Reynolds Number : Viscosity and Poiseuille flow Video Lecture | Physics for JEE Main & Advanced

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introduce another important term or
another important concept don't as
Reynolds number so what is a Reynolds
number and what is the significance of
Reynolds number let us learn about that
Reynolds number is a dimensionless
number whose value gives an idea whether
the flow would be turbulent or laminar
so now you understand the significance
of Reynolds number we studied long back
that broadly the types of fluid flow is
classified into two types by this
laminar flow or the steady flow and the
other one is the turbulent flow so how
do we know just from data that whether a
flow is a laminar flow or a turbulent
flow because a way both the flows I
defined is something like you need to
observe the motion of the particle right
but if you consider in our real life if
something is supposed to be fluid is
flowing you are not able to visualize
the flow of each of the particles always
right so there has to be some mechanism
or there has to be something with the
help of which we can directly say that
okay if this is this condition is true
then the flow is laminar if this
condition is false the flow is turbulent
so Reynolds number gave us an approach
like that it is basically a number the
number itself will below whether the
flow is
lamina or the florists turbulent it is
generally denoted by an e the subscript
insures our e with the e it shows
Reynolds the expression for Reynolds
number is our E is equal to Rho in V
into T divided by ETA here Rho is a
density of the fluid V is the velocity
of the fluid D is the diameter of the
pipe to which the fluid flows and eta is
the viscosity of the fluid now if we
know all these values we can activate
the value of Reynolds number and we can
find whether the flow is laminar or
turbulent if you see all these four
bearings are something which will be
knowing let us suppose if I tell you
there is a fluid say let us call oil oil
is going through a queue now the tube is
something which you can visualize so we
will know the diameter of Eugene
quite obviously or we can measure the
diameter of the tube we know that oil is
flowing through the tube
so oil is something whose density will
be known to us while there something
which is possibly will be known to us
and sells we see that the oil is flowing
through the tube we should also know
which what philosophy oil is flowing
through the tube so once we know all
these four quantities we can calculate
the value of two Reynolds number and we
can get it be same wherever flow is
laminar or turbulent so how does an
ensemble distinguish between laminar and
turbulent flow it says that if the value
of balance number reaches thousand if
it's valuable thousand the flow is
laminar and once the value of y orn
ensemble is greater than two
percent the flow is turbulent that means
laminar flow is denoted by less than
thousand and third billing flow is
denoted by greater than 2000 if the
value of your notes number is greater
than 2000 it is turbulent if the value
is less than 1000 it is laminar so what
is the binding lives between thousand
and two thousand in that case the flow
is unstable that means it is the flow is
in an intermediate State
the flow has some characteristics of
laminar flow it has some characteristics
of turbulent flow so he cannot classify
the flow as either of them and we say
that the flow is unstable okay so I
don't think there is much complication
in understanding you know its number it
is very simple and straightforward now
we will try to derive another expression
or an alternative expression for
Reynolds number so this expression of
the null somewhere maybe in terms of the
inertial force and the force of
viscosity because he already however we
have already expressed Renault number in
terms of a velocity coefficient of
viscosity and then a diameter of the
tube but now we will derive another
equation in terms of inertial force and
the force of this kazantip
now we have already expressed our we
already know that expression for
Reynolds number is tho into P into D
divided by theta as I already told you
what this will be handy now and not
writing it again
so let us concentrate other variation in
this we will derive that main ensemble
is equal to inertia force divided by the
force of this positive so let us
multiply both the numerator and
denominator
so multiply numerator and denominator by
D so what do you get you get ie is equal
to we'll see this way I'm sorry
you multiply numerator and denominator
if I feel that is velocity so you give
for this parity divided by ETA V so this
we can write it as Rho into v square
divided by ETA into v ID where we did
nothing just we rearranged the terms so
you can write it in this one now now let
us again multiply both the numerator and
denominator by capital K that what is
game it is nothing but area so what do
we get we get an e is equal to 0 into T
Square into a divided by ETA into V
divided by D into a so now what we will
do BBC since we had to prove that ie is
equal to inertial force by troops of
viscosity now we will prove that the
numerator here this is nothing but the
inertial force and the denominator which
we have here is nothing but the force of
this force P so that is what we will
nodes now so now let us see what is
inertial force so when I see inertial
force what is inertial force the force
which we talked about when we talked of
Newton's laws that is for subsequently
mass into acceleration that is the force
by virtue of inertia so now what is mass
mass mass is nothing but density into
volume but we
identity is recognized into volume and
what this acceleration acceleration is
nothing but change in velocity with time
selectors do not velocity by P and
mighty and volume by capital T so this
we can write it as Rho into velocity
into what is volume as we already
discussed volume is Alinea into
displacement so we can write volume as
area in in displacement and what we'll
get is placement stick and save it as
displace you one who is enough if you
just place and divided by time so this
we can write as Rho into T into a if you
displacement Italian taken what is to
say my time taking displacement covered
by time taken is nothing but there are
also people so you can write it as Rho e
square a so what is in actual force
inertial forces who is penny in which is
this numeric so we have proved that the
numerator is in action force now let us
look at the denominator this utilize
this space so let us talk about force of
this person T so what would be the force
of viscosity when I talk of course of
viscosity the coefficient of viscosity
has to come in people we know that
coefficient of viscosity that is kita is
equal to stress that is shearing stress
divided by shearing strain rate now what
is shearing stress it is force per unit
area and what is shear strain rate
streamgages displacement the perfect it
length displacement work it
then one Pony time like a steal
so this week I Drive a task force per
unit area divided by what is
displacement per unit time that is when
or something so you can write it as P by
M so this becomes F into L divided by L
into C so what is this missus if that is
equal to F into L divided by K into Z
they are two what is the force of this
quantity this F denotes the force due to
viscosity so we can say that F is equal
to income a C divided by M so what is
this this is nothing but ETA into T
divided by L what is this end in
represents nothing but the direction of
the two to which the fluid is flowing
and in this case in this definition what
was deep D was nothing but the diameter
of the pipe through which it was coming
so whatever n denotes here is what
denotes here it is just that both are
denoted by different alphabets so here
we gave you type V divided by L into a
so basically this is same as this
denominator so we proved that Reynolds
number is can be expressed as the ratio
of inertial force in the force of
viscosity thank you please visit
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