we nannies and Kid mechanics em
Continuum
Hypothesis
•
Viscosity
-
-
The resistance
E- pi -
de
to sheer stress .
dy
•
No -
slip condition :
molecules in contact
with the wall will stick to the wall kinematic viscosity -
V=
Mf Ideal Fluid :
velocity at wall is
always Zero .
Frictionless and
incompressible
The Boundary layer where the
flow Control
*
:
Volume and Control Surface
to the wall
velocity from zero
8
to value
increases
free stream
• Pressure Variation
p,
Vertical -
pressure force at top :
Area
) -- - -
Zz
Fz pz A
-
Classification
=
-
of Forces
Fluid of
-
Weight of fluid in column :
density p .
Surface forces -
act
only on
CS
Fw mg -
-
-
-
pg
A- (Zz -
Z . ) .. . . .- za
tf •
Body Forces -
act on ace elements of CV
f. A
-
-
fzAtpgA(za -
z. ) e.
•
Static Forces -
Present when fluid is stationary
Horizontal
A -
unaffected by fluid motion .
/
-
Fluid of
" Forces
P'
F Dynamic Absent in Shiu f hid
generated
' •
I
-
-
-
Paradox
Hydrostatic
-
by fluid motion .
pressure at the bottom of a
mg Ratio of inertial
forces
liquid filled container will REYNOLD's NUMBER -
to viscous forces
depend only on
filling height P
,
=
Pgh
L characteristic length
-
of container
PI
.
Re = M -
dynamic viscosity
Re
M u
-
flow speed High
Absolute pressure =
gauge pressure
t P -
density turbulent Flow
atmospheric pressure . Conservation of mass :
Low Re
U Tube Manometer J
p SA Pz SAZ Constant
-
: U =
uz
=
Laminar Flow
,
, ,
m - mass of
=p SAU flow rate
Pressure at B =
Pressure at C
QI =
Volumetric flow rate 8A =
so
, Bernoulli Equation
P
fatPgh RB zig constant H
Iz v2
=
ft pgz constant
peg
t z
- -
= t -
+ -
,
j t
unit volume
per unit
weight per
Inclined Pressure Pressure
velocity goes down
-
Manometer with
Leg goes up as
,
goes
down as
velocity goes up .
Is
sing
f-
=
K
ft v 't constant
pgz
=
l
The L L L .
Maronite car Total
Energy contained
kinetic
energy potential
energy
energy
(total
he made more sensitive
by adjusting the by random molecules
(static pressure )
%ffainn.YPYY.me, permit
(Elevation
volume
pressure)
pressure)
inclination g. the
leg .
Stagnation point at Vi O -
f f ,
-
-
,
t
ZZ v2
Continuum
Hypothesis
•
Viscosity
-
-
The resistance
E- pi -
de
to sheer stress .
dy
•
No -
slip condition :
molecules in contact
with the wall will stick to the wall kinematic viscosity -
V=
Mf Ideal Fluid :
velocity at wall is
always Zero .
Frictionless and
incompressible
The Boundary layer where the
flow Control
*
:
Volume and Control Surface
to the wall
velocity from zero
8
to value
increases
free stream
• Pressure Variation
p,
Vertical -
pressure force at top :
Area
) -- - -
Zz
Fz pz A
-
Classification
=
-
of Forces
Fluid of
-
Weight of fluid in column :
density p .
Surface forces -
act
only on
CS
Fw mg -
-
-
-
pg
A- (Zz -
Z . ) .. . . .- za
tf •
Body Forces -
act on ace elements of CV
f. A
-
-
fzAtpgA(za -
z. ) e.
•
Static Forces -
Present when fluid is stationary
Horizontal
A -
unaffected by fluid motion .
/
-
Fluid of
" Forces
P'
F Dynamic Absent in Shiu f hid
generated
' •
I
-
-
-
Paradox
Hydrostatic
-
by fluid motion .
pressure at the bottom of a
mg Ratio of inertial
forces
liquid filled container will REYNOLD's NUMBER -
to viscous forces
depend only on
filling height P
,
=
Pgh
L characteristic length
-
of container
PI
.
Re = M -
dynamic viscosity
Re
M u
-
flow speed High
Absolute pressure =
gauge pressure
t P -
density turbulent Flow
atmospheric pressure . Conservation of mass :
Low Re
U Tube Manometer J
p SA Pz SAZ Constant
-
: U =
uz
=
Laminar Flow
,
, ,
m - mass of
=p SAU flow rate
Pressure at B =
Pressure at C
QI =
Volumetric flow rate 8A =
so
, Bernoulli Equation
P
fatPgh RB zig constant H
Iz v2
=
ft pgz constant
peg
t z
- -
= t -
+ -
,
j t
unit volume
per unit
weight per
Inclined Pressure Pressure
velocity goes down
-
Manometer with
Leg goes up as
,
goes
down as
velocity goes up .
Is
sing
f-
=
K
ft v 't constant
pgz
=
l
The L L L .
Maronite car Total
Energy contained
kinetic
energy potential
energy
energy
(total
he made more sensitive
by adjusting the by random molecules
(static pressure )
%ffainn.YPYY.me, permit
(Elevation
volume
pressure)
pressure)
inclination g. the
leg .
Stagnation point at Vi O -
f f ,
-
-
,
t
ZZ v2
