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 2001, W. E. Haisler
Chapter 1: Introduction
1
ENGR 214
CONSERVATION PRINCIPLES
for
CONTINUOUS MEDIA
 2001, W. E. Haisler
Chapter 1: Introduction
THE BASIC
CONSERVATION
PRINCIPLE
some of IT + the rest of IT
= all of IT
(perhaps a little too simple!?)
2
 2001, W. E. Haisler
Chapter 1: Introduction
3
The general accounting/conservation statement
 Amount of

  Amount of

 accumulation of   Amount of

   E.P. entering system    E.P. leavinging system 
 

 E.P. within system  



during
time
period
during
time
period

 
 

during
time
period


 Amount of
  Amount of

 E.P. generated
  E.P. consumed




 with insystem
  with insystem


 

during
time
period
during
time
period

 

E.P. = extensive property  mass, linear momentum,
angular momentum, energy
 amount at end   amount at beginning 
Accumulation  



 of time period   of time period

 2001, W. E. Haisler
Chapter 1: Introduction
4
CONTINUUM
A SYSTEM that has MASS and VOLUME
AND whose
PROPERTIES and RESPONSE to INPUT
are continuous FUNCTIONS of SPACE and
TIME and have continuous derivatives
(USUALLY DESCRIBED BY
DIFFERENTIAL EQUATIONS)
 2001, W. E. Haisler
Chapter 1: Introduction
5
What is the difference between ENGR 211 and
214 approaches to Conservation Principles?
ENGR 211
ENGR 214
the free-body diagram of the problem
System
vs.
Continuum
Macro
vs.
Micro Scale
Entire Body vs.
Differential Element
the equations for the problem
Global
vs.
Local Equations
Algebraic
vs.
Differential Equations
 2001, W. E. Haisler
Chapter 1: Introduction
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Examples of System (Macroscopic) vs. Continuum
(Microscopic) Analysis
1. Fluid flow through pipe:
Macroscopic: Consider total flow rate of fluid only
(gallons/minute).
Microscopic: Determine velocity profile of fluid within the
pipe; define energy loss due to friction, etc.
 2001, W. E. Haisler
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Chapter 1: Introduction
2. Heat transfer through a layered wall:
Macroscopic: We know temperature on each side of wall
but cannot determine the details of how the temperature
changes through the wall.
Microscopic: We can determine the details of how the
temperature changes within each layer, the heat flux through
each layer, the effectiveness of insulation, etc.
T
Temperature A
specified on
right boundary
k1
k2
k3
L
1
L
2
L
3
x
TB
Temperature
profile through
thickness
T
C
T
D
h2

inf,2
Convection
specified on
right boundary
 2001, W. E. Haisler
Chapter 1: Introduction
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3. Structural analysis (Beams):
Macroscopic: We can determine only the net forces and
moments, but not the internal stress distribution.
Microscopic: We can determine the details of how the
externally applied loads cause internal forces in the structure
and what these internal forces are at every point in the
structure (can determine stress and strain-recall ENGR 202).