Chapter5 - 05-R3868 10:13 AM Page 119 CHAPTER MASS...

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MASS, BERNOULLI, AND ENERGY EQUATIONS 119 CHAPTER 5 OBJECTIVES When you finish reading this chapter, you should be able to Apply the conservation of mass equation to balance the incoming and outgoing flow rates in a flow system Recognize various forms of mechanical energy, and work with energy conversion efficiencies Understand the use and limitations of the Bernoulli equation, and apply it to solve a variety of fluid flow problems Work with the energy equation expressed in terms of heads, and use it to determine turbine power output and pumping power requirements Wind turbine “farms” are being constructed all over the world to extract kinetic energy from the wind and convert it to electrical energy. The mass, energy, momentum, and angular momentum balances are utilized in the design of a wind turbine. T his chapter deals with three equations commonly used in fluid mechan- ics: the mass, Bernoulli, and energy equations. The mass equation is an expression of the conservation of mass principle. The Bernoulli equa- tion is concerned with the conservation of kinetic, potential, and flow ener- gies 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 prin- ciple. In fluid mechanics, it is found 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 becomes the mechanical energy balance . We start this chapter with an overview of conservation principles and the conservation of mass relation. This is followed by 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 devel- opment 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 equa- tion to various engineering systems.
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5–1 INTRODUCTION You are already familiar with numerous conservation laws such as the laws of conservation of mass, conservation of energy, and conservation of momentum. Historically, the conservation laws are first applied to a fixed quantity of matter called a closed system or just a system , and then extended to regions in space called control volumes . The conservation relations are also called balance equations since any conserved quantity must balance during a process. We now give a brief description of the conservation of mass and energy relations, and the linear momentum equation (Fig. 5–1).
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