Bulk modulus - Mechanical Properties of Solids Video Lecture - Class 11

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some study the third type of modulus of
elasticity that is the bulk modulus but
modulus is the ratio of hydraulic stress
to the corresponding hydraulic strain so
now if you see that we have got three
types of modulus of elasticity for the
three corresponding types of stress and
strain so even in the case of bulk
modulus it is generally denoted by
capital B so we can say that B is equal
to minus P divided by Del V by Delta by
V what is this this is nothing but this
is hydraulic stress as I already as we
already mentioned why we were discussing
hydraulic stress that it is nothing but
hydraulic pressure hydraulic stress is
equal to hydraulic pressure in
magnitudes so we can write it as P and
what is hydraulic strength that is the
change in volume divided by volume it is
also known as the volumetric strain now
if you see there is a negative sign here
what does this negative sign indicate
this negative sign shows that an
increase in pressure increase in
pressure results in decrease in volume
so the negative sign shows that an
increase in pressure results in a
decrease in volume the SI unit of bulb
earth modulus is in Newton per meter
square or Pascal because it is force per
unit area so this will be Newton per
meter square because the strain in is
unitless it is observed that bulk
modulus is greater for solids it is the
greatest for solids and then fall
equates and it is the least for gases so
the value of bulk modulus is the great
in solids and it is the least in gases
when we talk of mirth modulars it is
very important to introduce the term
compressibility what is compressibility
as the name suggests what what do you
think of when when I say compressibility
compressibility means to what extent can
you compress a substance whether it is a
solid liquid or gas to what extent can
you compress it so how much compressible
the material means so that is basically
denoted by complication compressibility
compressibility is nothing but the
reciprocal of bulk modulus reciprocal of
bulk modulus is termed as
compressibility it is denoted by small K
and it is given by K is equal to 1 by
bulk modulus that is equal to minus 1 by
P into del tau V by n P so this is the
compressibility so since we saw that
bulk modulus is maximum for solids since
compressibility is that isopropyl of
bulk modulus so compressibility is the
least for solids then for liquids and
then for gases so you can see you can
think of it in real-life water it is
very easy to compressed gases right you
would have seen that it is easier to
compress a gas when compared to a solid
that is because the compressibility of
solid is very less it is very difficult
to compress the solid so that is all
about bulk modulus now let us go ahead
and look at few problems on bulk modulus
here comes the first problem it states
the bulk modulus for water is 2.1 Giga
Pascal calculate the contraction in
volume of 200 milliliter of water when
subjected to a pressure of 2 mega Pascal
so we have to calculate the contraction
in volume that means we have to
calculate the value of Delta V now what
are the values that
in here bulk modulus that is capital D
is given as 2 point 1 Giga Pascal now
what is Giga Pascal 1 Giga Pascal is
equal to 10 to the power 9 Pascal's
so these are basically higher units so
10 to the power 9 Pascal's what else is
given volume of 200 milliliters of water
that means the initial volume V was
hundred milliliter and pressure is given
as 2 mega Pascal so 1 mega Pascal is 10
to the power 6 Pascal's so this will be
2 into 10 to the power 6 Pascal's this
milliliter also we got to convert it
into meter cube we know that 1 meter is
equal to thousand centimeter cube right
we already know this relation so using
this relation so using this we can say
that 1 milliliter is equal to 10 to the
power minus 6 meter 3 now using this
relation we can say that it is 200 into
10 to the power minus 6 meter now using
these even values we can find out the
value of Delta V now we know that from
definition of bulk modulus we know that
bulk modulus is e Inc that is pressure
divided by Delta V by V this is the
modulus so from this we can say that
Delta V is equal to e in V divided by
bulk modulus so we can put the values as
2 in 10 to the power 6 into volume is
200 into 10 to the power minus 6 divided
by bulk
that is 2 point 1 into 10 to the power 9
so this comes out to be 1 point 9 into
10 to the power minus 7 meter cube so
this can be written as zero point one
nine milliliters so this will be the
contraction in volume so we did nothing
listen to use the formula for bulk
modulus and replace their values with
correct units so you should also have
some basic knowledge on the kind of unit
conversion so that you don't get
confused while converting units right so
you should have this basic knowledge on
unit conversion like how how is
gigapascal related to Pascal how is make
up a scale related with Pascal how do
you convert liter to be the cube or what
is the relation between liter and
centimeter cube and things like that now
let us go ahead and look at the second
problem the second problem says the
average depth of Indian Ocean is about
3000 meters calculate the fractional
compression they have V by V of water at
the bottom of the ocean even that the
bulk modulus of water is 2 by 2 into 10
to the power 9 Newton per meter square
if we have to take G as 10 to the 10
meter per second square so what are the
values that is given height is given as
3,000 meter that is the depth of the
Indian Ocean also the density of water
we know that density of water is
thousand kg per meter cube this is a
universal value so you should know all
these values so we have to calculate the
fractional compression that is Delta V
by V is what we need to calculate now we
know that bulk modulus is equal to
hydraulic stress which is nothing but
pressure divided by the hydraulic strain
that is Delta V by V so what we have to
calculate we have to calculate Delta V
by V
so this will be equal to pressure
divided by bulk modulus so if we know
the value of pressure if we can
calculate the value of pressure since
both modulus of any material bulk
modulus of water is already given so if
we can calculate the value of this
pressure we can get the value of Delta V
by V so how can we calculate pressure at
a certain height pressure at any certain
height is given by H ro G right this is
law which law this comes from the
Pascal's principle related to fluids so
we say that pressure at any height H is
given by H ro G at a height H from the
sea level so the height from the sea
level is 3000 meter so we can say it is
3000 into Rho that is density is
thousand and G is a so this comes out to
be 3 into 10 to the power minus 7 kg
meter inverse second to the power minus
2 so this is the value of pressure P
therefore the fractional compression
that is Delta V by V will be equal to
this pressure P that is 3 into 10 to the
power 7 divided by the bulk modulus
which is 2 point 2 into 10 to the power
9 so this comes out to be 1 point 3 6
into 10 to the power minus 2 so this
comes out to be 1 point P is this person
so when we have to calculate the person
please what we do to calculate the
percentage we just multiply it by 100
person so we get 1 point 3 6 person so
this would be your answer right so we
did nothing again we use the same
formula just that industries we had to
calculate the value of pressure so we
use the formula for pressure which is h1
sheet and then we calculated the
fractional change in volume let us again
go
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