# Chapter 5 Flow Analysis Using Control Volume (Finite Control Volume Analysis ) - PowerPoint PPT Presentation

Loading...

PPT – Chapter 5 Flow Analysis Using Control Volume (Finite Control Volume Analysis ) PowerPoint presentation | free to view - id: 57f6fa-YTdlM

The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

## Chapter 5 Flow Analysis Using Control Volume (Finite Control Volume Analysis )

Description:

### Flow Analysis Using Control Volume ... non-deforming control volume ---Control volumes containing a gas turbine engine on an aircraft in flight, and ... – PowerPoint PPT presentation

Number of Views:215
Avg rating:3.0/5.0
Slides: 63
Provided by: WangCh
Category:
Tags:
User Comments (0)
Transcript and Presenter's Notes

Title: Chapter 5 Flow Analysis Using Control Volume (Finite Control Volume Analysis )

1
Chapter 5 Flow Analysis Using Control Volume
(Finite Control Volume Analysis )
2
• Many practical problems in fluid mechanics
require analysis of the behavior of the contents
of a finite region in space (a control volume).
• for example,
• to determine the amount of time to
allow for complete
• filling of a large storage tank.
• to estimate of how much power it would
take to move
• water from one location to another
at a higher
• elevation and several miles away
may be sought.

3
• The bases of this analysis method are some
fundamental principle of physics , namely ,
• Conservation of mass
• Newtons second law of motion , and
• the first and second laws of
thermodynamics.
• The finite control volume formulas are easy to
interpret physically and are not difficult to use.

4
5.1 Conservation of Mass-The continuity
Equation
• 5.1.1 Derivation of the continuity Equation

5
(No Transcript)
6
t t-dt t
t t tdt
7
(No Transcript)
8
5.1.2 Fixed, non-deforming Control Volume
9
(No Transcript)
10
(No Transcript)
11
(No Transcript)
12
(No Transcript)
13
5.1.3 Moving, Non-deforming Control Volume
• Example of moving, non-deforming control volume
• ---Control volumes containing a gas turbine
engine on an
• aircraft in flight, and gasoline tank of an
automobile
• passing.

14
(No Transcript)
15
5.1.4. Deforming Control Volume
• A deforming Control volume
• Changing volume size control surface
movement.

16
(No Transcript)
17

18
5.2 Newtons Second Law --The linear momentum
and moment-of-momentum equations.
• Newtons second law of motion for a system is

gtAny reference or coordinate system for which
this statement is true is called
inertial. A fixed coordinate system is
inertial. A coordinate system that moves in
a straight line with constant velocity and
is thus without acceleration is also
inertial.
19
• When a control volume is coincident with a system
at an instant of time, the forces acting on the
system and the forces acting on the contents of
the coincident control volume are instantaneously
identical, that is,

20
• Furthermore, for a system and the contents of a
coincident control volume that is fixed and
non-deforming, the Reynolds transport theorem
allows us to conclude that

21
• For a control volume that is fixed (inertial) and
non-deforming, Eq.(5.19),(5.20), and (5.21)
suggest that an appropriate mathematical
statement of Newtons Second law of motion is
• Eq(5.22) is the linear momentum equation for a
fixed, non-deforming control volume.
• Body force -- gravity only
• Surface force -- exerted on the contents
of the control
• volume by material just outside the
control volume
• in contact with material just inside
the control volume

22
(No Transcript)
23
(No Transcript)
24
(No Transcript)
25
Several important notes
• (1) 1-D flow problem when the flow is uniformly
distributed
• over a section of the C.S.
• (2) Linear momentum is directional three
orthogonal
• coordinate directions.
• (3) Flux term is linear momentum-
• for Steady flow (In the
textbook ,it is aussmed

• Steady flow for the
momentam problem)
• (5) If control surface ? direction of flow
• ?Surface force exerted at these locations by
fluid outside the C.V. on fluid inside will be
due to pressure.

26
• (6) Uniform pressure on control volume
• (7) Positive external force if the force is in
the assigned
• positive coordinate direction. Negative
otherwise.
• (8) Only external forces acting on the contents
of the control
• volume are considered in the linear
momentum
• equation.(Eq.5.22)

27
(No Transcript)
28
(No Transcript)
29
(No Transcript)
30
(No Transcript)
31
(No Transcript)
32
(No Transcript)
33
(No Transcript)
34
(No Transcript)
35
• For a system and
• an inertial , moving , non-deforming control
volume that are both coincident at an instant of
time , the Reynolds transport theorem leads to
• This is the linear momentum equation for an
inertial, moving, non-deforming control volume
that involves steady flow.

36
(No Transcript)
37
(No Transcript)
38
(No Transcript)
39
5.3 First Law of Thermodynamics-The Energy
equation
• 5.3.1 Derivation of the Energy Equation
• The first law of thermodynamics for a system is,
in word

----(5.56)
40
• Eq.(5.55) is valid for inertial and non-inertial
reference system
• For the control volume that is coincident
with the system at an instant of time

41
(No Transcript)
42
(No Transcript)
43
(No Transcript)
44
(No Transcript)
45
(No Transcript)
46
5.3.2 Application of the Energy Equation
47
(No Transcript)
48
(No Transcript)
49
(No Transcript)
50
(No Transcript)
51
J/kg(N?m)/kg (kg?m/s?m)/kg m2/s2
52
(No Transcript)
53
5.3.3 Comparison of the Energy Equation with
the Bornoulli Equation
54
(No Transcript)
55
(No Transcript)
56
(No Transcript)
57
(No Transcript)
58
(No Transcript)
59
(No Transcript)
60
(No Transcript)
61
(No Transcript)
62
(No Transcript)
About PowerShow.com