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 Welcome To Survey Engineering .

 

This lesson is on flow measurement.

So, what are we expecting to gain from this lesson, let us see the instructional objectives.

So, after learning the lesson the student should be able to, number 1 describe the importance

of flow sensing and it is some of it is problems. 

Everybody describe the principles of operation

of different flow meters, actually there are various principles we have selected some based

on their industrial applicability. So, they will be able to familiarize themselves with

these principles of operation, how they basically work. They will be able to describe the basic

constructional features how it, what it looks like what are the different parts how they

are made and the different measurement aspects. What affects measurement when the measurement

is good when it is bad. Finally, they will be able to see the merits and demerits and

probably also compare when which particular flow sensor is to be used. So, these are the

things that we expect to gain from this lesson. Now, let us go on into it.

First the need for flow sensor. Flow sensors are needed flow is a very basic process parameter

and it is needed flow measurement is for flow control and for flow metering. So, we need

to know how much of a particular material has past sometimes. We also need to control

the flow and it turns out that flow control is a very, very, very important particularly

flow control is a very common and important control loop because of the fact that every

other control. For example, temperature control or composition control in a reactor.

Temperature control in a heat exchanger, level control in a tank or pressure control in let

us say an accumulator, where you know various time we accumulate hot gas. So, that you can

use that gas to preheat. So, we can do pressure control. So, for doing pressure control we

actually, I mean how do we control pressure, we actually open and close the inlet valve

and for controlling that inlet valve we sometimes have a flow loop. As we will see when we will

enter see the various process control loops in our process control module will see that

how that is to be done. So, it turns out that flow measurement is

becomes an integral part of these. This apart from the fact that operators apart from flow

metering and flow control just flow monitoring is important because operators need to keep

an eye of them. So, there are whole arrays of instruments which will display simply display

or log the flow.

 

So, having said that, let us basically try to characterize flow meters. So, flow meters

can be characterized in 2 ways. The first is obstructive or you know intrusive measurement.

So, intrusive means that the instrument or the sensor will be put in the flow. So, it

will affect the flow in even if in a small way, but it will affect the flow, it will

obstruct it. So, under the under this obstructive head

we have, various kinds of flow meters and today we are going to look at differential

pressure flow meters. Under that 2 major categories orifice meters and venturi meters.

Then rota meters which are also very, very common in the industry. Turbine flow meters

and well there is a variant of turbine flow meters called paddle wheel meters which are

also similar. So, we are going to look at only turbine flow meters. Then among the non-obstructive

ones or the non-intrusive ones where the big, the medium is utilized for sensing, but as

such the instrument is not placed in the flow. So, you are doing the measure if it is flow

in a pipe we are typically talking about flows in pipes we here we are not talking about

open channel flows. So, if it is flow in a pipe then we have we are going to make the

measurement from outside the pipe we are not going to put anything within the pipe. So,

we have among that we have electromagnetic flow meters, we have ultrasonic flow meters

and we have cross correlation flow meters. So, these are the various types of flow meters

that we are going to look at today. Start with differential pressure flow meter.

These are the most common and widely used for liquids and gasses in the industry and

basic idea is that you place we will see it very soon. Basic idea is that you place a

restriction in the pipe. That is the pipe is flowing at some point you obstruct the

flow and you make a hole. So, now the liquid which was coming from this side, upstream

when it meets the obstruction and the hole it has to flow through the hole.

So, in flowing past that hole where when the flow area is reduced it will develop a pressure

across this obstruction. It is this pressure, which is measured and then calibrated in terms

of the flow. So, this is that is why is called a differential pressure flow meter. So, basically

we are obstructing the flow creating a differential pressure across the obstruction. And then

measuring the differential pressure using some differential pressure measurement scheme

which we see in the pressure measurement module right.

Then the then the differential pressure output is to be calibrated in terms of the volume

flow rate. Incidentally in this particular case, we are only we are basically talking

a volume flow rate. We are not talking of mass flow rates. Mass flow rate measurement

requires 2 things. Firstly, it requires measurement of volume flow rates and it could also require

measurement of density or sometimes it is done like that sometimes it is done directly.

So, in this case we are talking about volume flow rates. We are also not talking of measuring

linear velocity profiles where the velocity profiles are varying at different points of

the flow field. So, there are there are actually various kinds

of flow measurement applications, but the vast majority of industrial applications require

to measure the volume flow rate. So, we are going to concentrate on that. This pressure

development when a flow is restricted is actually based on a principle called the Bernoulli's

principle. So, what is that principle.

So, that principle says that if you have a pipe which is, this is a pipe through which

the liquid is flowing let me select a pen here. So, the liquid is flowing this way.

So, initially when it is flowing, it is flowing through this area cross section then at this

point. This is cross section A 1 at this point there is an this is the obstruction it is

simple, it can be a simple plate or the pipe itself can be made such that the such that

diameter reduces. So, this is the obstruction. So, now, the

liquid which is coming will pass through like this and will again feel and go like this.

 

So, these are the you know the liquid if you draw the set of so called stream lines although

this is not laminar flow. Then the liquid flows like this. Now, So, you see that the

area effective area of cross section on the 2 sides this is the obstruction or continuously

changing. Here it is A 1 here it is slowly changing here it must flow through A 2, this

is A 2 or A 2 here. Then it can it can get further reduced and will reach a minima. This

position where the minimum area is reached is sometimes called the vena contractor.

Vena contractor and then it again spreads out and feels the pipe right. So, this is

what is going to happen and Bernoulli's principle says, that if you have a fluid going, that

is you know kind of it says that essentially there are three forms of energy in flowing

fluids. One is it is kinetic energy which is due to it is velocity another is it is

potential energy which is depending on at what height it is with respect to some daytime

level, in this case this is the daytime level. The third one is the pressure energy, which

is which dependent, which depends of the pressure that exists in the fluid at that point of

time. So, Bernoulli's principle says that if you assume that there is no friction loss

then this energy is conserved. So, anywhere the some of these three energies are going

to be the same.

So, it says that this is the pressure energy, pressure energy is P by row. So, this is the

pressure energy, this is the kinetic energy and this is the potential energy. So, it says

that at any 2 points these are going to be conserved roughly. So, you get this equation

if generally in our situation pipes are horizontal. So, if they are horizontal then Z 1 equal

to Z 2 and you can ignore these 2 terms generally. So, then you have this equation that P 1 by

row 1 plus V 1 squared by 2 equal is to this. It also often happens if it is a liquid that

the liquid is incompressible, and if it is a single phase liquid then it is density will

also be same at 2 point. So, this does not change. So, then you have. So, this is the

basic principle. So, then you have and this V 1 is obviously related to the volume flow

rate because A into V 1, the A into V 1 will give you the volume that. So, basically V

1 is Q by A where A is the cross section right and Q is a volume flow rate. So, you can relate

this V 1 with volume flow rate. So, that is why how this the volume flow rate is actually

related to the pressure right. So, let us see how this principle is used.

 

So, now we have an orifice meter which uses this principle. So, what. So, orifice meters

can have basic idea is same that we have a pipe, in the pipe we are going to put a plate

with a hole it that is all. We are going to measure pressure difference across this plate.

So, depending on where we measure the pressure there could be a different types of these

you know these are called the pressure taps. So, this is one pressure tap this is the upstream

and this is downstream tap. So, depending on the pressure tap positions you can have

some variations. So, in this case we have flange taps. So, which means that basically

how it is done is that, there is there is actually a flange. Flange means that there

is a pipe section coming here. So, you have. So, here actually somewhere here you have

that hole. So, actually this is the pipe upstream pipe

section this is the downstream pipe section and in between you connect this plate. You

connect it and you bolt it here, this plate place you bolt it such that it stays. On this

flange you have this pressure taps. So, you have flange taps, similarly you can have various

other positions of taps like you can have what is known DD by 2 taps where the position

of the taps are related to the pipe diameter. So, on the upstream side you have if the diameter

is D, then you have a tap at distance D from the plate and the downstream side you have

at D by 2. So, these are all you know could you have.

So, you can have various other kinds you can have vena contractor taps that is the put

the tab where the area becomes minimum right. So, you can have corner taps. So, with the

there are various tapping conventions you can adopt 1 anyone of them the other case

is venturi tube. So, in the orifice plate we are we have pipes and we put a simple plate

inside while in the venturi we actually have a pipe section, where the diameter gradually

reduces right. So, here we have the venturi. So, what happens

here is this is the upstream side. This is the upstream side and these are you know actually

do not have a single tap you can have you can have taps all across the periphery. So,

that you can take this measurements. You have flow measurement one thing must be understood

that flow measurement because of turbulent this Bernoulli's principle, this uses turbulent

flow conditions. So, because turbulent there is always a pressure fluctuations. So, measurements

are generally tent to be noisy. So, it is a good idea to you know make this pressure

measurements and average them. So, that is why people can use different

you can if you have if you have a number of taps along the periphery.

 

Then you can use it for averaging and you will get noise reduction. So, you have this

taps on the upstream side and this is called the throat of the venturi. So, the diameter

here the pipe section is made such that the diameter reduces and sometimes it is smooth

also this looks sometime this is made smooth. So, that you do not have energy loss and then.

So, principle is the same again measure pressure here measure pressure here and then apply

Bernoulli's principle. So, there are some advantages, if you have

a smooth surface, first of all there is no you know if you see the other one. In the

other one you have in the pipe you have certainly have an obstruction. So, you have if you have

any kind of you know particulate matter suspended matter in the thing, this creates an obstruction

all of a sudden this is if the flow is not smooth. So, what happens that you can have

metal material deposition around this point because the suddenly the fluid comes and fills

the obstruction. Here there is I mean there is there is a point

where things tent will tent to settle and that will change the flow properties, this

will change flow properties such things can happen. While they do not happen in the venturi.

In the venturi the things smoothly flow out and the pipe diameter is reduce. So, therefore,

there is no such material deposition and even if you have venturi can measure flow even

for in whatever is known as dilute slurries. That is I mean liquids with some suspended

solid particles, while orifices can also do that, but they are not generally use for doing that.

 

So, this is the basic principle and if you see the flow measurement law.

It turns out that the flow is actually related to, this is the pressure right, this is the

P 1 minus P 2 is delta P which is the pressure difference across the obstruction. So, if

you take one of the taps the upstream taps will have pressure P 1 the downstream tap

will have pressure P 2 and the flow will be related to this thing, A 2 and A 1 we have

all ready seen they are diameters of, they are cross sectional areas of the pipe upstream

and downstream. It turns out that if you take Bernoulli's

law and actually derive the flow rate, then you will get this part. If that is, if you

measure the pressure exactly at the plate at that point, but it turns out as we have

seen that we are actually measuring the pressure elsewhere. Slightly away from the plate. So,

therefore, we have to it should actually A 2 should stand for the area where you are

making the pressure where we are measuring the pressure.

So, now since this is a sort of geometric parameter, you have designed the plate. So,

you know it, but therefore you need to add a factor. So, this is the ideal one would

have given, if I measured the flow right at the plate, but I am not doing that. So, therefore,

I will apply a correction factor and this correction factor I will experimentally determine

right. So, first of all we must know under what condition

this this law is actually used for the measurement with some CD value which have to be chosen

based on manufacturers guidelines given. So, we have to know when this is valid. It is

valid on a turbulent flow when the Reynolds number which is again parameter, which can

be calculated based on density, viscosity, velocity of the fluid and some dimensions

of the place, where it is flowing in this case the diameter.

 

So, based on that we calculate a parameter called Reynolds number and when the Reynolds

number becomes greater than ten to the power four evaluates too, we can assume that the

these measurements equations will hold. These equations are actually given for incompressible

fluids, that is a liquid. While if we have if you use we can use it also for gas this

kind of measurement is also can be used for gas.

Only thing is that the assumption of a constant row will not hold in that case. So, therefore,

we have to apply corrections further corrections. So, we have to add which is called an expansibility

factor which it depends on various things like CP by CV pressures etcetera. So, we now

this A 2 is actually stands for the cross sectional area for the fluid flow where we

are making the measurement P 2. So, that depends on various kinds depends on the obstruction

depends on the position of the downstream, pressure tap.

Sometimes depends on the obstruction that is whole parameters. So, they have to be there.

So, based on this, but. So, actually we do not we do not use that value. So, we actually

use the whole value, whole parameter and instead apply a correction factor called the discharge

coefficient. Which is experimental determine by the manufacturer. So, from manufactures

tables we can get this value.

So, value of discharge coefficient depends on various things. It can depends on the type

of flow meter there is an orifice or venturi and each manufacturer for each model will

give you a detail description of how to obtain the discharge coefficient. Reynolds number

and diameter ratio that is, what is the diameter of the upstream pipe and what is the diameter

of the hole you are using. So, the ratio which is often called beta that

is this refractors primarily determine the discharge coefficient also the fluid type.

That is obviously there and experimental or values or regression equations for CD are

available for various flow meters over a wide range of fluid velocities. So, we can use them

So, this is the basic principle. Now, if we what are the plus points no moving parts robust,

very cheap you are just putting a plate. Of course, venturi is not that cheap maintainable,

very well established had been used in the industry under various flow condition for

long long times and good very good amount of data is available found on CDs and the

various things that happen. So, no problem in getting information. This is the point

that these meters because they create an obstruction they actually create a.

They actually create permanent head loss actually what happen this needs to be understood is

that, suppose you have a pipe and if you have an obstruction here then liquid flows out

like this. So, what happens that here suppose you have P 1 as you are going down area is

decreasing. So, velocity is increasing the same volume of liquid is flowing through a

smaller area. So, velocity V is increasing. Therefore pressure is falling actually.

Here the pressure will be minimum, because the velocity is the maximum and then it will

again rise, but it turns out that it cannot rise fully. So, the pressure curve actually

if you see down the pipe stream suppose the pressure was here the pressure will fall and

then it will rise, but it will not rise fully. So, there is a permanent pressure loss which

is to be, which is shown in terms of the pump energy loss. So, actually suppose you need

a pressure P it is the down side that you have putting an equipment.

So, you need to create a certain amount of fluid pressure there. So, if you need a fluid

pressure of P here, then you have to create a pressure which is on the upstream side by

using a pump which will compensate for this drop. Therefore, you we are going to lose

some energy. So, this is the price that you pay in these flow meters. In certain cases

this could be significant. So, this as we have seen that the flow is

or other the pressure is actually proportional to the square of the flow right it is root

over delta P is coming is K into root over delta P. If we assume that that constant proportional

defector is constant. Then you have an equation which is K into Q is equal to K into root

over of delta P. So, what you are measuring is delta P. So, the delta P is again some

K 1 into Q square. So, it is actually square relationship which means that, suppose the

flow becomes 0.25 times or twenty five percent of the rate in flow.

So, then the pressure measurement pressure drop will become point zero. So, about 5,

6 percent of the flow and this pressure sensors, when the instruments operate at very low range

they actually become, I mean they actually become inaccurate because there are some fixed

errors. So, as percentage of readings they you will

have lot of errors. It turns out that because of this non-linearity these instruments are

not very good at measuring low flow rates right. So, range ability is the ratio of maximum

value of the measurement to minimum value of measurement or other minimum value of measurement

to maximum value of measurement. So, this is not very high this ratio. This ratio is

rather low because you cannot have very low measurements. So, that is another problem.

Discharge coefficients can change with where, actually you have the in the orifice plate

the sharpness of the edge it is flowing through the hole and the edge of the plate which is

made. So, the edge of the plate is made like this. The edge of the plate on the. So, you

have plates with edges like this. So, you have a sharp edge here. If this edge due to

use this edge gets rounded, then the discharge coefficients will change and your flow measurements

can become erroneous. So, it needs maintenance. It generally applicable for clean fluids,

although some amount of suspended particles can be used for especially for venturi. There

are sometimes installation constrains in the sense that it is required that, suppose if

you place the meter in a position where just upstream of the meter there is a there is

a bend then this meters will not read correctly. So, there are restrictions that is the upstream

and an especially upstream there should be straight pipe lengths. So, there are installation

constrains.

If you compare venturi meters with orifice meters turns out let us see, what is happening

here. So, you have venturi meters can work with or work on very high ranges. You can

have very big venturi. They are expensive compare to orifice meters because you need

to make the whole pipe section they are nicely machine not just a plate, but they are definitely

offer good accuracy and lowest permanent pressure loss.

So, even if cost you are going to make up some of that costs by wasting less energy,

less pump energy. So, that is a good thing about venturi they are long working life because

they are smooth and the liquid passes. So, once you install it very little maintenance

is required and it can also measure flow of fluids with suspended solid. On the other

hand, orifice meters are the least expensive, but they have lower working life. Due to where

in the edge and generally they are good for clear fluids not for with. So, fluids with

particulate matters, although sometimes it is used with an eccentric hole that the hole

is not placed in the center, but in the bottom. So, that when the fluid passes it actually

it will wash away any suspended particle that that can accumulate all right. So, next we

have the rota meter.

So, in the rotameter is sometimes called the variable area of flow meter. So, you might

have seen this. So, what happens is that you have a tube right. This tube can be made of

metal this tube can be made of glass generally made of glass in the common case. So, the

fluid is coming in and flowing out. So, you will there are there all there always to be

installed in the upright condition because the use. So, they cannot be installed horizontally,

they have to be installed vertically all the time and the fluid will flow this way and

go out this way. So, let us if you see the force is acting

on the fluid. There is what is known as a float or a bob which in if the flow is not

there than this bob will actually sit here. This in this bob will actually sit here. So,

it will sit here. So, as the as the flow increases gradually the bob will rise. So, at various

flow rates the bob will actually settle at a certain position. If you readout from a

scale where is the bob is settling at the present time, then this scale is sort of calibrated

in tube. So, this will directly give a readout of the

fluid flow rate. It is called the variable area of flow meter because the area through

which the fluid flows here and the area which through which the fluid flows here. This area

through which the fluid flows continuously varies as the float goes up and down. So,

the flow area is vary, I mean contrast this with the venturi. There the flow areas are

constant right. It is the pressure, which is vary why here what is going to be the pressure.

See a free body diagram or forces then where will the float be stationary. The float will

be stationary when the force is on it will, actually balance out. So, when will it balance

out. So, what are the forces. So, the forces on these are the buoyancy force which is upward.

Then there is the weight, it is wait which is downward and it has a you see what is happing

here, is that again the pressure on this side there is actually a the pressure you see here

the liquid is actually flowing through a constriction right.

So, it is velocity is. So, what is going to happen is that there will be drag force. There

will be a force which will be this side. So, this is buoyancy force, there will be force

due to the due to the flow, flow fluid will try to drag it up and there will be a force

on the weight. So, when these will balance out the float will be stationary right correct.

So, now, it turns out so that means, that see, the drag force that is developed must

always be the same that is it is the difference between the buoyancy force and the weight

which are constant for a flow. So, it is the force which is constant, but at different

flow rates to achieve this force, the float must settle at a different position.

So, now for example, this is what it looks like. So, you see that this is the pipe actually

this taper is actually see can you make out the taper, probably you can make out the taper

see here the diameter is less and here the diameter is more. This is the float and there

is a guide rod given. So, that the float does not mover here and there in the within the

tube and the calibration here in this case is made directly on the glass. So, you can

and this is the input port and this the output port. So, this is what it looks like and it

comes in a wide variety of sizes when. So, it could look different ways.

So, this is the principle operation, that the float remain stationary when the weight

for the float is balanced by the buoyancy and the drag force. The annular area between

the float and the vertical tube varies continuously. Actually that is why you must have a taper.

The rotameter would not work if you made a cylindrical tube. Although the taper is very

low to have a large range, but it is varying. So, when the float is in a particular position

for a flow rate the differential pressure varies with this square of the flow rate.

This we have seen this is this is from Bernoulli's principle right. So, the pressure across it

will actually vary will actually vary because in relationship with the flow.

So, therefore, to keep differential pressure constant for some other flow rate, the area

must vary. So, the flow rate is if the flow rates changes basically it depends on the

velocity. So, therefore, if the flow rate changes then that area must also as the flow

rate increases. So, the area must also increase to have a certain velocity because we need

a constant velocity to be reached. So, that the differential pressure develop due to this

velocity can balance between balance the difference between the buoyancy and the weight.

So, therefore, as the float rate increases the area must increase to keep the velocity

constant. So, when does a area increase when the when the bob goes up. So, as the flow

rate increases the bob will now go up up and settle at a higher position. So, therefore,

to keep the differential pressure constant for some other flow rate, the annular area

in between the float and the vertical tube must change. This is the principle of measurement

and the position for the float can be made. Now, if you carefully fabricate, the tube

in such manner that the area varies linearly with position. Then as Q varies A must vary

K, K must track if Q become double A must become double to keep V 1 constant and therefore,

if A becomes double when the height becomes double, then you have linear measurement of

Q with X right. So, you have to make the tube such that the area where is linearly with

height.

So, typically the volume flow rate is given as again in using Bernoulli's formula. In

this case if we do that weight balancing then you find out, this is bit of manipulation

which we can find any standard instrumentation book. It turns out that this AT minus AB,

AB is the area of the bob, AT is the area of the tube at a particular height, CD is

a discharge coefficient, VB is the volume of the bob row B is the density, row F is

the density of the fluid. So, it turns out that, the flow rate is given like this and

if you have... So, you see this part is constant because

if we assume that the fluid density is constant. So, this part is a constant here if you have

AT minus AB is much smaller compared to AT. If this factor you can be neglected it is

actually small. So, then if you assume it to be 1 then what happens is that, you can

have, you have actually Q is proportional to AT minus AB. So, the annular area AB is

the area of the float AT is the area of the tube. So, that. So, AT minus AB is actually.

So, let me draw it here itself. So, this is AT this is AB float. So, this is AT minus

AB, this part, this annular part, this is the area through which the fluid flows out.

So, if the denominator equals 1 and CD is constant then you can have. So, you have proportionality

there that is what is used for measurement.

If you if you vary AT minus AB proportional to X, then you have a measurement Q is equal

to K 1 plus K 2 X. The rotameter is usually accurate and you can see that, here the measurement

is linear with X and you have better range ability than that of the orifice. You are

not measuring pressure drop here. So, there is no square relation, there is a linear relation

and accuracy is not that high for a rotameter, but some it is a very simple instrument nothing

is there just a tube. You can just put in and you will get a reading. So, that is why

it is quite widely used. Sometimes you can have automated float flow detection using

magnetic methods or using optical methods.

Next we have turbine flow meters. These are, here the idea is simple, the idea is that

you put a small turbine within the pipe and the turbine is made, in such a manner we will

see how it is made that as the fluid flows it keeps pushing the blades. So, it keeps

pushing the blade. So, the turbine start rotating and if we analyze the mechanics, then you

will find that the rotational speed because it is done by momentum transfer. So, the linear

momentum of the flow some of it gets transferred to the angular momentum of the turbine.

So, therefore, the flow rate becomes proportional to rotational velocity of the turbine and

this rotational velocity of the turbine must be sense from outside the pipe. The turbine

is placed inside. So, therefore, people use either use optical means where as the blade

rotates some light beam is going to be obstructed or they use a magnetic means, where there

will be magnet and as the as this metallic blades pass. There will be electric pulses

or voltage or current pulses generated. So, you count the pulses then you know at what

speed this turbine is rotating. This is the basic principle of operation and if you see

the cross section area.

You will find that this is the blade. So, you see this is the blade and actually it

is not properly drawn if the blade is like this. So, when the liquid passes it actually

pushes the blade it pushes the blade. So, the turbine rotates right. It actually the

blades are made slightly slant right. So, when they are made slant when the fluid will

pass it will push the blade this. So, that is how it rotates.

If you see the magnetic pickup principle, it is simple that you have a magnet, which

is outside the pipe right. So, you have a pipe here. So, the pipe is inside, the turbine

is inside and the magnet is outside. So, now, as it rotates what will happen is that, this

is an electromagnet. So, the flux lines will pass like this, actually this blades are actually

should must be exaggerated, that is they come actually quite near they should come near

it. So, as you can see that if the blades are facing the magnet then there reluctance

path of this path is iron. So, therefore, the reluctance path is somewhat reduced.

While if this point is facing the magnets then the reluctance of this path is not, it

is still here. So, therefore, more reluctance. So, what happens is that as the wheel rotates

the reluctance of the magnetic circuit periodically varies. As the teeth comes close it become

small as the teeth goes away and the space between the teeth come facing the magnet the

reluctance grows large. You have a certain MMF because you are driving

certain current into this coil. So, the flux also flux is MMF by reluctant by reluctance.

So, therefore, the flux also keeps oscillating. So, when the blades come close the flux increases

because reluctance is lower and vice versa. So, now, if you.

 

So, basically and what is this frequency of oscillation. This frequency of oscillation

is actually n times, that is n times the rotational speed because once the turbine rotates n teeth

will pass at this flux pulsation will go through n cycles. So, actually this flux pulsation

is an n times higher frequency of that of the angular velocity, that is what I should

be realized. So, this phi as if matter of theta is can be expressed as in this term

alpha plus beta cause n theta. So, you see that it varies if the as theta varies from

0 to 2 phi this go through n pulsations this phi.

So, now we can it is a simple matter to calculate what is e, what is the induced EMF in the

coil that is nothing, but we have we actually have a permanent magnet. So, permanent magnet

means the magnetic strength is constant and we have we have put the coil across which

an EMF is induced as flux pulsates. So, that is given by simple d phi d t and it turns

out that this is simple calculates will tell that it is beta n omega sign omega T.

So, what do we see where omega is rotational velocity. So, therefore, what do we get, we

get actually a sine wave if we see the EMF e will get a sine wave whose amplitude will

also vary with omega and will frequency will also varying with omega. So, both are increasing

with omega as we can see here. So, we can for signal conditioning we can either try

to detect the amplitude or try to detect the frequency. So, now this will as we have said

that it turns out that the angular velocity raised again proportional to Q. So, therefore,

the frequency is also proportional to Q and the amplitude is also proportional to Q.

 

So, that is what we do. So, we measure either the frequency or the amplitude. It turns out

that these are to be used mainly in clear fluids, but they can give you quite accurate

readings. Although they cause a permanent head loss and if there are not so rugged and

reliable as you know orifice meters there also more expensive. So, they are typically

you know it can be used in things like you know acids, which are single phase clear fluids

with low viscosity and they are available in various ranges for liquids and gases. This

is a typical picture of thing.

Of such a meter, you can see that this is the magnetic peak off and these are the pipe

sections which you can connect with it and this is meter. So, you have connect the pipe

section the turbine is already put inside it. So, this completes our obstructive flow

meters and we take a quick look at the un-obstructive ones. For example, electromagnetic flow meter.

So, here what we are is let us see the parts we have a pipe. So, there is a pipe this is

a pipe line, the actual flow is through this part. So, what we have created is that we

have created a magnetic field these are coils. These are coil assemblies, these two. So,

we have created a created a magnetic field by sending through this coils. These are actually

schematic connections, when there is just shown that this is they actually connected

to 2 sources. Now, if you have. So, here is a magnetic field

and if a fluid with some conductivity that is some free charges. If it flows past it

then what will happen is that is that by the Hall effect we will generate some voltage

across the electrodes. So, Hall effect says that if you have a magnetic field and if you

have conductor conducting current through it, then across the 2 sides perpendicular

you will actually develop some voltage and that is. So, it is like you know e is equal

to BLV kind of thing. So, these coils will cut the flux and there

will be some EMF generated. So, it is this EMF which is actually sensed using these 2

electrodes and this is the signal that you are going to get and the magnitude is given

by something like BLV. So, B is constant B is constant by excitation, and L is the L

is the length which is which in this case is actually the diameter. So, it so the EMF

is actually proportional to the velocity or the volume flow rate.

 

So, this is the simple method. There are some measurement issues involved in the sense that

you should use the excitation of this V and some bit of signal processing is required

because there are some you know you can have thermoelectric potentials etcetera. So, you

can have drift if you use DC. So, pure DC should not be used and some you can use fifty

hertz DC also, but fifty hertz DC has some fifty hertz interference problem sometimes.

So, you can use where we have current excitation and then generate. Take many samples and then

average. So, any offset will go away. So, such simple signal processing is possible

after that. So, you see that this is completely from outside the pipe.

Similarly, we have we have an ultrasonic, this is not a transit time flow meter this

is actually, this is wrong title that we have got, this is a Doppler flow meter here is

a. So, what we are doing is, this is use for particulate. So, you see in the fluid we have

some solid suspended particles right. So, you have an ultrasonic transmitter and you

have an ultrasonic receiver. So, at this transmitter is transmitting an ultrasonic pulse which

is sound pulse in this direction. So, what will happen is that at frequency

F. So, it turns out that by Doppler effect, the frequency that will appear to, suppose

and it will come to the, it will hit some particulate matters and this particulate matters

will actually scatter it. When they scatter it some of that scattering will get back to

the receiver. So, we are going to transmit it is going to be scattered by the various

particles. Some of that is scattering we are going to receive using another piezoelectric

twister and from. So, now, we are going to measure the frequency

that with which we transmitted and the frequency which we receive. Now, it terms out that if

we transmit with frequency F, then to this scattering particles this is by Doppler effect.

This appears the frequency will be proportional to the relative velocities. So, what is the

relative velocity, while it is going this way, suppose the velocity is this way. So,

it has a component this has a velocity component this way and what is that velocity component,

that velocity component is V cos theta, this is theta.

So, the relative velocity is C plus V cos, this is the relative velocity of sound with

respect to this particle. So, it will now see a corresponding frequency F double dashed

F dashed. Now, so it will when I see a frequency F dash it will also scatter that frequency

back, but that frequency will now appear to the receiver of a certain other frequency

which is F double dashed. What is the relative velocity between when it is transmitting back,

the relative velocity is actually C minus V cos theta. So, therefore, what will appear,

this receiver will now see a totally different frequency because the relative velocities

in the 2 direction are different. So, now if you see because of these suspended solids.

So, if you now see the…

So, if you see the, I am sorry this I do not know it is creating a bit of problem. This

diagram is to be ignored. So, if you see the frequency difference. If you see frequency

difference between these 2, then you will find that the frequency difference will actually

with this F is constant, this is the transmission frequency, theta is also constant depends

on the angle which we have put the transmitter in the receivers, C is constant velocity of

sound in the medium. So, therefore, it will be this frequency difference

is going to the proportional to the velocity which is again volume flow rate. So, this

is the principal of Doppler flow measurement, then we also have, actually that is a slide

mix up about transparence is here. Let me tell you that this is now in this slide let

us ignore this. You can also measure by having what is known as transit time flow meter in

a transit time flow meter, what you do is here you have 1 here ,you have 1 piezoelectric

crystal here you have another one. So, you transmit from here and receive here

and you measure the time. When you see you are you are corrected to electronic. So, at

the same precision time you transmit a sound pulse and count the time after which you receive it.

 

So, then what is the transit time T, T 1 will be given by the relative velocity of

sound in this direction, which is actually C plus V cos theta. If you see similarly,

if you transmit in the other direction then you will get C minus V cos theta.

So, therefore, the transit times are going to be different in the 2 cases. If you measure

delta T, you will again find that is the difference between the transit times in the 2 directions,

then you will again find that is proportional to velocity. So, this is the principal of

measurements in transit time flow measurement. So, we are going a little fast now. So, with

the…

So, the last we will actually the last one is correlation flow meter. I will just explain

the basic idea without going into details because there is lack of time. So, the idea

is that if you want to this is typically used in situations where you have 2 phase flow

that is you have bubbles in a gas or you have sand in air or you have line dust in air.

You want to measure the measure the volume flow rate.

So, now what happens is that it is rather difficult to measure these things using for

example, orifice meters are not good for having this kind of you know, gas bubbles right.

So, what will happen is that, what you do there is that you measure the flow at 2 different

points. You measure some properties for example, you can measure capacitance or you can measure

charge collected at these 2 points. If the fluid flowing then actually this because of

because the because the sands suppose the sand is being carried through air.

So, the sand particle will actually form clouds when they are when they are passing through

air. So, each cloud will have a signature, will have a signature kind of signals. So,

then you first obtain the signature in terms of capacitance or in terms of charge from

this point. If and then you obtain the signature from another point. Then you try to find out

the time difference between these signatures by some numerical technique which is called

cross correlation. So, once you can find this time, then you know that it travels this distance

over this time and therefore, you know the velocity. So, these you know some kind of

what is known inferential or numerical techniques. So, I am going to skip this because we do

not have time.

So, you can put electrodes on the pipe and from this electrode, for example, in this

case it will collect charge. So, you collect charge from this point and you collect charge

from this point and then you correlate these 2 charges. That way you can measure the velocity.

So, we are going to skip this.

We finally, come to the points to ponder which is. So, there are several questions which

you can think of for example, can you think of two condition for flow measurement by differential

pressure flow meters right. So, think of two conditions under which, they are applicable.

One of them is that the flow must be turbulent, it is not applicable for laminar flows. So,

can you think of another point. What happens if the float in the rotameter

floats in the fluid. Obviously, you are not going to get a ready why. So, the float must

be generally heavier than the float density. What is the preferred signal processing method

for turbine meters and why. So, you have two choices, one is amplitude measurement another

is frequency measurement, which one do you prefer and why do you prefer it. When is an

ultrasonic flow meter appropriate. So, when should you use an ultrasonic flow meter, other

than an obstruction flow meter. When can you use a cross correlation flow meter. And finally,

when should you use an electromagnetic flow meter. These flow meters are use useful under

certain conditions. So, which is apprehend from the principles. So, study the principle

and try to find that condition. So, that is all for today.

Thank you very much, see you in the next lesson.