Terminal velocity - Mechanical Properties of Fluids Video Lecture - Class 11

hello friends this video on the ankle
properties of fluids 528 is brought to
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please make sure that you have washed
all the metals from part 1 to 527 before
going ahead seat 528 now we will
understand another term or terminal
velocity what else terminal velocity so
all this terminal I'm very sure that if
this particular lesson that is
mechanical properties of fluids you are
learning a lot of new terms new laws and
new concepts so it is very important
that you remember each of them in an
ordered way like when I talk of strokes
lower terminal porosity
they all have related to this positive
right so please try to correlate things
as we keep like in Kings in the lesson
so what is terminal velocity it is the
maximum velocity of a body moving
through a viscous fluid as we do as I
told in just now when a body moves to a
viscous fluid the retarding force also
keeps increasing with the velocity of
the body so let us suppose any object
when it moves too obsessed to it if its
velocity is increasing then the
retarding force will also keep
increasing so as pH will come when the
velocity will stop increasing so time in
the velocity is the maximum then or
something that the body can attain when
it moves you a viscous fluid that means
the velocity and on increase above that
particular value so terminal velocity is
attained and the force of resistance of
the medium is equal and opposite to the
force of gravity that is what I told you
just now that means initially the
velocity of the body the increase now as
the velocity will increase the force of
s stands for the retiring
force will also keep invisible so a
spirit come when the force of resistance
will become equal to the force of
gravity after that point the velocity
will not increase any further that means
that was the point when the body again
their maximum positive velocity so the
body against maximum velocity when the
force of resistance becomes equal to the
force of gravity terminal velocity is
generally denoted by V G subscript T
denotes terminal now we will derive an
expression for terminal velocity how do
we mathematically Express terminal
velocity so in order to get an
expression for terminal velocity
we know that terminal velocity is
attained when the lately guiding force
for then the force of resistance becomes
equal to the force due to gravitational
attraction right according to so so what
is the force of resistance that a body
experiences it is six five ETA R P but
it is the coefficient of the specific ad
is the radius of the object or the
sphere and V is the velocity with which
the sphere is moving now what would be
the force due to gravity made a surface
of this is the sphere the gravitational
force would be nothing but the weight of
the sphere that is mg and this would
mean that it adding force so this will
be equal to mg now we can write it as 6
PI ETA T is equal to what is mass we
know that density is equal to mass per
unit volume so we can write mass as
density into volume MGP right now what
would be the density of this sphere if
you see as I told you the medium is
surface
right so when the sphere forged to the
street he'll let us suppose the density
of the sphere is Rho and the density of
the medium to which to us for domestic
one so what would be the net density of
the sphere it would be nothing but 2
minus Sigma when Rho and Sigma are the
densities of the sphere and the william
respectively so we can write it as
density is Rho minus Sigma into C now
what would be the volume of the sphere
why democracy s we are developing but 4
by 3 PI R cube where R is the radius of
the sphere so we can write it as 4 by 3
PI R cube into G and on the left side we
already had six five gives R P so Phi
and Phi will cancel I will get cancel
with one R so we will be left with this
velocity V is equal to Rho my Sigma in
teaching full-time team R square into 1
by 6 into ETA so we can cancel this 2 to
the 4th which is 6 so this can be
written as 2 R square so minus Sigma
into G divided by 9 ETA so this value of
velocity is nothing but terminal
velocity so this is terminal velocity so
this will be our expression for time in
a velocity so here we can write whether
system / velocity is equal to terminal
velocity then source of resistance is
equal to the force due to gravity
gravity so the equated with equation and
we arrived at this explanation for 10
min and the last
now let us look at a problem based on
what European study the problems is
calculate the terminal velocity in air
of an oil drop of radius 2 into 10 to
the power minus 5 meters from the
following data G is equal to 9 point 8
meter per second coefficient of
viscosity of air is 1 point 8 into 10 to
the power minus 5 Pascal second density
of oil is 900 kg per meter cube
the actress top air made neglected keep
this is an oil draw which is falling in
air so this is a super spoil focus : in
this way so we have to calculate the
value of terminal velocity we are given
the radius of the sphere as 2 into 10 to
the power minus 5 meters G is equal to 9
point 8 meter per second square
coefficient of viscosity of care is 1
point 8 into 10 to the power minus 5 as
to the second density or oil that is Rho
is equal to 900 kg per meter cube now if
this is a crust of air is neglected so
when we derive the formula for the
terminal velocity we introduce an
article for Sigma C the Sigma came into
picture due to the after stop here now
up just a VM is neglected so there is no
Sigma so we can write down the
expression for traveler there are also 2
directly or they can be within this
shape the way which will act in downward
order force which will be which will
favour the machine is mg that is due to
the weight of the oil drop and the
regarding force or the force of
resistance will give the upward
direction so timing and there are steam
velocity will approach terminal velocity
when the total pull s still force that
is 6 PI ETA I think according to Stokes
knots with equal to energy now what will
be M mass is nothing but density into
volume versus density and what would be
volume Mumbai
I'm actually picking G so if this is the
specific activity so DT will be equal to
here we can write 6 prime i dt v i will
get cancel this i will get cancelled and
this will become a square so it will be
2 into R square into G 0 divided by 9
meter so now we will put the values
which are given 2 into R is important to
into 10 to the power minus 5 whole
square into G that is 9 point 8 into 0
that is 900 divided by 9 into ETA eta is
1 point 8 into 10 to the power minus 5
if this value comes out to be 4 point 3
6 centimeter per second so this would be
the regular then also T of the volume
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