI306.67-68 153

Applications

• Used for measurement of propagation velocity of the

shock in shock-tube experiments.

Electromagnetic Flow meter

9AEI306.69-70 155

Electromagnetic Flow Meter

9AEI306.69-70 156

Electromagnetic Flow Meter

9AEI306.69-70 157

• The basic principle of operation of Electromagnetic

flow meter is faradays laws of electromagnetic

induction

Principle of Electromagnetic Flow Meter

9AEI306.69-70 158

Faradays Laws of Electromagnetic Induction ?

• First law states that whenever a conductor cuts lines of

magnetic field ,an induced emf is generated.

• Second law states that the magnitude of this emf is

proportional to the rate of which these lines are cut.

• The emf is perpendicular to the plane of conductor and

the magnetic field.

9AEI306.69-70 159

9AEI306.69-70 160

Principle of electromagnetic flow meter

B

9AEI306.69-70 161

Construction

• A permanent magnet or electromagnetic it may either ac or dc around a non conducting pipe

• Two electrodes are inserted in tube, their surfaces being flush with the inner surface of the tube and in contact with liquids

• As the conductive liquid flows through the insulated tube with an average velocity v,

• It may be considered as a series of flat conductor discs passing through the magnetic field

9AEI306.69-70 162

Electromagnetic flow meter

9AEI306.69-70 163

According faradays law induced emf generated by

• E = induced voltage in volts

• B= magnetic flux density in tesla

• D=the distance between the electrodes in m

• V= the average velocity of liquid in m/s

810 (1)e Bdv

Mathematical Expressions

9AEI306.69-70 164

From equitation …1

810BdeV

Mathematical Expressions

9AEI306.69-70 165

• The volume flow rate Q= Av

• A= cross sectional area of the pipe

• V= Average velocity of the fluid

Substituting the value of from equation(1) in equation(2)

80 10BdAeQ

Mathematical Expressions

9AEI306.69-70 166

• As A,B and d are constants for particular electromagnetic flow meter,

• the induced voltage is proportional to the volume flow rate

9AEI306.69-70 167

9AEI306.69-70 168

Advantages

• Good Accuracy and reliability

• Simplicity and ruggedness

• Fast response.

9AEI306.69-70 169

Disadvantages

• Expensive

• Not suitable for conductive fluids

9AEI306.69-70 170

Applications

• It is particularly suitable for flow velocity or volume measurement of

• Slurries

• Corrosive acids

• Sewage

• Detergents ,greasy and sticky fluids

Ultrasonic flow meter

Ultrasonic Flowmeters works in two different

principles :

• Doppler Effect Ultrasonic Flowmeter

• Transit time/Time of flight Ultrasonic Flowmeter

9AEI306.71-72 172

9AEI306.71-72 173

Doppler Effect Ultrasonic Flowmeter

Fig 38.1

9AEI306.71-72 174

Fig 38.2

Principle of operation

• Ultrasonic Signals are passed through the fluid,

• the particles suspended in the fluid shows a frequency

shift

• It is proportional to the velocity of the fluid

9AEI306.71-72 175

Working Principle :

• It is used for reflected electronic sound to measure the

fluid velocity

• Measuring frequency shift between frequency source ,

receiver , fluid carrier , relative motion is measured

• Resulting frequency shift is called doppler effect

9AEI306.71-72 176

9AEI306.71-72 177

Circuit diagram

Expression

Fluid Velocity expressed as :

V = C( fr – ft) / 2ft cosØ

9AEI306.71-72 178

Expression

Where :

• fr = received frequency

• ft = transmission frequency

• v = fluid flow velocity

• Ø = relative angle between the transmitted ultrasonic

beam and the fluid flow

• c = velocity of sound in the fluid

• This method requires there is some reflecting particles in

the fluid9AEI306.71-72 179

Advantages

• Obstructs less flow

• Can be installed outside the pipes

• The pressure drop is equal to the equivalent length of a

straight pipe

• Low flow cutoff

• Relative low power consumption

9AEI306.71-72 180

Limitations

• Doppler flow meters performance highly dependent on

physical properties of fluid Such as :

• Sonic conductivity

• Particle density

• Flow profile

9AEI306.71-72 181

Ultrasonic flow meter animation

9AEI306.71-72 182

Transit Time Ultrasonic Flowmeter-Principle

• The Time for the sound to travel between the

transmitter and a receiver is measured

• This method is not dependable on the particles in the

fluid

9AEI306.71-72 183

9AEI306.71-72 184

Transit Time Ultrasonic Flowmeter

Fig 39.1

Transit Time Ultrasonic Flow meter

9AEI306.71-72 185

Receiver ‘B’Receiver ‘B’

Transmitter ‘A”Transmitter ‘B’

Flow’ v’

Principle

An Ultrasonic flowmeter is mounted at an angle or

parallel to the pipe wall

Short duration Ultrasonic waves are transmitted across

the fluid

The velocity of the ultrasonic waves is increased or

decreased by the fluid velocity depending upon the

direction of fluid flow

9AEI306.71-72 186

Construction

The figure shows the schematic arrangement of

ultrasonic flowmeter of transit time type

Two transmitters of piezo electric device A&B are at

the down side of the flow tube with an angle

Two piezo electric receivers A&B are connected to the

pipe at top side with an angle

9AEI306.71-72 187

Operation The fluid in the pipe flows at a velocity

The transmitter transmits short duration ultrasonic

signals through the fluid at a velocity ‘l’

The signal received by the receiver A is increased to

C+ cos θ because it is in the direction of fluid flow

The reception frequency of the receiver pulse fA will be

fA = (C+ cos θ)/(l)

9AEI306.71-72 188

Operation

Where θ= angle between the path of sound and

pipe wall

l = distance between the transmitter and

receiver

The velocity of the ultrasonic signal transmitted by A is

received by the receiver B will reduced by the fluid

velocity

It creates a retardation of C+ cos θ 9AEI306.71-72 189

Operation

If the reception frequency is given by fB = (C- cos θ)/(l)

The difference in frequencies is given by

Δf = fA- fB = (2 cos θ)/l

Time duration = ΔT= (l)/ (2 cos θ) (since ΔT=1/Δf )

9AEI306.71-72 190

Operation

By measuring the difference in repetition frequency Δf

and by knowing the value of θ and l the velocity of fluid

can be measured

Or

The flow velocity can be computed by measuring the

time difference between the two pulses in either

directions

9AEI306.71-72 191

Advantages

Bidirectional measuring capability

Good accuracy

Fast response

Wide frequency range

Used for any size of pipes

Measurement is independent of the velocity of sound ‘c’

9AEI306.71-72 192

Disadvantages

High cost

9AEI306.71-72 193

Applications

Used mostly for liquids without any pressure

9AEI306.71-72 194

Limitations

It requires reliability high frequency sound transmitted

across the pipe

Liquid slurries with excess solids or entrained gases

may block the ultrasonic pulses

These are not recommended for primary sludge, mixed

liquor ,septic sludge and activated carbon sludge

Liquids with entrained gases cannot measured reliably

9AEI306.71-72 195

Laser Doppler anemometer

What is LASER ?

LASER - Light Amplification by Simulated Emission of

Radiation

9AEI306.73-74 197

Fig.1 Laser Beam

Laser Beam

9AEI306.73-74 198

Fig.2 Laser Beam

Laser Doppler Anemometer

• It is most recent advancement of flow meter

• It is also known as optical type velocity meter

• It measures the instantaneous velocities of gasses or

liquids flowing in a transparent (glass) channel

9AEI306.73-74 199

Principle animation

9AEI306.73-74 200

Principle

• It is based on the Doppler shift in frequency of the light

scattered by an object moving relative to the radiating

source

• The technique basically consists of focusing laser beams

at the point in the fluid where velocity is to be measured.

• At this focal point the laser light scattered from the fluid

or fluid particles contained in the fluid

9AEI306.73-74 201

Principle

• Signal processing of the photo-detector output gives the

magnitude of Doppler frequency shift.

• Which is directly proportional to instantaneously velocity

of the flow

9AEI306.73-74 202

Features of LASER

• It provides much higher quality of monochromatic (single

wavelength) light source

• It is coherent i.e. it stays in phase with it self over long

distances

• Its frequency is very stable .this enables to accurately

detect the Doppler shift frequency

• Its wave length is less effected by changes in ambient

pressure ,temperature or humidity.

9AEI306.73-74 203

Materials suitable for production of laser beams

• Ruby (aluminium oxide crystal doped with a small

amount of chromium)

• Nd-YAG ( type of garnet stone doped with a small

amount of neodymium)

• Carbon dioxide gas

• Neon gas

9AEI306.73-74 204

• Ionized argon gas.

• Nd-glass (glass doped with neodymium)

• Helium-neon

• Semiconductor crystal gallium arsenide.

9AEI306.73-74 205

Working

• The laser source (helium-neon laser) produce laser

beam .

• This laser beam is split in to two equal parts by means of

a beam splitter .

• The beam splitter is either a rotating optical grating or an

optical prism as shown in the figure 3 .

• The focussing lens is put in the front of the beam splitter

• It focuses the two beams at a point where the velocity of

the fluid is to be measured

9AEI306.73-74 206

9AEI306.73-74 207

Fig.3 Laser Doppler Anemometer in dual beam

9AEI306.73-74 208

Fig.4 Laser Doppler Anemometer in dual beam

9AEI306.73-74 209

Fig.5 Laser Anemometer

• At the focal point the two split beams cross each other.

• Thus forms an interference fringe pattern.

• It consists of alternate regions of low and high intensity,

as shown in the figure.

• If the small traces particles (dust or dirt particles present

in tap water or air flows) pass through the region of high

intensity ,they would scatter light and cause a Doppler

shift in the frequency of the scattered light.

9AEI306.73-74 210

• This scattered light received by the photo detector will

show a varying electrical signal.

• The frequency of this electric signal is proportional to the

rate at which the particles cross the interference fringes.

9AEI306.73-74 211

• The spacing between the fringes is given by the

expression

• Where = The angle between two converging beams

• = The wave length of the laser beam

x sin (1)2 2

x

9AEI306.73-74 212

• The tracer particles( assumed to have a velocity equal to

that of the fluid flow) pass across the fringes with a

velocity ‘v’ in the direction perpendicular to the fringes.

• The signal experiences a Doppler shift in frequency given

by

= The wave length of the laser beam in the fluid.

)2(2

sin2

vf

9AEI306.73-74 213

• The equation (2) can also be written as

• Where n = The index of refraction of the fluid

• 0 = The wave length of the laser beam

in the vacuum.

)3(2

sin2

0

nvf

9AEI306.73-74 214

• If n, 0 are constant Doppler shift in frequency is

proportional to the velocity of the fluid at particular point

9AEI306.73-74 215

Advantages of Laser Doppler Anemometer

• There is no transfer function involvement i.e. the output

voltage of the instrument is proportional to the

instantaneous velocity of the fluid.

• Non –contact type of measurements i.e. no physical

object is inserted in the flow field.

• Flow rate is undisturbed by measurement.

9AEI306.73-74 216

Advantages of Laser Doppler Anemometer

• It has very high frequency response, in MHz range

• It has very high accuracy

• Suitable for measurement in both gas and liquid flows

9AEI306.73-74 217

Disadvantages of Laser Doppler Anemometer

• It involves the need for a Transparent channel

• The measurement technique is not suitable for clean

flows

• It is highly expensive and requires a high degree of

experience and skill in operation .

9AEI306.73-74 218

Applications of Laser Doppler Anemometer

• Remote sensing of wind velocities

• Blood flow measurements.

• Measurement of flow between blades of turbines and jet

propulsion system

• Used for both laminar and turbulent flow measurement

9AEI306.73-74 219