Mechanical Properties of Fluid
Mechanical Properties of Fluid
Mechanical Properties of Fluid
Fluids
&
PRESSUR
E
PRESSURE
Pressure is defined as a normal force exerted by a
fluid per unit area.
Units of pressure are N/m2, which is called a
pascal (Pa).
Since the unit Pa is too small for pressures
encountered in practice, kilopascal (1 kPa = 103 Pa)
and megapascal (1 MPa = 106 Pa) are commonly
used.
Other units include bar, atm, kgf/cm2
Pressure
Pressure is the force per unit area, where the force is
perpendicular to the area.
p= g h
pressure increase in
depth (m)
increase
The pressure at a given depth in a continuous, static body of liquid is
constant.
p1 p3 p1 = p2 = p3
p2
Pressure
Pressure is the ratio of a force F to the area A over which it is
applied:
Pressure = Force
Area ;P = F
A
A = 2 cm2
F (1.5 kg)(9.8
P = =2
m/s
A ) 2 x 10-4 m2
1.5 kg
P = 73,500 N/m2
The Unit of Pressure (Pascal):
Pascal: 1 Pa = 1 N/m2
P = 73,500 Pa
Fluid exerts forces in many directions. Try to
submerse a rubber ball in water to see that an
upward force acts on the ball.
mg m V Ah
P A; h
V ;
Vg Ahg
P A A
Area
mg
P = gh
h = 20 m; g = 9.8
m/s2
P = 196 kPa
Atmospheric Pressure
One way to measure atmospheric
P=0
pressure is to fill a test tube with
mercury, then invert it into a bowl at at
m m h
of mercury.
Patm = 101,300 Pa
Absolute Pressure
Absolute Pressure: The sum of the 1 atm = 101.3 kPa
pressure due to a fluid and the
pressure due to atmosphere.
Gauge Pressure: The P = 196 kPa
h
between the absolute pressure and
difference
the pressure due to the atmosphere:
• Hydraulic lift
• Hydraulic Brakes
Hydraulic lift
Fin Fout
Ain
Example 3. The smaller and larger pistons of a
hydraulic press have diameters of 4 cm and 12 cm.
What input force is required to lift a 4000 N weight
with the output piston?
D Area
R 2;
R2
(4000 N)( )(2 cm)2
Fin
(6 cm)2
Rin= 2 cm; R out = 6 cm
F = 444 N
Hydraulic
brake
The hydraulic brake is an arrangement
of braking mechanism which uses brake fluid,
typically containing ethylene glycol, to transfer
pressure from the controlling mechanism to
the braking mechanism. When brakes are
applied suddenly in a moving vehicle, there is
every chance of the vehicle to skid because
the wheels are not retarded uniformly. In
order to avoid this danger of skidding when
the brakes are applied, the brake mechanism
must be such that each wheel is equally and
simultaneously retarded. A hydraulic brake
serves this purpose. It works on the principle
of Pascal’s law.
Hydraulic Brake
SURFACE
TENSION
Surface tension is the property of any
liquid by virtue of which tries to
minimize its free surface area.
Adhesive Force
The force of attraction acting between the molecules of different
substances is called adhesive force, e.g., the force of attracts acting
between the molecules of paper and ink, water and glass, etc.
Cohesive Force
The force of attraction acting between the molecules of same
substan is called cohesive force. e.g., the force of attraction acting
between molecules of water, glass, etc.
Cohesive forces and adhesive forces are van der Waals’ forces.
• Surface tension S = Force/Length = F/l = Work
done/Change in area
• Its SI unit is Nm-1 or Jm-2 and its dimensional formula
is [MT-2].
• It is a scalar quantity.
• Surface tension is a molecular phenomenon which
is due to cohesive force and root cause of the force
is electrical in nature.
• Surface tension of a liquid depends only on the
nature of liquid and independent of the surface
area of film or length of the line .
Applications of surface tension
In the case of a plane liquid surface, the pressure on the liquid side is
equal to the pressure on the vapour side.
But when the free surface of the liquid is curved the pressure on the
liquid side is different from the pressure on the vapour side.
Excess of pressure is always on the concave side
Excess pressure inside a liquid drop
Consider a liquid drop of
radius R. The molecules
lying on the surface of liquid
drop, due to surface tension
will experience resultant
force acting inward to the
surface.
Let S = Surface tension of
liquid drop P = excess
pressure inside the drop Due
to excess of pressure, let
there be increase in the
radius of the drop by a small
Then work
quantity done by the excess pressure. W =
in figure
Force x Displacement
Excess pressure inside a soap bubble
Pancake
syrup
Substances with higher
viscosity take longer to
flow down the ramp.
v1 A1 A2 v2
Pressure, kinetic and potential energy of liquids
A liquid in a steady flow can possess three kinds of energy. They are (1) Kinetic energy, (2)
Potential energy, and (3) Pressure energy, respectively.
i) Kinetic energy: The kinetic energy of a liquid of mass m moving with a velocity v is
given by
Mathematically,
Application of
Bernoulli’s Theorem
AIRFOIL
• Bernoulli’s
Principle is
what allows
birds and
planes to fly.
• The secret
behind flight is
‘under the
wings.’
LIFT
THRUST
DRAG
GRAVIT
Y
On top: greater air speed and less air pressure
V2
v1
2) Spoiler – airfoil reversed:
3) Attraction between two
closely parallel moving boats
(or cars):
When two boats or buses move
side by side in the same direction,
the water (or air) in the region
between them moves faster than that
on the remote sides. Consequently in
accordance with Bernoulli’s principle
the pressure between them is reduced
and hence due to pressure difference
they are pulled towards each other
creating the so called attraction.
4) Action of atomiser:
The action of carburetor,
paint-gun, scent-spray or
insect-sprayer is based on
Bernoulli’s principle. In all these,
by means of motion of a piston P in a cylinder C, high
speed air is passed over a tube T dipped in liquid L to be
sprayed. High speed air creates low pressure over the tube
due to which liquid (paint, scent, insecticide or petrol) rises
in it and is then blown off in very small droplets with
expelled air.
5) Blowing off roofs by wind storms: During a tornado or
hurricane, when a high speed wind blows over a straw or tin
roof, it creates a low pressure (P) in accordance with
Bernoulli’s principle.