FLOW OVER-INCLINED FLAT PLATE govind ram jat

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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