flow over-inclined flat plate govind ram jat
TRANSCRIPT
MEWAR
UNIVERSITY
PRESENTATIONON
FLOW OVER-INCLINED FLAT
PLATE
(Transport
Phenomena)
GUIDED BY:-M.ALAM SIRHOD & Asst.ProfessorDept. of Chemical EngineeringMewar University
PRESENTED BY:-GOVIND RAM JAT B.Tech.(Chemical Engineering)(5th sem.,3rd year)( TP)
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CONTENT
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FLOW OVER-INCLINED FLAT PLATE
x ρgsinβ
y
β
β
δ
L
g
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INTRODUCTION
Such film have been study concentration with wetted wall tower , Evaporation & Gas Absorption.
Geometry and selection of co-ordinate:-
a)Co-ordination , co-ordinate x, y, z.
b)Body force is the force of
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ASSUMPTIONS &
0z
v
y
v
x
v zyx
0z
vz0
dz
dvz0, V
0yx
z
vv
xfv
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Cont………..
)(zfVz
direction)is xbaseβ(assumed gBaseso
directionxinComponent
directionzisbaseassumedgBaseg
Base
Hypotenuse
Base
sin ,
g
Base 90cos
) (coscos
cos
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EQUATION OF MOTION
gρvμpDt
Dvρ
2
zzzzz
zz
yz
xz
y
yyyy
z
y
y
y
x
y
xxxxx
zx
yx
xx
gz
v
y
v
x
v
z
p
z
vv
y
vv
x
vv
t
v
gz
v
y
v
x
v
y
p
z
vv
y
vv
x
vv
t
v
gz
v
y
v
x
v
x
p
z
vv
y
vv
x
vv
t
v
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
Cartesian Coordinate ( x, y, z):-
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zzzzz
zz
yz
xz
y
yyyy
z
y
y
y
x
y
xxxxx
zx
yx
xx
gz
v
y
v
x
v
z
p
z
vv
y
vv
x
vv
t
v
gz
v
y
v
x
v
y
p
z
vv
y
vv
x
vv
t
v
gz
v
y
v
x
v
x
p
z
vv
y
vv
x
vv
t
v
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
0 0 0 0 0 0 0
00 0
0 00
0
000
000 0
By Putting The Value Of Assumption In The Equation Of Motion:
0
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Dt
DV
0Dt
DV
V2
gvp 2.0
2
2
:
x
viscomponentleftThe
equationthesolvingBy
z
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EQUATION OF
MOTION
so,
Now we explain pressure component:-
presentz
pdirectionzin
z
p
y
pdirectionyin
y
p
presentx
pdirectionxin
x
p
0
gx
vp z
2
2
.0
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EQUATION OF
MOTION
Gravity component:-
x-direction
y-direction
z-direction cos
0
sin
gg
g
gg
z
y
x
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Overall balance equation:-X-direction
Y-direction
Z-direction
So we get velocity profile by z-direction equation.
EQUATION OF
MOTION
cos0
000
sin00
2
2
gx
v
z
p
y
p
gx
p
z
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Boundary Conditions:-
1. At (no slip condition)
2. At x=0
EQUATION OF
MOTION
cos2
2
gz
p
x
vz
0zvx
xz.max
0dx
dvz
dx
dvzxz
0xz11/14/2013 14
EQUATION OF
MOTION
)(
0
xfv
dx
dv
z
z
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SIMPLIFICATION
OF MODEL
SIMPLIFICATION OF MODEL:-
Film is falling under the action of gravity only.
There is no pressure gradient.
The Vz is only function of x.
Then we replace the partial to total derivatives
0p
cos2
2
gdx
vd z
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SIMPLIFICATION OF MODEL
CONT………..
cos2
2 g
dx
vd z
1
cos cx
g
dx
dvthen z
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SIMPLIFICATION OF MODEL
CONT………..
2
2
2
2
1
1
2
cos
0,x
-:1
2
cos
cos
,0
0cos
0
-: 2
cg
v
ConditionBoundryApply
cxg
v
Axg
dx
dv
BecomeNowEquationc
cg
ConditionBoundryApply
z
z
z
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Simplification of above equation-
SIMPLIFICATION
OF MODEL
22
22
2
cos
2
cos
2
cos
xg
v
gxgv
BecomeEquationThen
z
z
ixg
vz
22
12
cos
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No. Of Properties
2
cos2
.
gv Maxz
dxxg
wQ
wdzvQ
mareavQ
RateFlowVolumetricii
z
zz
zz
22
0
0
3
2
cos
.sec
, ;0 .max, isthatxatclearlyisvVelocityMaximumThei z
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3
cos ischarge
136
cos
32
cos
3
3
32
gwQD
gwQ
gwQ
z
z
z
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3
2
3
cos
3
cos
.max
.
23
..
z
avgz
avgzavgz
v
v
g
w
gwv
w
Qv
VelocityAverageiii
31
2
32
3
cos
3
cos
sec
Width Per Unit Flow RateMass
gThicknessFilm
g
w
Q
m
kg
ThicknessFilmi
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on.h Dimenssistic LengtCharacteriδWhere,
μ
δ
The Systemumber For
νρ
4
4Re
N Reynold
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ECCENTRIC LOAD
The moment is given by:-
Me=We Lo
We=dead weight of the equipment
Lo=distance between the centre of gravity of the equipment and the column centre line.For Your Attention
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