Download - Fluid Motion-Continuity-Euler-2015.ppt
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Fluid in Motion
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Kinematics of
Fluid Mechanics
Fluid Motion
Flow Field
Stream lines
)Displacement, velocity, acceleration, ..etc. (
Flow
Non-viscous Flow Real Flow
)Ideal( )Real(
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Steady and Unsteady Flo
Steady
Unsteady
A steady flow is one in which the conditions
(velocity, pressure and cross-section) may differ
from point to point but DO NOT change with
time
If at any point in the fluid, the conditions change with time,the flow is described as unsteady
Fluid !alve
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Uniform and Non-uniform flow
Uniform flow:If the flow velocity is the same magnitude and
direction at every point in the flow it is said to be uniform.
That is the flow conditions DO NOT change with position.
Non-uniform: If at a given instant the velocity is not the same
at every point the flow is non-uniform.
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!tream "ine !tream Tube and #athline
v
v
v
A stream lineis a line that is everywhere tangent to
the velocity vector at a given instant of time. Astreamline is hence an instantaneous pattern.
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A tubular surface formed by streamlines along which the fluid flows is known as a
stream tube, which is a tube whose walls are streamlines. ince the velocity is
tangent to a streamline, no fluid can cross the walls of a stream tube.
A pathline is the actual path traversed by a given (marked) fluid particle.
!tream tube
#athline
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$%uation of &ontinuity
&ontrol volume
' control volume is a finite region chosencarefully by the analyst for a particular problem
with open boundaries through which mass
momentum and energy are allowed to cross
conservation of mass
For steady flow
(ass entering per unit time ) (ass leaving per unit time
(ass entering per unit time ) (ass leaving per unit time *&hange
of mass in the control volume per unit time
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$%uation of &ontinuity:
1- For One dimension
!2!1
Flow
ds2
ds1
dt
ds
A!dt
ds
A!"
""
#
## =
"onservation o# mass
$ividin% &' dt( we o&tain
"""### $A!$A! =
)1)2
*1!1ds1+ *2!2ds2
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,
.%onst$A!$A!m """### ===
.ere is t.e mass #low rate/m
+ *!)
( ) &!A$d =
mFor constant * !
1
)1
+ !2
)2
+ 0
&
$
d$
A
dA
!
d!=++
.ere 0 is t.e volume #low rate/
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$+ample-,
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$+ample-
If pipe , diameter ) /mm mean velocity m0s pipe diameter 1/mm
ta2es 3/4 of total discharge and pipe 3 diameter 5/mm. 6hat are the
values of discharge and mean velocity in each pipe7
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'ne imensional teady low
#- *uler+s *uation uation o# Motion
7
) 78d7
+ !ds
)d)
9
d9
1
2
ds
!::l'in% Newton;s law
< F + mass = acceleration
! > d! - !ds "os
+ !ds )ds
d$
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ds
dcos=
ds
d$! > d! - !ds + !ds)
ds
d-
$ividin% &'
!ds we o&tain
> > +
ds
d-
ds
d/
0
#
g
#
ds
""$d
&dg"
"$d
0
d/ =+
+ uler?s uation
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"-1ernoulli+s *uation
rom *uler+s *uation: for incompressible, one-dimensional by
integration and take and g as constants.
%onstantd
g"
"$d
0
d/ =+
+
2g"
$
0
/"
=++
3here: 2 is constant and termed as the total head
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@ Steady flo
4he 1ernoulli euation can also be written
between any two points on the same streamline
as
D'TU(
88,
p0g
v0g
p,0g
v,0g
,
TOT'" 9$'D
"
"""
#
"## -
g"
$
0
/-
g"
$
0
/++=++
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9ydraulic rade "ine ;9"< and
$nergy rade"ine ;$"-,-