Bernoulli and energy equations
cen54261_ch12.qxd
12/9/03
1:30 PM
Page 519
CHAPTER
BERNOULLI AND ENERGY
E Q U AT I O N S his chapter deals with two equations commonly used in fluid mechanics: the Bernoulli equation and the energy equation. The Bernoulli equation is concerned with the conservation of kinetic, potential, and flow energies of a fluid stream, and their conversion to each other in regions of flow where net viscous forces are negligible, and where other restrictive conditions apply. The energy equation is a statement of the conservation of energy principle and is applicable under all conditions. In fluid mechanics, it is found to be convenient to separate mechanical energy from thermal energy and to consider the conversion of mechanical energy to thermal energy as a result of frictional effects as mechanical energy loss. Then the energy equation is usually expressed as the conservation of mechanical energy.
We start this chapter with a discussion of various forms of mechanical energy and the efficiency of mechanical work devices such as pumps and turbines. Then we derive the Bernoulli equation by applying Newton’s second law to a fluid element along a streamline and demonstrate its use in a variety of applications. We continue with the development of the energy equation in a form suitable for use in fluid mechanics and introduce the concept of head loss. Finally, we apply the energy equation to various engineering systems.
T
12
CONTENTS
12–1 Mechanical Energy and
Efficiency 520
12–2 The Bernoulli Equation 525
12–3 Applications of the Bernoulli
Equation 534
12–4 Energy Analysis of Steady-Flow
Systems 541
Summary 549
References and Suggested
Reading 551
Problems 551
519
cen54261_ch12.qxd
2/6/04
1:10 PM
Page 520
520
FUNDAMENTALS OF THERMAL-FLUID SCIENCES
12–1
z
Atmosphere
·
W
h = 10 m
1
0
· m = 2 kg/s
·
· P1 – Patm
· ρgh ·
Wmax = m ––––––––– = m ––– = mgh ρ ρ
= (2 kg/s)(9.81 m/s2)(10 m)
= 196 W
12/9/03
1:30 PM
Page 519
CHAPTER
BERNOULLI AND ENERGY
E Q U AT I O N S his chapter deals with two equations commonly used in fluid mechanics: the Bernoulli equation and the energy equation. The Bernoulli equation is concerned with the conservation of kinetic, potential, and flow energies of a fluid stream, and their conversion to each other in regions of flow where net viscous forces are negligible, and where other restrictive conditions apply. The energy equation is a statement of the conservation of energy principle and is applicable under all conditions. In fluid mechanics, it is found to be convenient to separate mechanical energy from thermal energy and to consider the conversion of mechanical energy to thermal energy as a result of frictional effects as mechanical energy loss. Then the energy equation is usually expressed as the conservation of mechanical energy.
We start this chapter with a discussion of various forms of mechanical energy and the efficiency of mechanical work devices such as pumps and turbines. Then we derive the Bernoulli equation by applying Newton’s second law to a fluid element along a streamline and demonstrate its use in a variety of applications. We continue with the development of the energy equation in a form suitable for use in fluid mechanics and introduce the concept of head loss. Finally, we apply the energy equation to various engineering systems.
T
12
CONTENTS
12–1 Mechanical Energy and
Efficiency 520
12–2 The Bernoulli Equation 525
12–3 Applications of the Bernoulli
Equation 534
12–4 Energy Analysis of Steady-Flow
Systems 541
Summary 549
References and Suggested
Reading 551
Problems 551
519
cen54261_ch12.qxd
2/6/04
1:10 PM
Page 520
520
FUNDAMENTALS OF THERMAL-FLUID SCIENCES
12–1
z
Atmosphere
·
W
h = 10 m
1
0
· m = 2 kg/s
·
· P1 – Patm
· ρgh ·
Wmax = m ––––––––– = m ––– = mgh ρ ρ
= (2 kg/s)(9.81 m/s2)(10 m)
= 196 W