Flow measurement

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 4
Domestic Water 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

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Head Type Flow Meter

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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.

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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 2
1 1 2 2
1 2 (1)
2 2
p v p v
h h k
g gρ ρ
+ + = + + = − − − −
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
2
22
2
11
−−−−+=+
g
vp
g
vp
ρρ
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 2
1 2 2 1
2
P P V V
e g
− −
=

9AEI306.59-60 20
2 2
2 1 1 2
2
( ) (4)
g
V V P P
e
− = − − − − − −
2
1 2 2
1
(5)
A
v v mv
A
= = − − − −
[ ]2
1
(5) (4)
A
m substituting in
A
=Q
2 2 21 2 1 2
2 2 2
2 ( ) 2 (( )2
(1 )
(1 )
g p p g p pg
v m v x
mρ ρ
− −
− = → =
−
1 2
2 2
2 ( )1
(1 )
g P P
v
m ρ
−
=
−

9AEI306.59-60 21
2 2( )rA V Q=Q
= velocity approach factor

9AEI306.59-60 22
2
2 d
v
gP
Q CEA
e
=
v dQ pα Since all other parameters are
constant

9AEI306.59-60 23
• The orifice plate is basically a thin metal
plate with circular opening
Definition

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Classification of Orifice Plate
• Concentric
• Eccentric
• Segmental
• The concentric type is by far the most widely used.

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• The materials used for construction of
orifice plates are
• Mild steel
• Stain less steel
• Phosphor bronze
Orifice Plate

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• 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

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Fig-b
Orifice Plate

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• 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

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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

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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 –
2
2 d
v
gP
Q CEA
e
=

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

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

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Fig-2
Venture Flow Meter

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• Equation of Bernoulli's theorem
1 2
2
1
2 ( )g P P
Q EA
e
φ
−
=

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Construction
• Converging conical section
• Cylindrical throat
• Diverging Section
• Venturi meter consists of

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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 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

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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 2
2
1
2 ( )g P P
Q EAφ
ρ
−
=

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

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• 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 .

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• 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 2
1 2
2A A gh
Q
A A
=
−

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Advantages
• Simple in operation
• Low pressure loss
• Good reliability
• No moving parts.

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Venturi Flow Meter

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Disadvantages
• The venture tube has high cost
• It is large in size

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Applications
• It can measure flow velocity all shapes
(circular, square, rectangular) pipes

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

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Industrial Applications of Pitot Tube
PITOT TUBE

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Pitot Tube

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• 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

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

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• 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.

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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.
g
VP
g
VP
22
2
2
2
2
2
1
1
1
+=+
ρρ

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• 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

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• 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
ρρ
2
2
11
2
p
g
vp
=+

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• v1= 2g(p2-p1)
ρ
• G and ρ are constant for particular fluid
• The pressure difference is proportional to the
velocity of fluid

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S-type Pitot Tube

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Pitot Tube With Manometer

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Pitot Tube

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• 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

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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

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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

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
2
2 d
v
gp
Q CEA
ρ
= ------------------- (A)
C = Discharge coefficient
E = Approach factor
A2= Orifice area
Pd= Pressure difference
ρ = Density

9AEI306.63TO64 87
• Earlier we have discussed orifice , venturi tube ,pitot
tube.
• If C, E, A2 ,g, ρ 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, ρ 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 (ρ2 - ρ1) --------------(1)
• Where Vf = Volume of the float
ρ2 = Material density of the float
ρ1 = density of the liquid

9AEI306.63TO64 92
Fig. Force acting on a float in a Rota Meter

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 (ρ2– 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 (ρ2– 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
V
p p
A
ρ ρ− = − − − − − −

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 1
v 2
f 1
Vρ ρ
Q cEA 2g (9)
Aρ
 −
= − − − − − ÷
 

9AEI306.63TO64 102
• The equation (9) can be written as
• Where = Proportionality constant
2 1
1
2 (10)
f
v
f
V
Q KcxE g
A
ρ ρ
ρ
 −
= − − − − − ÷
 
2A
K
x
=

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)
f
v
f
V
Q Kcx g
A
ρ ρ
ρ
 −
= − − − − − ÷
 
2 1
1
1
2 (12)
f
v
f
V
Q Kcx g
A
ρ ρ
ρ
ρ
 −
= − − − − − ÷
 

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

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Description
• It is non- friction displacement type of mechanical
flow meter
• It consists of two parts
• The rotor with multiple blades
• Variable reluctance tachometer

9AEI306.65 112
• 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 .

9AEI306.65 115
• A permanent magnet is encased in the rotor body
and pick-up coil is placed on the frame as shown in
the figure 2.

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

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

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Types of Anemometer
• Cup-type Anemometer
• Hot-wire/Hot-film anemometer

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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=I2
R
• 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
• I2
R= a (vρ +b)1/2
• V=[I4
R2
/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.

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.

9AEI306.69-70 160
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
8
10 (1)e Bdv −
= × − − − − − − −
Mathematical Expressions

9AEI306.69-70 164
From equitation …1
8
10×=
Bd
e
V

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)
8
0 10×=
Bd
A
eQ

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

9AEI306.69-70 168
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 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

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 fluid
9AEI306.71-72 179

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 ν
 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+ν cos θ because it is in the direction of fluid flow
 The reception frequency of the receiver pulse fA will be fA
= (C+ν 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+ν cos θ
9AEI306.71-72 189

Operation
 If the reception frequency is given by fB = (C-ν cos θ)/(l)
 The difference in frequencies is given by
Δf = fA-fB = (2ν cos θ)/l
Time duration = ΔT= (l)/ (2ν 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

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 θ = The angle between two converging beams
• λ = The wave length of the laser beam
x sin (1)
2 2
λ θ 
= − − − − − − − − − ÷
 
( )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
∀ λ = The wave length of the laser beam in the fluid.
)2(
2
sin
2
−−−−−−−−−−





=∆
θ
λ
v
f
9AEI306.73-74 213

• The equation (2) can also be written as
• Where n = The index of refraction of the fluid
• λ0 = The wave length of the laser beam
in the vacuum.
)3(
2
sin
2
0
−−−−−−−−−−





=∆
θ
λ
nv
f
9AEI306.73-74 214

• If n, λ0 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

Flow measurement

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