Fluid Motion-Continuity-Euler-2015.ppt

7/24/2019 Fluid Motion-Continuity-Euler-2015.ppt

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1

Fluid in Motion


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2

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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3

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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4

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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5

!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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7

$%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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8

$%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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1

$+ample-,


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11

$+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

$nergy rade"ine ;$"-,-

Fluid Motion-Continuity-Euler-2015.ppt

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