Pressure
Pressure is defined as the force acting per unit
area surface.
Pressure = force/ area =F/A……1
S.I unit is Nm is also called 1Pascal (Pa).
Pressure is scalar quantity.
Pressure is inversely proportional to the area.
i.e. force acting on the small area exerts more
pressure.
Pressure is directly proportional to the applied
force.i.e. more pressure is exerted if the force
is increased and vice-versa.
Liquid pressure:
The pressure exerted by the liquid in a vessel is
called liquid pressure. Consider a liquid with
density d in a beaker of cross sectional area A
and height of liquid column is h.
P=F/A
P=m g/A
P=ρ Vg/A
P=ρ A hg /A
P=ρ h g ……..1
The factors affecting the liquid pressure are:
Density of the liquid (ρ)
Depth of liquid (h)
Acceleration due to the gravity (g)
Consequences of liquid pressure:
⊕The pressure exerted by a liquid increases with
depth.
⊕A liquid finds its own level
⊕The pressure at any point in a liquid acts in all
direction.
Pascal’s Law: Pascal’s law of liquid pressure
states that, “The pressure is equally exerted
perpendicularly on all sides as pressure is
applied on a liquid kept in a closed container.”
Instruments based on Pascal’s Law are:
Hydraulic Brake and Pistons.
Up thrust: Up thrust is defined as the resultant
thrust that a liquid uses to push up a body
immersed in the liquid. Its SI unit is Newton.
Density: Density of the substance is defined as
the mass per unit volume of that substance.
Density (ρ) = mass/volume
Density is measured in kg/m in S.I system.
And In c.g.s system it is measured in g/cm .
Relative density: The ratio of the density of the
substance to the density of the substance at
4 C is called relative density of the substance.
It is unit less.
Archimedes Principle:
It states that,” When a body is partially or wholly
immersed in a liquid, it experiences an up thrust
equal to the weight of the liquid displaced by
it.” This principle is used to calculate up thrust
or apparent weight of an object.
Let us consider a cylinder of height h and cross-
sectional area A completely immersed in a
liquid as shown in figure.
Top face be at height of h and bottom face be
at height h
Thrust acted on the upper face of the cylinder
due to liquid = pressure *area
F₁ = p *A
F₁ =ρgh₁*A …………………1
Similarly upthurst acting on the bottom face
F₂ = p₂*A
F₂ = ρgh₂ * A
Total up thrust acting on the body = F₂ – F₁
U = ρgh₂* A – ρgh₁*A
U = ρgA(h₂ – h₁)
U = ρgAh
U= ρgV
So the up thrust of the body immersed in a
liquid is directly proportional to
⊗Density of the liquid (ρ)
⊗Acceleration due o gravity (g)
⊗Volume of the liquid (V)
Also, the weight of the liquid displaced = ρgV,
which is equal to the up thrust acting on the
body.
Law of flotation:
Law of floatation states that, "The weight of the
floating body is equal to the weight of the liquid
displaced by the body."
The density of liquid is directly proportional to
the floatation of the object. It means that if the
density of liquid is more than the object, then
the object floats whereas if the density of liquid
is less than that of the object, then the object
will sink. Hydrometer is a device which is based
on the principle of flotation and used to
measure the specific gravity and density liquids.