Z(B)FLUIDS AT REST
Fluid: Fluid is the name given to a substance which begins to flow when external force
is applied on it. Liquids and gases are fluids. The study of fluids at rest is called
hydrostatics and the study of fluids in motion is called hydrodynamics
Fluid Exerts Thrust: When a fluid is kept in a container, the molecules of the fluid in
random motion due to their thermal velocities are constantly colliding with the walls of
the container and rebounding from them. They suffer a change in momentum, due to
which they transfer some momentum to the walls. This momentum transferred to the
walls per unit time by the molecules of fluid accounts for the force or thrust of fluid on
the walls of the container.
Liquid in Equilibrium: A liquid in equilibrium of rest always exerts a force normal to the
surface of contact. Consider a surface CD in contact with a liquid at rest. Let the liquid
be exerting a force F on the small area of the surface at B along AB, which is not
perpendicular to the surface but is inclined at an angle with the surface. In reaction
the surface will exert an equal and opposite force R (=F) along the direction BA.
Resolving the reactional force R (= F) into two rectangular components. F cos 6 acts
along BD and F sin e along BE. Since a liquid cannot resist any tangential force,
therefore, the liquid near B should begin to flow along BD. But the liquid is at rest, hence
no component force should act along BD i.e.
F cos 0 = 0. Since F : 0,
FSme
Cos e = 0 or 90
Fse
Thus the liquid at rest exerts a normal force on the surface in contact with it.
Thrust and Pressure of The Liquid: The total normal force exerted by liquid at rest on
a given surface in contact with it is called thrust of liquid on that surface. S. I. unit of
thrust is newton and its cgs unit is dyne.
The normal force (or thrust) exerted by a liquid at rest per unit area of the suface in
contact with it is called pressure of liquid or hydrostatic pressure.
P=F/A
UNIT of Pressure in system S.I. is Nm or Pascal and in cgs system it is dyne / cm.
Pressure is a scalar quantity because at one level inside the liquid, the pressure is
exerted equally in all directions, which shows that a definite direction is not associated
with hydrostatic pressure.
Pressure Exerted by a Liquid Column: Consider a liquid of density p contained in a
cylindrical vessel of cross sectional area a. Let h be the height of liquid column, and g
be the acceleration due to gravity. The weight of liquid will exert a downward thrust on
the bottom surface of the vessel. Therefore, pressure due to liquid acts on that surface
Weight of liquid inside the vessel = volume x density of liquid x acc. due to gravity.
-ah x px g
Thrust of liquid on area a = weight ofliquid = ah pg
Liquid pressure on the base of vessel is
thrust ahpg
P -**
=hpg
area
Pascal's Law: It states that the increase in pressure at one point of the enclosed liquid
in equilibrium of rest is transmitted equally to all other points of the liquid and also to the
walls of the containers, provided the effect of gravity is neglected.
Pascal's Law (Effect of gravity): Consider a liquid of density p contained in a vessel in
equilibrium of rest. Let C and D be two points inside the liquid at a vertical distance h.
Imagine a cylinder of liquid with axis CD, cross-sectional area A and length h, such that
the point C and D lie on the flat faces of the cylinder, The mass of the liquid in theB
imaginary cylinder will be
M=volume x density = Ah xp= Ahp
Let Pi and P2 be the pressures of liquid at points C and D respectively. The liquid
cylinder is under the action of following vertical forces
(i) Force Fi= PiA, acting vertically downwards on the top face of the cylinder
() Force F2 = P2A, acting vertically upwards on the lower face of the cylinder
(ii) Weight, Mg = Ahpg of the liquid cylinder acting vertically downwards
, As the liquid is in equilibrium of rest. Therefore, the net force on it must be zero ie
Fi+ Mg - F2 = 0
P1A+Ahpg - P2A=0
P2-P1 hpg
If points C and D lie at the same level in liquid, the h=0.
P2-P=0 or PiP2
In the presence of gravity, the pressure is same at all points inside the liquid lying at the
same horizontal plane
If gravity effect is neglected (i.e. Mg=0 or g = 0), then from (2)
P2-P = 0 or P2=P1
It means the pressure at every two point inside the liquid is same in the absence of
gravity
Hydraulic Lift: It is used to lift the heavy loads. Its working is based on Pascal's law. C
and D are two cylinders of different areas of cross section connected to each other with
a pipe E. Let a, A be the areas of cross sections of the pistons in C and D respectively
where as A . The cylinders are filled with an incompressible liquid
Let a downward force f be applied on the piston of C. Then the pressure exerted on the
liquid, P fla. According to Pascal's law, the pressure is transmitted equally to piston
of cylinder D.. Upward force acting on the piston of cylinder D will be
A
F PA= A = f ---
--------
C
LOAD
d a
As A>> a, therefore F>>f
This shows that the small force applied on the smaller piston will be appearing as a very
large force on the large piston.
Hydraulic Brakes: The working of hydraulic brakes is based on Pascal's law. It
consists of a master cylinder M filled with brake oil and provided with air tight frictionless
piston P. When the brake pedal is pressed, the piston P of the master cylinder is
pushed inwards There will be increased pressure on liquid at P, which is transmitted
equally to P; and P2 of wheel cylinder in accordance with Pascal's law. Due to which P
and Pa move outwards. They force the brake shoes to move away from each other
which in turn press against theinner rim of the wheel and hence retard the motion of the
wheel i.e. the brake becomes operative. ToOTHER
WHEELS M
When the pressure on the brake pedal is released, the brake shoe return to their
normal positions by the action of spring, which in turn forces the brake oil to return from
wheel cylinder to master cylinder.
Atmospheric Pressure: The gaseous envelope surrounding the earth is called earth's
atmosphere , which extends upto a height of many kilometers above the surface of
earth. The pressure exerted by atmosphere is called atmospheric pressure. This is due
to weight of the gases of the earth's atmosphere. The atmospheric pressure is
maximum the surface of earth and goes on decreasing as we move up into the
earth's atmosphere. The value of atmospheric pressure on the surface of earth at sea
level is nearly 1.013 X 10" Nm or Pascal in S.I. and 1.013 X 10°
system. It is also measured in torr (1 mm of mercury column) OR 1 bar =dyne/cms
in cgs
10° Pascals
Buoyancy: When a body is partially or wholly immersed in a fluid, it displaces the fluid.
The displaced fluid has a tendency to
regain its original position. Due to this, an upward
force is exerted on the body is called
upthrust or Buoyant force
Archimede's Principle: It states that when a body is immersed wholly or partly in a
liquid at rest, it loses some of its weight. The loss in weight of the body in the liquid is
equal to the weight of the liquid displaced by the immersed part of the body.
Force of adhesion or adhesive force: It is the force of attraction acting between the
molecules of different substances. For
example, water wets the surface of a glass
container. This is due to force of adhesion between water and glass molecules.
Force of cohesion or cohesive force: It is the
force of attraction the
molecules of the same substance. For example: Mercury does not wet theamongst surface of a
Fluid: Fluid is the name given to a substance which begins to flow when external force
is applied on it. Liquids and gases are fluids. The study of fluids at rest is called
hydrostatics and the study of fluids in motion is called hydrodynamics
Fluid Exerts Thrust: When a fluid is kept in a container, the molecules of the fluid in
random motion due to their thermal velocities are constantly colliding with the walls of
the container and rebounding from them. They suffer a change in momentum, due to
which they transfer some momentum to the walls. This momentum transferred to the
walls per unit time by the molecules of fluid accounts for the force or thrust of fluid on
the walls of the container.
Liquid in Equilibrium: A liquid in equilibrium of rest always exerts a force normal to the
surface of contact. Consider a surface CD in contact with a liquid at rest. Let the liquid
be exerting a force F on the small area of the surface at B along AB, which is not
perpendicular to the surface but is inclined at an angle with the surface. In reaction
the surface will exert an equal and opposite force R (=F) along the direction BA.
Resolving the reactional force R (= F) into two rectangular components. F cos 6 acts
along BD and F sin e along BE. Since a liquid cannot resist any tangential force,
therefore, the liquid near B should begin to flow along BD. But the liquid is at rest, hence
no component force should act along BD i.e.
F cos 0 = 0. Since F : 0,
FSme
Cos e = 0 or 90
Fse
Thus the liquid at rest exerts a normal force on the surface in contact with it.
Thrust and Pressure of The Liquid: The total normal force exerted by liquid at rest on
a given surface in contact with it is called thrust of liquid on that surface. S. I. unit of
thrust is newton and its cgs unit is dyne.
The normal force (or thrust) exerted by a liquid at rest per unit area of the suface in
contact with it is called pressure of liquid or hydrostatic pressure.
P=F/A
UNIT of Pressure in system S.I. is Nm or Pascal and in cgs system it is dyne / cm.
Pressure is a scalar quantity because at one level inside the liquid, the pressure is
exerted equally in all directions, which shows that a definite direction is not associated
with hydrostatic pressure.
Pressure Exerted by a Liquid Column: Consider a liquid of density p contained in a
cylindrical vessel of cross sectional area a. Let h be the height of liquid column, and g
be the acceleration due to gravity. The weight of liquid will exert a downward thrust on
the bottom surface of the vessel. Therefore, pressure due to liquid acts on that surface
Weight of liquid inside the vessel = volume x density of liquid x acc. due to gravity.
-ah x px g
Thrust of liquid on area a = weight ofliquid = ah pg
Liquid pressure on the base of vessel is
thrust ahpg
P -**
=hpg
area
Pascal's Law: It states that the increase in pressure at one point of the enclosed liquid
in equilibrium of rest is transmitted equally to all other points of the liquid and also to the
walls of the containers, provided the effect of gravity is neglected.
Pascal's Law (Effect of gravity): Consider a liquid of density p contained in a vessel in
equilibrium of rest. Let C and D be two points inside the liquid at a vertical distance h.
Imagine a cylinder of liquid with axis CD, cross-sectional area A and length h, such that
the point C and D lie on the flat faces of the cylinder, The mass of the liquid in theB
imaginary cylinder will be
M=volume x density = Ah xp= Ahp
Let Pi and P2 be the pressures of liquid at points C and D respectively. The liquid
cylinder is under the action of following vertical forces
(i) Force Fi= PiA, acting vertically downwards on the top face of the cylinder
() Force F2 = P2A, acting vertically upwards on the lower face of the cylinder
(ii) Weight, Mg = Ahpg of the liquid cylinder acting vertically downwards
, As the liquid is in equilibrium of rest. Therefore, the net force on it must be zero ie
Fi+ Mg - F2 = 0
P1A+Ahpg - P2A=0
P2-P1 hpg
If points C and D lie at the same level in liquid, the h=0.
P2-P=0 or PiP2
In the presence of gravity, the pressure is same at all points inside the liquid lying at the
same horizontal plane
If gravity effect is neglected (i.e. Mg=0 or g = 0), then from (2)
P2-P = 0 or P2=P1
It means the pressure at every two point inside the liquid is same in the absence of
gravity
Hydraulic Lift: It is used to lift the heavy loads. Its working is based on Pascal's law. C
and D are two cylinders of different areas of cross section connected to each other with
a pipe E. Let a, A be the areas of cross sections of the pistons in C and D respectively
where as A . The cylinders are filled with an incompressible liquid
Let a downward force f be applied on the piston of C. Then the pressure exerted on the
liquid, P fla. According to Pascal's law, the pressure is transmitted equally to piston
of cylinder D.. Upward force acting on the piston of cylinder D will be
A
F PA= A = f ---
--------
C
LOAD
d a
As A>> a, therefore F>>f
This shows that the small force applied on the smaller piston will be appearing as a very
large force on the large piston.
Hydraulic Brakes: The working of hydraulic brakes is based on Pascal's law. It
consists of a master cylinder M filled with brake oil and provided with air tight frictionless
piston P. When the brake pedal is pressed, the piston P of the master cylinder is
pushed inwards There will be increased pressure on liquid at P, which is transmitted
equally to P; and P2 of wheel cylinder in accordance with Pascal's law. Due to which P
and Pa move outwards. They force the brake shoes to move away from each other
which in turn press against theinner rim of the wheel and hence retard the motion of the
wheel i.e. the brake becomes operative. ToOTHER
WHEELS M
When the pressure on the brake pedal is released, the brake shoe return to their
normal positions by the action of spring, which in turn forces the brake oil to return from
wheel cylinder to master cylinder.
Atmospheric Pressure: The gaseous envelope surrounding the earth is called earth's
atmosphere , which extends upto a height of many kilometers above the surface of
earth. The pressure exerted by atmosphere is called atmospheric pressure. This is due
to weight of the gases of the earth's atmosphere. The atmospheric pressure is
maximum the surface of earth and goes on decreasing as we move up into the
earth's atmosphere. The value of atmospheric pressure on the surface of earth at sea
level is nearly 1.013 X 10" Nm or Pascal in S.I. and 1.013 X 10°
system. It is also measured in torr (1 mm of mercury column) OR 1 bar =dyne/cms
in cgs
10° Pascals
Buoyancy: When a body is partially or wholly immersed in a fluid, it displaces the fluid.
The displaced fluid has a tendency to
regain its original position. Due to this, an upward
force is exerted on the body is called
upthrust or Buoyant force
Archimede's Principle: It states that when a body is immersed wholly or partly in a
liquid at rest, it loses some of its weight. The loss in weight of the body in the liquid is
equal to the weight of the liquid displaced by the immersed part of the body.
Force of adhesion or adhesive force: It is the force of attraction acting between the
molecules of different substances. For
example, water wets the surface of a glass
container. This is due to force of adhesion between water and glass molecules.
Force of cohesion or cohesive force: It is the
force of attraction the
molecules of the same substance. For example: Mercury does not wet theamongst surface of a
