10

FLUID
MECHANICS
Page
1
Introduction
•
Fluid
is
a
matter
in
a
state
which
can
flow.
Liquids,
gases,
molten
metal
and
tar
are
examples
of
fluids.
•
Fluid
mechanics
is
studied
in
two
parts:
( i )
Fluid
statics

Study
of
the
forces
and
pressures
acting
on
stationary
fluid.
Pascal’s
law
and
Archimedes’
principle
and
surface
tension
are
discussed
in
fluid
statics.
( ii )
Fluid
dynamics

Study
of
motion
of
fluid
and
properties
related
to
it
as
a
result
of
forces
acting
on
fluid.
Bernoulli’s
theorem
and
its
applications
and
viscosity
of
fluid
are
discussed
here.
Fluid
dynamics
is
studied
in
two
sections:
Hydrodynamics
and
Aerodynamics.
10.1
Pressure
Pressure
is
the
force
acting
on
a
surface
per
unit
area
in
a
direction
perpendicular
to
it.
It
is
a
scalar
quantity
and
its
S
I
unit
is
N
/
m
2
named
pascal
( Pa )
in
honour
of
the
French
scientist
Blasé
Pascal.
Its dimensional
formula is
M
1
L

1
T

2
.
Thus,
Pressure,
P
( Pa )
=
)
m
(
A
Area,
)
N
(
F
,
Force
2
.
A
bigger
unit
of
pressure
is
‘bar’.
1
bar
=
10
5
Pa.
1
atmosphere
pressure
( atm )
=
1.013 × 10
5
Pa
or
N
/
m
2
=
760
mm
( 76
cm
)
of
Hg
column.
Density:
Density
is
the
ratio
of
mass
to
volume
of
an
object.
It
is
a
scalar
quantity
and
its
S
I
unit
is
kg
/
m
3
.
Liquids
are
almost
incompressible.
Hence,
the
density
of
a
liquid
remains
almost
constant
at
a
given
temperature
for
small change
in
the
value
of
pressure.
Gases
are
compressible.
Hence,
the
volume
of
gas
decreases
and
density
increases
with
increase
of
pressure.
Relative
density / Specific
density / Specific
gravity:
“Relative
density
also
known
as
specific
density
or
specific
gravity
of
a
given
substance
is
the
ratio
of
its
density
to
the
density
of
water
at
277
K ( i.e.,
4
°
C ).
”
It
is
a
dimensionless
quantity
and
hence
does
not
have
a
unit.
Also,
Relative
( specific )
density
of
an
object
=
K
277
at
water
of
volume
same
the
of
Mass
object
an
of
Mass
10.2
Pascal’s
Law
“A
change
in
pressure
applied
to
an
enclosed
( incompressible )
fluid
is
transmitted
undiminished
to
every
point
of
the
fluid and
the
walls
of
the
containing
vessel.
”
This
statement
is
known
as
Pascal’s
law.
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10

FLUID
MECHANICS
Page
2
Pascal’s
law
is
also
given
as
“If
the
effect
of
gravitation
is
neglected,
the
pressure
at
every
point
in
an
incompressible
liquid,
in
equilibrium,
is
the
same.”
Applications
of
Pascal’s
Law:
The
figure
shows
the
principle
of
a
hydraulic
lift
used
to
raise
heavy
loads.
This
device
has
two
vertical
cylinders
of
different
diameters
connected
by
a
horizontal
tube.
A
liquid
is
filled
in
this
vessel.
Air
tight
pistons
having
crosssectional
areas
A
1
and
A
2
(
A
1
<
A
2
)
are
fitted
touching
the
liquid
surface
in
both
the
cylinders.
According
to
Pascal’s
law,
in
equilibrium,
the
pressure
on
liquid
in
both
the
arms
is
the
same.
Hence,
1
1
A
F
=
P
1
=
P
2
=
2
2
A
F
⇒
F
2
=
F
1
1
2
A
A
Thus,
a
large
force,
F
2
,
is
generated
using
a
small
force,
F
1
,
as
the
magnitude
of
F
2
is
1
2
A
A
times
the
magnitude
of
F
1
.
Using
Pascal’s
law,
devices
like
hydraulic
lift,
hydraulic
jack,
hydraulic
brake
and
hydraulic
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 Spring '06
 Smith
 Fluid Dynamics, Fluid Mechanics, mechanics, Force, Surface

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