Page 29 - Advanced thermodynamics for engineers

12 CHAPTER 1 INTRODUCTION AND REVISION

This equation can be written as a rate equation giving
2 2 2
!
v V V V
_ _ i e
Q W ¼ U þ þ gz _ m i h i þ þ gz i þ _ m e h e þ þ gz e (1.29)
vt 2 2 2
cv
Equation (1.29) may be simplified to
v V 2 V 2
_ _ i e
Q W ¼ ðEÞ _ m i h i þ þ gz i þ _ m e h e þ þ gz e (1.30)
cv
vt 2 2
Equation (1.30) is called the unsteady flow energy equation (USFEE). It is unsteady because the
conditions existing in the control volume may be functions of time, i.e. v ðEÞ s0.
vt cv
1.5.8.2 Steady flow energy equation
The steady flow energy equation is a particular case of the USFEE, and may be derived from Eqn
(1.30) by making the following assumptions:

• _ m e ¼ _ m i ;
• all velocities, enthalpies and elevations remain constant with time;
• v ðEÞ ¼ 0.
vt cv
Then
2 2
V V i
e
_
_
Q W ¼ _ m h e h i þ 2 þ gðz e z i Þ (1.31)
These assumptions mean that to an observer there appears to be no change in the state of the system
with the passage of time, even though the fluid inside the system is continuously changing.
1.5.8.3 Applications of steady flow energy equation
Applications of the steady flow energy equation are discussed in the web version (http://booksite.
elsevier.com/9780444633736) of Chapter 1.

1.6 CONCLUDING REMARKS
This chapter has summarised the basic definitions of thermodynamics. It has also introduced the
concepts of work and heat – and most importantly emphasised that these are forms of energy transfer.
Work and heat are transitory phenomena that exist only when a system interacts with its surroundings.
However, the net effect of work and heat transfers is to change the energy of the system. The chapter
has also introduced the concepts of open and closed systems, and derived forms of the energy con-
servation equation for both types of system. This chapter provides the building blocks of engineering
thermodynamics up to the First Law: the Second Law is introduced in Chapter 2.

1.7 PROBLEMS
Revision problems relating to this chapter are given in the web version (http://booksite.elsevier.com/
9780444633736) of Chapter 1.