Buoyancy
If you swim into the sea, you ever have noticed that as we
go down into the sea you will notice an increase in the up trust pressure as
you down. The pressure increases as we go downward with the depth of the sea.
The pressure at the bottom of the sea is greater than the pressure at the top.
This difference in the pressure cause an upward force on the body. That is why the
body feels upward push when to swim down.
The magnitude of this force is proportional to the pressure
difference and is equivalent to the weight of the displaced.
This can only be done in the non- inertial reference frame.
Before going into deep concepts we need to define some terms
which may help out for a better understanding of the concepts.
What is upthrust?
Any object which is completely or partially submerged into
liquid experienced pressure from its bottom surface, which cause an upward
force or pull. This force is called upthrust.
An object is displacing some amount of fluid, the upthrust
force is equal in size to the weight of the fluid displaced by the object.
Non- inertial reference frame:
Non- reference frame is a frame of reference that undergoes
acceleration concerning an inertial frame.
Center of buoyancy :
The center of buoyancy of an object is the center of gravity
of the displaced volume of fluid.
Difference between the force of buoyancy and the center
of buoyancy?
The force of buoyancy is the vertical force.
The center of buoyancy is the point situated at the center
of the gravity of the liquid that is being displaced by the object submerged.
Density:
The density of a substance is defined as mass per unit
volume. It is a measure of the tightness of material.
Density: mass/volume
The SI unit of density is kilogram per cubic meter.
Relative density:
The relative density of a substance is defined as the ratio
of the density of a substance to the density of the reference point at a temperature
in celsius.
Relative density = density of a substance/ density of water at c0
Write are conditions for a substance to sink or float?
It depends upon the relative density of the material
·
If the relative density of an object is greater
than that of the fluid in which it is submerged then it tends to sink.
·
If the relative density of an object is less
dense then liquid, then the object keeps afloat.
What is the dependence of buoyant force?
Buoyant force depends upon
·
The volume of the body immersed is equal to the
volume of fluid displaced.
·
The density of the fluid.
What is buoyancy?
If an object is immersed in the static fluid then, the
pressure on the bottom of the object is higher than the pressure on the top of
an object. The variation in pressure is due to gravity. The force on the bottom pushes up and the
force on the top pushes down. The difference of pressure caused a buoyancy
which is opposite to the sides of an object immersed in a static fluid.
“The upward force
applied by the fluid on the object when an object is submerged in the fluid is
called buoyancy.”
When an object is submerged in a fluid, an upward force is experienced
by the object. The force is applied by the fluid on the object which makes it rise
is called the force of buoyancy. The force is precisely equal to the amount of
fluid displaced.
What is a force of buoyancy?
Force of buoyancy:
Consider a two ball one is made up of steel and the other
with plastic having equal volume. When we place them into the water, the steel
ball sinks into the water while the plastic afloat. This is because of the difference
in their average density. So, when an object is put in water, it
displaces some amount of water concerning its weight.
“The amount of displaced water is measured by the
object’s average density which relates to volume. It is an upward force exerted
by the fluid that opposes the weight of an object immersed in a fluid. This
upward force is called buoyancy force. “
Example:
if you drop wood into water, buoyancy will keep it afloat.
Mathematical formulation:
If an object is immersed in the static fluid then, the
pressure on the bottom of the object is higher than the pressure on the top of
an object. The force on the bottom pushes up and the force on the top pushes
down. This force is called buoyance force. This force is designated by B.
B = F bottom
- F top
As we know,
The pressure is equal to force per unit area
P
= F/A
:. F = PA
B = P bottom A
- P top A
The variation is pressure is due to gravity
P
= qgh
B = (Q
fluid g h bottom - Qfluid g h top )
A
B = q
fluid g delta h A
B = q
fluid g V
B = m
fluid g
B = W
fluid
It is an upward force exerted by the fluid on an object that
is equal to the weight of the object displaced by an object.
Archimedes’ principle:
For floating and
sunken objects in liquid as well as in gases, Archimedes discovered the
Archimedes’ principle in 212 BC.
Archimedes’ principle states as
“ The
buoyant force on an object immersed in a fluid is equal to the weight of the
fluid displaced.”
The weight of the fluid displaced is directly proportional
to the volume of the displaced fluid.
Among completely submerged objects with equal masses, objects with
greater volume have greater buoyancy.
Apparent weight:
Consider a rock suspended by a string having a weight of 15
newtons. If the rock is displaced into the
water of weight 5 newtons. The force that exerts on the string from which it
hangs would be 15 newtons minus the 5 newtons of buoyancy force 15 – 5 =10
newtons. Buoyancy reduces the apparent weight of objects that have sunk
completely to the seafloor.
The apparent weight (w’) of an object immersed in a fluid is
given by
W’ =
w -B
W’ =
mobjectg - mfluid g
W’ = ( Q object V – Qfluid V)g
W’
= ( Q obj – q fluid ) Gv
W’ = Q’ g V
Relative density :
Q’ = Q
object -- Q fluid
Q obj greater than q
fluid =
the apparent weight is positive
but less than the actual weight
Q obj = Q fluid the apparent weight is positive
but less than the actual weight
Q obj less than q fluid the apparent weight is negative and
the object is said to be lighter.
Application:
It is important phenomenon that have vast application in
each field. The few are
·
swimming
·
Submarines
·
Fish
·
Ship
·
Hot air balloon
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