Lecture -13 Flow meter -II
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Welcome to the lesson 13 of Industrial Instrumentation.
We will continue with the flowmeters. So, in the lesson 12 also we have
seen the flowmeters, because as I told you earlier, that the flow, the, the variety of
the flow, I mean the variety of the instruments for
measuring the process parameters like flow is, are the huge in number. So, what we have
to do? We have to cover lot of sensors; unlike the temperatures and pressure level, very
few number of sensors are available. But, due to the varieties and the environment
conditions, the number of flowmeters are quite large in number. So, this lesson 13 also is
for the flowmeter. So, we have given the name Flowmeter II. You see here, the contents of this lesson
is Pitot tube, which is extensively used for, not
only for the flow measurement, also for the velocity measurements. If I can install and
it is basically mostly used for the, not for
the liquid, but for the gas. Even for high speed
vehicles also I can use this for measurement of the speed of the vehicles by using the
1 Pitot tube. One of the common, I mean applications
of the Pitot tube is the aircraft, the speed measurements, where in high altitude,
so the, there is a differential pressure and another important thing this Pitot tube as
well as, as well as the elbow meter which is
next, you will find basically depends on the differential pressure measurements. We have seen that differential pressure, differential
pressure measurement technique is utilized in the case of orifice meter and
Venturi meter. So, in Pitot tube and elbow meter
also, you will see that we will use the same principle. That means there is a differential
pressure and that pressure is calibrated in terms of flow, flow velocity or the volume
flow rate. So, the contents are Pitot tube, elbow
meter, then rotameter is another example, but
rotameter as you know, it is a, it is not the differential, it is not the flowmeter.
It depends on the, based on the differential pressure
measurement, it is basically variable area meter.
So, that we will discuss in detail how it works actually and also we will solve one
problem on the Venturi meter. So, the differential pressure meters, so either Venturi or
orifice, so in this particular lesson we will consider one problem on the Venturi meter,
right? 2 So, at the end of this lesson, the viewer
will know the principle of working of Pitot tube,
advantages and disadvantages of elbow meter, also its principles also we learn in this
process. So, principle is common. Principle of working of Pitot tube, I mean elbow meter,
your rotameters, everything will be, all will be discussed here. But also we will discuss
advantage and disadvantage of the elbow meter. Also we, we will see that rotameter can
be used as a linear sensor that is a great achievement, because in most of the differential
pressure, in all differential pressure measurement based flowmeter, you will find its
relation between the flow and the differential pressure is non linear, so which creates a
problem. So, we need some other circuitry to linearize, which is not necessary in the
case of rotameter. Though it is usually used for
very short range of flow measurement, range is not much, right? So, Pitot tube, you see, it is like this.
It measures the velocity at a point in a fluid, right?
That means, it will measure particularly velocity at a point. Unlike the, unlike the orifice
meter and Venturi meter which measures a, over a area, I mean, if you look at the, along
the pipe, if you go along the pipe, so but the Pitot tube basically measures the velocity
at a point, particular point in a fluid, right? 3 So, this is very important that means what
I am saying, here you see if I have, if I take a
white board, that means what I am saying that if I have a pipe, you have seen that in the
case of orifice meter or if I have a, in the case of Venturi meter we have seen, so it
is average the velocity at the whole point. So,
it is like this only, it average the velocity. If I
am interested by the Pitot tube, if I am interested to measure the velocity, suppose at this
point of the fluid or at this point of the fluid or this point of the fluid or this of
the fluid that is not possible by Venturi or orifice
meter, right? But, it is possible by the Pitot tube and
another important thing is it is an open channel meter, it is not closed. So, you can use it
as a closed channel meter, but you can use it as
well as open channel meter. That means I have a tube what we actually do we will
discuss in details. So, this tube is installed inside the pipe. Suppose this is a pipe, so
depending on installation, I can move it little up here in this here or I can move it down.
So, I can, at a particular point I can measure the velocity of the fluid, right, like where
this is also an open channel meter, but we can use it as a closed channel meter also. 4 It measures the velocity at a point in a fluid.
It is an open channel meter that I told you. It
is suitable for investigation around an aerofoil in a wind tunnel or the measurement of
velocity profile in a pipe, prior to the installation of the permanent flowmeter.
Sometimes, some estimation is necessary. That means how much is the flow, I mean
before I mean installing your flowmeters like Venturi meters or orifice meter or … tube
and flow nozzles, so we need some estimation. So, in that type of situation, Pitot tubes
can be easily inserted and take the measurement, because you know that in the case of
orifice meter, Venturi meter, it is a very cumbersome device, it needs a lot of time
for estimation. This is not, you cannot spend
that much amount of time, neither what will allow to disturb the, the installation. But, by using the Pitot tube you can overcome
that type of difficulties; that I can estimate. As well as I can measure quite accurately
the flow, flow velocity or flow measurement. You can see, there in the case of Venturi
meter and orifice meter also we are actually measuring the velocity, then we are multiplying
the area of cross section, finding the, finding the total volume flow rate. Here,
we will find the velocity, then with the area, if
you, of the cross session of the pipe if I multiply, obviously you will also get the
volume flow rate. 5 The principle of operation of a Pitot tube
is like this. If a solid body is held stationary in a
pipe in which the fluid is flowing with a velocity, as the fluid in the tube approaches
the body, the fluid particles are decelerated
and until at a point directly in front of the solid
body, the velocity of the fluid is zero, right? What does it mean? Let us take a blank page,
then it will be more clear. 6 See here, so what I am saying, suppose a fluid,
I have a pipe and liquid is flowing through this, right? Now, I put an object,
suppose like this one, a solid object, then what
will happen? See, here the liquid will flow; flow in this direction, flow in this direction,
all this direction? What will happen to the flow which is coming to this, hitting this
portion? It is coming to rest at that position. Supposed to be the, if it is raised the pressure
will be very high compared to the pressure of the fluid here, right? So, that means the
liquid which is coming to the rest in contact, so liquid, so what will happen? The fluid
will be decelerated. When it is approaching this solid body, suppose
if I take, this is the solid body, fluid, the
fluid will be decelerated. So, at this point, it will be total stop, totally stopped. So,
the velocity of the liquid at this point will
be zero exactly, identically zero and the velocity of
the fluid, suppose this is V, so this liquid is also flowing with the velocity V, then
it is flowing out. Again it is flowing out, right?
But, whenever the fluid is flowing here, so obviously the, just in front of this one,
if we look at here, at this position the fluid will
come to rest. Using this principle actually people developed the Pitot tube, right? Just take the, so again I will repeat. 7 If a solid body is held stationary in a pipe
in which the fluid is flowing with a velocity, as
the velocity in the tube approaches body, the fluid, that solid body, obviously this
is the pipe and the solid body, the fluid particles
are decelerated until at a point directly in front
of the solid body, the velocity of the fluid is zero, velocity of the fluid is zero, right?
So, accompanying the deceleration is an increase
in pressure, right? That means whenever I told you earlier also that means what will
happen? That means I have a solid body here. Again,
I am telling, so liquid is coming and hitting here, so velocity at this point is zero, right,
velocity V, it is flowing, right? This is a pipe,
pipe is flowing, so what will happen here? I will take a new page. 8 So, like this one, it is flowing like this,
right? So, what will happen, you see here. So, I
have a solid body, so which is coming and coming to …. So, the pressure at that point
will be high compared to the or highest I should say, compared to the fluid, I mean
static pressure here, right? So, accompanying the
deceleration is an increase in pressure. 9 So, it is the process of converting the velocity
head to an additional static head, right? We
are calling it head, because it is a, basically if we look at, it is basically we are, we
are writing the equations in terms of the liquid
head, right? That is the reason we have to, because I mean if the pressure is, as you
know, hdg if you divide by density and the acceleration due to gravity, so obviously
it can be expressed in terms of only the height. That means assume the liquid, the pressure
is usually defined by this one, is not it? P equal to height into d into g. So if you
express it, if you multiply it, I mean divide by d
and g, obviously I will get a, if I write the Bernoulli’s equation only in the, sorry,
only in the case of, in the terms of height, so it
will be all in, I mean head. So, that is the reason
sometimes we call it head. 10 It is a process of converting the velocity
head to an additional static head, right, because
additional static head is coming, velocity is becoming zero, the pressure is increasing,
so that head is also increasing. The velocity
of the fluid can be found by measuring the differential pressure. Again, the same principle,
because this also depends on the, basically the principle of work depends on
the measurement of differential pressure. At
the impact hole or stagnation point, the fluid is brought to rest and this point therefore
has no kinetic energy, right? If the velocity
is zero, obviously that what is the kinetic energy?
Half MB square; if the velocity is zero, the kinetic energy also will be zero, right? 11 So, here you see the, a Pitot tube. Look at
very carefully. Right? So you see, this is the
Pitot tube, our liquid is flowing. It is installed in a pipe; I am not showing the pipe, so
pipe will be there, right, pipe will be there, so and inside, the pipe it is going. If I
take a different colour pen, so it is installed in
a pipe. Please note, always installed in a pipe,
right? So, this impact hole should be always in a direction opposite to the flow. Flow
is, flow in this direction, so directly it is
impacting here. So, it is to be installed in a direction
where this that means I am saying like this one. If I can see the camera here like this
one, you see the, this is Pitot tube suppose, right?
So, this is our static hole, right, impact hole
or stagnation point I should say, so what will happen here? See, the liquid is flowing
here and hitting this position, right and liquid
is flowing over this one. So, there is a hole on
this, on this side. This side there is a hole. The fluid is flowing in this direction and
it is going out. So, liquid is, I mean this, it
is impacting here, so there is a point where the
velocity of the fluid will be zero. If we consider this as solid body, so velocity of
the fluid at this point will be zero, kinetic energy
will be also zero. But, there is a pressure …..
inside the pipe also. That pressure we are calling it static pressure, right? 12 And this pressure, the pressure at this one
will be the stagnation pressure so obviously the
stagnation pressure see the velocity is zero will be much higher than the static pressure
right so this static holes usually can be collected
as it happens in the case of Venturi meters this static holes can be this static pressure
can be sense by physio meter rinse that means it is averaging the ah pressures and this
impact hole stagnation pressure we can be measured by if i just take out one hole here
and take it out so these two will give you differential pressures
right this minus this this pressure P one minus P two will give you the differential
pressure as a flow velocity increases P one will
increase obviously delta P will increase what you have to see the delta P differential
pressure so this is equal to P one minus P two right
so this P one minus P two so this is {stag} this pressure differential pressure
so this is our stagnation pressure so the {vel} of velocity increases P one will
be also increase so delta P also will increase right so this
way so this by measuring this differential pressure so i can calibrate this in terms
of flow velocity right and if i know the area of
cross sections of the tube where it is installed that Pitot tube i can measure the volume
flow rate 13 or if i installed on a some moving body this
entire Pitot tube is install and a moving body
is like an aircraft obviously what will happen you know that um having measure the
aircraft velocity velocity of any vehicles also only thing the
problems we need a flits because if the there is a if there is
a this hole is the this is small hole you can see here if this hole is clot by some
particles or dust so that will give us error in reading right
that is happened actually in the case of aircraft as you know when it goes to {lar} i mean huge
height so as you know the goings and all this things
they are going very height and around thirty three thousand feet three thirty five thousand
feet at the situation there is a ah ice formations and the stagnation point then what
they do they put a heater coil around this one right
so continuously is melting that ice so there is no question of entiting erroneous reading
so the flow can be calibrated in terms of actually
measuring the differential pressures i can measure the flow velocity or the velocity
of the {vehi} vehicles and aircraft on which it is installed lets go back theory
again right now this is the you see the this relation
between the velocity of a air passes the differential pressure right x axis we have
plotted the velocity of air and y axis we have
plotted the differential pressure delta P 14 which is in Pascal and velocity air is in
meter per second and density of one point two kg
per meter cube and differential pressure versus velocity of air measured by Pitot tube
right so this is the figure as you can see we will
give some calculation is non linear in nature you can see okay so this creates a problem both the kinetic
energy and the pressure energy we will present at the static holes because fluid is moving
at those positions right assuming energy conservation and no frictional
loss and no heat loss obviously we can write P one by rho zero gz one P two by rho
plus V two square by two into gz two you can look at very carefully all the units
of this one will be in you see here that reducing if i take meters or seconds square
right so g will be ah z will be in meter so it will be meter per second whole square
this one this also will be meter per second square right P two it can be as a pressure
so Newton per meter square right so if you ah if
you simplify this one suppose this Newton’s in kg P is in Newton right
so it means ah it means that ah P is in Newton means signifying that is a kg meter per
second square so if you divide by rho that is kg per meter cube again it will be so this
P by rho will find will be in meter per second
square right so it will be like this right so all the units
are same units of which item will be same because this is the there is no velocity of
the ah velocity at the stagnation this is a 15 stagnation part the Bernoulli’s equation
is applied at the stagnation point this is the
Bernoulli’s equations apply at any other point of fluid right
here P one is a stagnation pressure P two is the static pressures the z one
is the elevation of the static i mean stagnation point and z two is the elevation of the your
static point right if we have this slide we can go to the next slide so where z one z two are the elevations of
the holes above the datum line and g is the acceleration due to gravity which is nine
nine point eight one meter per second square and if z one equal to z two then we can simply
write v equal to two P one minus P two rho so this equation number two
now whether the rho varies let us look at that now from equation two we can write delta
P equal to so this is delta P delta P equal
to ah v square into rho divided by two isn’t it
differential pressure equaled half of rho v square 16 where delta is a differential pressure P one
minus P two so v obviously i can see here you
can see this most important equation count for all differential pressure from it you
can see this is v equal to v proportional to root
over delta P right so delta P if you calibrates in terms of v
obviously there is non linear relationship right
so for air at twenty degree centigrade and pressure P two of ten to the power of
five Pascal that is static pressures and i am talking about with rho equal to one point
two kg per meter cubed gives delta P equal to
point six v square thus at v equal to ten meter per second we
have delta P equal to {sixteen} sixty Pascal and delta P by P two equal to
six into ten to power minus four 17 and at v equal to hundred meter per second
delta P equal to six into ten to the power three
Pascal’s and delta P by P two into six into ten to the power minus two
what does it mean it means the when the flow velocity ah the this the low value of delta
P by P two ratio means that for the velocity
less than hundred meter per second hundred meter per second is quite fast and quite high
speed right that mean the difference it’s a extremely
high speed hundred meter per second right the
difference in density between the air at the stagnation point and static holes is negligible
right the error introduced by considering the incompressible
fluid is within one percent right now differential pressure transmitter is a
special type of {difren} differential pressure transmitters is necessary for ah
particularly in this case due to low differential pressure because if the ah if the fluid {velo}
fluid is actually air gas so the differential pressure also will be
less because ah as you know the differential pressure also depends on the density of the
fluid right so the air as a lesser density so due
to low differential pressure so the your differential pressure also will be low
so we need some more sensitive differential pressure sensing element because this
differential pressure first you will sense and before converting to the electrical domain
that is four to twenty milli ampere of current domain i need some ah i need some high ah
i {nee} i need some higher pressure higher differential pressures right 18 so i need some more sensitive ah i mean this
type of system which will convert this ah your differential pressure to some other change
like capacity change or any other change displacement change that can be converted
in the electrical current domain of four to twenty milli ampere so it gives a four to twenty that voltage
LVDT unbalanced voltage that means the secondary voltage which is in positions can
converted easily to the current domain of four
to twenty milli ampere output for differential pressure
a scheme of velocity you see everywhere its likes this one you have seen that in the case
of this LVDT having the case of this flow measurement also what is a minimum flow that
must be described right what is maximum flow that also in the process it is fixed
so what will do will accordingly we will fix of four to twenty milli amperes so the
calibration is most important all the calibers so for the minimum flow velocity we must
get four milli ampere of current for maximum flow velocity we must get it twenty milli
ampere of current accordingly our electronic circuit that converter
which will convert because always you know that ah there are many simple circuits
are available for to convert this type of signals voltage to current signals right
so depending on the whether you suppose have a zero ten volt accordingly for zero volt
i want four milli ampere for ten volt i want
twenty milli ampere 19 so that type of things can easily made right
so similarly here also instead of suppose zero
volt i have a input voltage output sign getting suppose ah ah zero two five
volt no problem see if it is zero to five volt accordingly
i can set my circuit some reference voltage raised
terms by which i can make four to twenty milli ampere of current right now scheme of
velocity measurement is shown in figure three you see here that you can see here the input
is velocity v right i have a Pitot tube i am
getting into differential pressure of delta P so i have DP transmitter so DP transmitter
is basically here not capacitive it is a heavy
duty based in four to twenty milli ampere of
current is coming we have data acquisition system
and we have PC data acquisition system is obviously it will convert this current to
the voltage domain then it is digitizing it before
we giving feeding to the {p} PC where i can record the the flow velocity and
if i have to take some action that means i have to feed back suppose this PC output through
that data acquisition card again can go back to the control one to reduce the flow
ultimately the what is a use of this Pitot tube and all this things i have to set some
already the pre prescribed the this much of oxygen
will flow this much of hydrogen will flow in
the pipe so to set that so i have to measure this i mean velocity then if feed it back
to the some control valve 20 so that by which it will either open or close
to keep to being flow velocity to the prescribed level right now elbow meter ah with this ah elbow meter
is a different kinds of system it is actually usually used in a huge installation of the
pipe is not is not suitable for the small bending
of pipe so for the large bending of the pipe now in all the cases except Pitot tube Pitot
tube usually used for the gas you find that ah
you will find that the there is a large differential pressure and and and there is a loss
permanent loss have the permanent loss in the both in the case {or} orifice
meter or Venturi meter in the case of orifice meter we have seen
that this loss is more in the case of Venturi meter permanent loss is more in the case of
Venturi meter we have seen the permanent loss is less
now aerometer is an instrument its also based on the differential pressure measurement
but that permanent pressure loss is not there but in fact it is there in fact not in that
way because whenever there is a pipe bending there is a pressure loss as you now head loss
is their so utilizing that principles without having any addition loss for the installation
of the installation of the ah meter we can have a elbow meter 21 let us look at what is that the orifice meter
flow nozzle dall tube and Venturi meter we have seen cause permanent pressure loss in
the system this will create permanent pressure loss in the system right all this flow nozzle
dall tube less or more so obviously it will make some permanent pressure loss
we have seen that in the case of Venturi meter there is a i mean there are different types
Venturi but long short in the long we are much {be} better pressure recovery
the short we have less pressure recovery in the case of orifice meter pressure recovery
is watts right aerometer does not introduce any
additional losses in the system send it simply replaces and existing elbow or pipe
bending that is being used to change the direction of flow right in a process we will
find the always you need this type of things i
am need some pipe bending somewhere okay because pipe cannot all pipe cannot be straight
in the process so you find a some there is pipe bending so in that bending will install
that meter so that no additional loss will be there so
aerometer does not introduce the any additional losses in the system since its
simply replaces and existing elbow or pipe bending that is being used to change the direction
of flow right you see here the elbow meters we have it looks
like you see that i have this is a this a ah
section of pipe bending i have shown here you see this is a section of pipe bending
you 22 can see here this is a section of pipe bending
right that means there is a pipe here there is
a pipe here the continuous pipe and there is pipe going also here in this direction
right so just that pipe bending at the {a} at the
pipe bending i have installed this elbow meter fluid is flowing through a velocity
v and it is coming out going out through this velocity and there is a two only two
pressure tapings there one will be inside the pipe
another will be {ins} outside the pipe you see what will happen the liquid which
is flowing through this {pi} outer side of the pipe it will must faster velocity
than the pipe which is the liquid is flowing through the inside this one right it is usually
increases in this direction it is maximum here and by {min} velocity is
maximum here in this direction and minimum in this {dire} here every where
the flow velocity if you take any point to flow velocity suppose to be same
right but here what will happen the liquid which is flowing very near to the pipe bending
it has much higher lower flow velocity and here we have a higher flow velocity according
to the {bondis} Bernoulli’s theorem obviously what will happen the pressure
to this one will be on the liquid side excuse me liquid i mean will be much
higher compare to the pressure because here the flow velocity will be flow
velocity will be higher right so we have ah datum point Zi and Zo from the datum level
we have taken the height of the pressure tap this is the ah i mean inside the {paperpe}
pressure tap this is outside pressure tap
this is our basic principal in the elbow meter so what the advantage that means you see
that i am not putting any restrictions inside the pipe like orifice or Venturi clear 23 so velocity pressure and elevation above the
datum level for pressure taps on the inside and outside surfaces of a ninety degree elbow
can be related by the expression is that shape is ninety any bending in a industrial
process is ninety degree that is the reason we call it ninety degree
elbow can be related by the reexpression Ck equal to Ck multiplied by v square by two
g P naught by rho g plus Z naught minus Pi by
rho g minus Zi equal to this equation number three right where Ck is the co efficient that depends
on the of the elbow that means shape and size of the elbow a normal of Ck
range from one point three to three point two
units you see here if i go back 24 so Ck v square by two g Ck v square by two
g P naught by rho g Zo Pi rho g so all this units let us look at P is a Newton per meter
square rho is kg per meter cube and g is meter per second square
so all the units all the heads are in meter you can look at so P by rho g is in meter
and Z is meter so all are in coming in meter right so volume flow rate will be expressed as Q
equal to Av A root over Ck two g P naught by rho g plus Z naught minus
Pi by rho g minus Zi C into A we have combined ah instead of writing A and root
over Ck we write C into A two g P naught by rho g plus Z naught minus P naught up and
rho g minus Zi equation number four right where A is the this should be where please
note where A is the area of cross section of
pipe in meter square 25 the value of C ranges from point five six
to point eight eight and the primary advantage of the elbow meter is the savings of {ex}
extra pumping cost for the range installation that is a ah good amount of saving
right so the primary disadvantage is that of each
meter must be calibrated on the site its very difficult to i mean find the flow coefficients
as we know there is value of this C ranges from here all has given the range
so we have to install it depends on the slight pipe bending is not exactly ninety degree
something else may happen suppose it is {exa} internal cross section exactly
not in circular in shape so obviously everything will ah change the
installation change the calibration constants or
the your the {da} discharge co efficient C right a flow co efficient C so that
creates the problem so each and every installation that is um
true for even for {al} almost all the installations right though we can suppose
ah we have a thermo we can calibrated we can calibrate in the
laboratory but it’s better to install {inst} calibrate at the site itself
the primary disadvantage is that each meter must be calibrated on the site right so the
low operating cost can usually justify the calibration
cost the low operating cost and usually justify the calibration cost 26 the elbow meter again the that restrictions
the upstream flow restrictions and the downstream flow restrictions that means obstructions
that means any pipe bending this that ah will be there so that is rather restriction
is there which we had previously in the case of orifice and Venturi
the elbow meter requires a minimum of twenty to thirty pipe diameters of unobstructed
upstream flow to reduce the turbulence and swirl for accurate measurement otherwise the
flow straightners ah are to be installed in to stabilize the flow as it is used in the
case of orifice meter
it’s a bundle of tubes all held by insert and put inside the pipe so the liquid will
be i mean so it will eliminate on the turbulence or
reduce the turbulence and where swirl right 27 now rotameter is ah slightly different ah
um it’s a ah meter it basically depends on the ah
ah is a variable area flow meter first of all so with this we are finishing this differential
pressure meters we are starting now rotameters rotameter you see the basic principle is widely
used for meter for flow rate indications it is not used for transmitting instruments or
rather so i mean {monite} it’s basically monitoring instrument
but you will find this meter is extensively used for many ah crucial applications or vital
applications like biomedical applications also and also in the process we will find
these are in plenty right
but basically it is a so far if the ah if the indicating instrument is concerned i think
rotameter as the only choice if we look at the flow meters we have a several flow meters
transmitting facilities and all these things but if i want to make a simple ah i mean indicating
type of instrument or monitoring type of instrument rotameter is the only choice
please note that the meter consists of a float or bob bob is
typically called in the industry people call it
bob i don’t know why anyway ah with in a vertical or transparent tube tapered to an
increasing cross sectional area at the outlet it must be tapered okay
if its ah if does not tapered that is not a rotameter so the meter consists i will repeat
the meter consist of a float or bob typically
called by the engineer in process within a vertical
transparent tube tapered to an increasing cross sectional area at the outlet right 28 the fluid entering through the bottom passes
over the float which is free to move only in
the vertical directions the float can move only in the vertical directions right that
is a problem rotameter always use to be install
in the vertical direction right rotameter is always installed in the upright
positions or in vertical directions when the fluid is flowing through the meter the three
forces are acting on the bob these are let us
look at the rotameter now 29 you see this is our rotameters right i have
a can i take yes see there is flow in the liquid is
flow in this directions and liquid is flowing out this directions so it is to be always
install in this directions vertical direction right
there is a graduated square rotameter is {com} accompanied by graduate {sc}
you see this tapering is so small that it is very difficult to if you look at the
rotameters it’s like a very difficult it’s a usually it size like this pen most of the
rotameter we find
it’s like this pen the size is very small it’s not that very huge in size you will
find this size right and it is slowly increased in taper
angle is slowly so bottom it is a smaller angle included angle
so it is slowly increasing right so that means it is increasing here slowly it is increasing
in this direction but this tapering is so small that is with
the naked eye it is very difficult to visualize because these rotameter since it is made of
hot i mean ah glass or i mean strong glass what they do is you find its puts on a casing
also the back side it is getting only some front side you can see right
that you have seen in the case of the in the our first lesson one we have shown some
rotameter so liquid is coming in this direction that is through pipe it is coming in this
direction it is going up then it is moving in this direction
again i will tell liquid is flowing in this direction it is going inside the pipe inside
the rotameter liquid is flowing through this then
it is going out right and the float is moving inside the pipe float can only move in this
{di} vertical directions right float can when the flow increases the float
will move like this and when the flow decreases float will come down here and it
will totally fit the inside diameter of the pipe
float is designed like that it will fit the inside diameter of the pipe right
there are different shape of the float that we will discuss later on so three forces
you see the three forces are acting on the rotameter what are those forces weight of
the system okay mass of the system buoyancy force
and drag force now weight of the system that will act down
word and buoyancy and the drag force will act up ward right so this FW will always balanced
by FD and FB then FW equal to FB plus FD that is always so rotameter you can
see this basically in auto balancing system 30 because you see is FW and FB will remain constant
because that is the weight and the buoyancy of a {liqu} the liquid is same if
the liquid is same that means same type of liquid is flowing through the pipe
it does not matter what is the velocity density will remains same
if the density is remains same density of the fluid remains same here buoyancy force
is also will remains same and since we are not
changing the bob that FW also will remains same so FB plus FW will be equal to FD then
FD also should remain same that is the main main interesting point in
rotameters rotameter is a basically when it is auto balancing systems if we look at
its very interesting part this is a auto balancing systems right let us look at that principle of operations
how it works for a given flow rate the float remains stationary when the weight of the
float is balanced by the buoyancy and the drag
force buoyancy and drag force will act up ward because
flow of the liquid is always from the lower to like flow of the liquid is always
like this one that means i have a rotameter here
so flow of the liquid is always in this direction right {buo} buoyancy and the
drag force so the float will this will act down ward FB that’s we have seen already
FB weight and FD and FB like this one 31 it is a auto balancing system that’s you
must note how the why i am calling it auto balancing system it will be create from this
subsequent points the annular area between the float and the vertical tube varies continuously
with the vertical displacements of the float or bob how this annular area is changing
means yes obviously it will change you see look at let we take a white page you
see rotameter is looks like this let me take a
different color pen um let me take another one so we have a rotameter here
if i look from the top what will happen it will
look like this you see here the liquid is flowing
through this 32 so what is this annular area as you move bob
what will happen the area cross section if you find leaving this one we increase area
cross section will remain i mean it is always increasing as we go up right as we go up the
area cross section will increasing area cross section of the float is also same
so the annular area that means if you look at
here annular area which is the shaded area will change as the this flow goes up
the means i am telling that the area of annular area at the position of the float
you had think of the {ar} annular area at the position of the float that will
increase if the float goes up even the at the float {go} comes in it is annular
area will be no more so at that time what will happen float will just fit on this one
in that case it will there is no no annular area so at the flows this float goes up annular
area increasing and increasing right this principles we are discussing clear
we are so the annular area between the float and the vertical tube varies continuously
with the vertical displacement of the float or bob right for a particular liquid the weight of the
float as i told you the weight of the for a particular
liquid weight of the float is constant buoyancy force is also constant therefore the drag
force is to be maintain as a constant level that for must be constant also for a particular
liquid the weight of the float and the buoyancy force are constant therefore the drag force
is to be maintain at a constant level right 33 since the area of cross section of the float
is constant the pressure drop across it should be
constant since the area of cross section of the float is constant the pressure drop across
it should be constant right this is a key point
now when the float is in particular position for a flow rate the differential pressure
varies with the square of the flow rate clear when
the float in a is in a particular position for a
flow rate the differential pressure varies what is the differential pressure across the
flow across the float differential pressure across the float when the float is in particular
position a flow rate for flow rate the differential pressure varies with the square
of the flow rate right so now therefore to keep this differential
pressure constant for some other flow rates when the differential pressure differential
pressure must be constant otherwise the drag force will not be constant that force must
be constant because it is equal to FW plus FD
FW plus ah sorry i mean ah FW equal to FD plus F buoyancy weight
must be counter balanced by the balance in the drag force so drag force must
be constant so to keeps in the differential pressure is
constant so obviously what will happen the area
of the annular area must change that means the float must move up and down right 34 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 must change means if the differential pressure as the flow increases
differential pressure is constant so to keep that drag force constant what will
happen the flow area must change right right now the variable area is provided by this
vertical tube this variable area as i told in the
earlier when see between the float annular area that’s if it if you doing the tap or
then there is type of thing will not be achieved
so the position of the float can be made essentially linear with the flow rate by making
the area of cross section of the tube vary linearly with the vertical height right considering the incompressible flow the volume
flow rate is expressed as it is expressed as this is the equation Cd equal to At minus
Ab two gV Vb rho b rho f Ab rho f At Ab so let us look at what are those so this is
the flow coefficient or the this such coefficient At is the area of the tube area of cross section
of the tube area of cross section of the float sorry bob or float whatever area of cross
section of the tube area of cross section of the
float area of cross section of the tube this is the volume of the bob okay this is
the density of the material of the bob this is the
density of the fluid this is the area of the bob and this is the density of the fluid okay
we have written all this in the in the all the legends are given in the next slide let
us look at where keys is the volume flow rate in meter
meter cube per second 35 then Cd is the discharge coefficients At is
the area of cross section of the tube in meter square Ab is the area of the cross section
of the float or the bob in meter square Vb is the
volume of the float in meter cube rho b is the density of the float in of material
kg per meter cube rho f is the density of the
flowing fluid in kg per meter cube okay now if you assume that there is no variation
of the discharge coefficient with the float position we assume that discharge coefficient
does not changes with the float position we changes obviously
36 and if we assume that At minus Ab square by
two is much much less than one if i go to the previous slide is more clear okay
i am assuming that the Cd is constant okay and this portion that’s At minus this portions
that means i am talking of this portion this At minus Ab by At whole square is much
much less than one then okay
is At minus Ab less than the equation five can be simplified to Q equal to K At minus
Ab because all that items to be constant is not
a in that equation so the volumetric flow rate
equal to K At minus Ab where K is equal to Cd root over another square
root two g volume of the bob Vb rho v minus rho f upon Ab into rho f right this
is our constant K so now if the cross sectional area of the
vertical tube varies linearly with the float position
with the if we vary the cross section of that i mean tube in such weight varies linearly
with the i mean with the float position then i can write the volume flow rate equal
to Q equal to K one plus K two x okay to constant and x x is the position of the float
right position of the bob right so the rotameter usually has an accurate range
of ten is to one that is better than the square root sensor so that is quite obvious
so it is a square root sensor much better than
the square root sensor 37 square root sensor we have seen that at the
ah um twenty five percent less than twenty five percent of the maximum full skill range
the error is this reading is very much erroneous that is not the case in the case
of rotameter right now shape of the {rotam} so what will see
that ah in the case ah previous we find that that’s we have seen also that and we take
a ah a different color so we have seen that its
tapered like this one okay the float is moving like this one so it’s in a casing okay and
it is graduator scale is there right
so this is liter or we need all liter per second whatever the way you like actually
represented right so this is the float so this is calibrate in the i mean volumetric
flow rate or i mean velocity
so is the volumetric flow rate it is calibrated so whenever by looking at the position of
the bob i can if i look at here i can tell that
the what is the flow velocity right so this is very
important in the case of ah rotameter so it is basically used for ah the basically
used for the monitoring instrument or indicating instrument but not for the in transmission
instrument right but that does not neccesarily mean that’s accuracy is poor accuracy is
quite good in the case of rotameter as i told you i mean you will find that it
is extensively used in the case of anesthesia as
you know that ah when the patient i mean under operation first they put an injection 38 physicians for ah to go the patient under
this say that ah the patient will go some subconscious state right to maintain that
state they must have continuously supply the gas
so that the patient will remain so to how much gas they will put to the patient nose
so that will be the measure by the flowmeter that
the rotameter and there are the float ah ah let
me go back again i am sorry shape of the rotameter you will find ah that ah the float is actually they are
using some light heavy plastic short of thing so by
looking at the position of the float i can tell how much gas is i am giving to the patient
that because this very important those who who are the anesthesia for the actually
looking at and determining the regulating the valve there controlling the
how much liquid is flowing how much fluid is
going to the patient right now floats with sharp edges are less sensitive
to fluid viscosity that changes with temperature right so the ah you find that’s
because viscosity of the liquid as you know the
changes with temperature right so the but if i make the float the sharp edges that will
almost independent to viscosity right vertical tube of the rotameter is made of
glass to make it a monitoring instrument rotameters are used in applications so the
accuracy is not of prime concern but it’s not
that in accurate also otherwise it cannot be used in biometric application 39 such like very crucial when the because if
you give more gas ah to the patients we patient will die and if you i mean ah and if you reduce
this supply of gas to the patient so what will happen patient will come out
of the subconscious state i mean physicians cannot operate so till the operation is complete
the patients will be on the that state now here now we will solve one problems on
the Venturi meter you see here now problem looks like this a Venturi meter is to be used to measure the
flow rate of water in a pipe of diameter D will be point two meter the maximum flow rate
is two one three six meter cube per minute Venturis with throat diameters of point
one zero meter point one two meter and point one four meters are available
choose the most suitable Venturi meter assuming the differential pressure at maximum
flow is nine one eight kg per meter cube 40 and calculate the accurate value of the differential
pressure developed across the chosen Venturi at maximum flow rate right this is
our now we are given some ah chart also yes it tells for orifice plate this is beta
equal to ah we have seen that some chart for Reynolds numbers how much the ah flow coefficient
changes 41 so table for Venturi also we are given this
is a pipe and throat diameters for the different Reynolds numbers how the discharge coefficient
changes okay that is we have given these are tables are
necessarily for solving the problems of the Venturi meter or orifice plate meter right
this is another chart we are given last chart we are giving that is the the Reynolds
numbers have the beta changes you know if orifice plate of point zero five mille
{met} ah meter that is a dimensions of the orifice ah so we find that the how much
the Reynolds number changes right so let us solve the problem 42 here you see the problem is like this one
ah here Cd we can see for Cd is equal to point one okay it is not right yeah for point ah
sorry let me take new page so rho equal to one thousand kg per meter
cube so from that if i apply the our Venturi meter formula will find that Q equal
to i am getting three forty meter cube per second
now here i am taking that d ah ah equal to point zero one meter for which Cd is coming
from the chart point nine eight eight okay Venturi meter always you know the flow
coefficients is very high right 43 then we have we can find for d equal to point
one two meter we have calculated from the formula that that Cd will come point nine
eight seven so the Q two the this is a Q one if i assume
the Q two will be equal to ah five zero seven point six meter cube per second right so if we take a new page now for D equal to
point one four meter will find Cd equal to point nine eight five meter point
nine point nine eight five so Q three equal to
equal to seven three seven meter cube per second
so we can see that the point ah the orifice meter with point one zero ah meter diameter
is the {be} best chose right
because that is the most close one and in this case for this type of situations now
in the case ah we can calculate that the delta P
ah max if i apply this again this our main formula
so now will apply this one point two zero that means it will be ah will if i take a
new page it will like this one 44 so it will be three point five six into ten
to the power four point nine eight eight by point
nine six eight you will find so you will put the all other pi twenty five root over two
delta Pg you will find that the delta P max will
be one zero zero six point one kg per meter square right
so this is our equation right so this is so best chose is point one zero meter and delta
P max will be one thousand six point one kg
per meter square this ends the lesson thirteen thank you 45

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