Technology & Engineering
Energy Equation
The energy equation is a fundamental principle in physics and engineering that describes the conservation of energy within a system. It states that the total energy of a system remains constant, with energy being transferred or transformed but never created or destroyed. The equation is often used to analyze and solve problems related to energy transfer and conversion in various engineering applications.
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6 Key excerpts on "Energy Equation"
eBook - PDF- Donald F. Elger, Barbara A. LeBret, Clayton T. Crowe, John A. Robertson(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
228 CHAPTER 7 • THE Energy Equation 7.1 Technical Vocabulary: Work, Energy, and Power Conservation of energy is perhaps the single most useful equation in all of engineering. The key to applying this equation is to have solid knowledge of the foundational concepts of energy, work, and power. In addition to reviewing these topics, this section also defines pumps and turbines. Energy Energy is the property of a system that characterizes the amount of work that this system can do on its environment. In simple terms, if matter (i.e., the system) can be used to lift a weight, then that matter has energy. Examples • Water behind a dam has energy because the water can be directed through a pipe (i.e., a penstock), then used to rotate a wheel (i.e., a water turbine) that lifts a weight. Of course, this work can also rotate the shaft of an electrical generator, which is used to produce electrical power. • Wind has energy because the wind can pass across a set of blades (e.g., a windmill), rotate the blades, and lift a weight that is attached to a rotating shaft. This shaft can also do work to rotate the shaft of an electrical generator. • Gasoline has energy because it can be placed into a cylinder (e.g., a gas engine), burned, and expanded to move a piston in a cylinder. This moving cylinder can then be connected to a mechanism that is used to lift a weight. The SI unit of energy, the joule, is the energy associated with a force of one newton acting through a distance of one meter. For example, if a person with a weight of 700 newtons travels up a 10-meter flight of stairs, then their gravitational potential energy has changed by ΔPE = (700 N)(10 m) = 700 N∙m = 700 J. In traditional units, the unit of energy, the foot-pound force (lbf) is defined as energy associated with a force of 1.0 lbf moving through a distance of 1.0 foot. Another way to define a unit of energy is describe the heating of water.
- S. Bobby Rauf(Author)
- 2021(Publication Date)
- River Publishers(Publisher)
Law of Conservation of Energy The law of conservation of energy states that energy can be con-verted from one form to another but cannot be created or destroyed . This can be expressed, mathematically, as: 8 Thermodynamics Made Simple for Energy Engineers ∑ E = ∑ Energy = Constant Table 1-3. Rankin Temperature Conversion Formulas Table 1-4. Kelvin Temperature Conversion Factors FORMS OF ENERGY IN MECHANICAL AND THERMODYNAMIC SYSTEMS Potential Energy Potential energy is defned as energy possessed by an object by vir-tue of its height or elevation. Potential energy can be defned, mathemati-cally, as follows: E potential = m.g.h, {SI Units} Eq. 1-8 E potential = m.(g/g c ).h, US Units} Eq. 1-8a When the change in potential energy is achieved through performance of work, W : W = Δ E potential Eq. 1-9 9 Introduction to Energy, Heat, and Thermodynamics Kinetic Energy Kinetic energy is defned as energy possessed by an object by virtue of its motion. Kinetic energy can be defned, mathematically, as follows: E kinetic = ½.m.v 2 {SI Units} Eq. 1-10 E kinetic = ½. (m/g c ). v 2 {US Units} Eq. 1-10a Where, m = mass of the object in motion v = velocity of the object in motion g c = 32 lbm-ft/lbf-s 2 When the change in kinetic energy is achieved through performance of work, W : W = Δ E kinetic Eq. 1-11 Energy Stored in a Spring 2 Potential energy can be stored in a spring—or in any elastic object— by compression or extension of the spring. Potential energy stored in a spring can be expressed, mathematically, as follows: E spring = ½.k.x 2 Eq. 1-12 And, W spring = Δ E spring Eq. 1-13 Where, k = The spring constant x = The contraction or expansion of the spring 2 Note: In steel beam systems, beams act as springs, when loaded, to a certain degree. The defection of a beam would represent the “ x ,” in Eq. 1-11. Pressure Energy Energy stored in a system in form of pressure is referred to as pres- 10 Thermodynamics Made Simple for Energy Engineers sure energy.
eBook - PDF- Donald F. Elger, Barbara A. LeBret, Clayton T. Crowe, John A. Roberson(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
The Energy Equation CHAPTER ROAD MAP This chapter describes how conservation of energy can be applied to a flowing fluid. The resulting equation, called the Energy Equation, can be applied to solve many problems; see Fig. 7.1 for an example. CHAPTERSEVEN LEARNING OUTCOMES WORK AND ENERGY (§7.1) ● Define energy, work, and power. ● Define a pump and a turbine. ● Classify energy into categories. ● Know common units. CONSERVATION OF ENERGY FOR A CLOSED SYSTEM (§7.2) ● Know the main ideas about conservation of en- ergy for a closed system. ● Apply the equation(s) to solve problems and answer questions. THE Energy Equation (§7.3) ● Know the most important ideas about the Energy Equation. ● Calculate α. ● Define flow work and shaft work. ● Define head and know the various types of head. ● Apply the Energy Equation to solve problems. THE POWER EQUATION (§7.4) ● Know the concepts associated with each of the power equations. ● Solve problems that involve the power equation. EFFICIENCY (§7.4) ● Define mechanical efficiency. ● Solve problems that involve efficiency of compo- nents such as pumps and turbines. THE SUDDEN EXPANSION (§7.7) ● Calculate the head loss for a sudden expansion. THE EGL/HGL (§7.8) ● Explain the main ideas about the EGL and HGL. ● Sketch the EGL and HGL. ● Solve problems that involve the EGL and HGL. FIGURE 7.1 The Energy Equation can be applied to hydroelectric power generation. In addition, the Energy Equation can be applied to thousands of other applications. It is one of the most useful equations in fluid mechanics. Penstock Flow Generator Power lines Power house Turbine 184 Technical Vocabulary: Work, Energy, and Power 185 7.1 Technical Vocabulary: Work, Energy, and Power Conservation of energy is perhaps the single most useful equation in all of engineering. The key to applying this equation is to have solid knowledge of the foundational concepts of energy, work, and power.
eBook - PDF- Donald F. Elger, Barbara A. LeBret, Clayton T. Crowe, John A. Roberson(Authors)
- 2022(Publication Date)
- Wiley(Publisher)
CHAPTER ROAD MAP This chapter describes how conservation of energy can be applied to a flowing fluid. The resulting equation, called the Energy Equation, can be applied to solve many problems. CHAPTER 7 The Energy Equation 7.1 TECHNICAL VOCABULARY: WORK, ENERGY, AND POWER Conservation of energy is perhaps the single most useful equation in all of engineering. The key to applying this equation is to have solid knowledge of the foundational concepts of energy, work, and power. In addition to reviewing these topics, this section also defines pumps and turbines. Energy Energy is the property of a system that characterizes the amount of work that this system can do on its environment. In simple terms, if matter (i.e., the system) can be used to lift a weight, then that matter has energy. Examples • Water behind a dam has energy because the water can be directed through a pipe (i.e., a penstock), then used to rotate a wheel (i.e., a water turbine) that lifts a weight. Of course, this work can also rotate the shaft of an electrical generator, which is used to produce electrical power. LEARNING OUTCOMES WORK AND ENERGY (§7.1) • Define energy, work, and power. • Define a pump and a turbine. • Classify energy into categories. • Know common units. CONSERVATION OF ENERGY FOR A CLOSED SYSTEM (§7.2) • Know the main ideas about conservation of energy for a closed system. • Apply the equation(s) to solve problems and answer questions. THE Energy Equation (§7.3) • Know the most important ideas about the Energy Equation. • Calculate α. • Define flow work and shaft work. • Define head and know the various types of head. • Apply the Energy Equation to solve problems. THE POWER EQUATION (§7.4) • Know the concepts associated with each of the power equations. • Solve problems that involve the power equation. EFFICIENCY (§7.4) • Define mechanical efficiency. • Solve problems that involve efficiency of components such as pumps and turbines.
eBook - PDFApplied Energy
An Introduction
- Mohammad Omar Abdullah(Author)
- 2012(Publication Date)
- CRC Press(Publisher)
1.3.2 The Energy Availability Equation (Second Law of Thermodynamics) The energy availability equation can be expressed in a simple equation as follows: ds ≥ 0 (1.13) where s is the entropy for an isolated system. A simple definition of entropy s is that it is the amount of energy that is not available for work for a system. In other words it is the energy form of a system that relates to its internal state of disorder ∗ — which contributes to loss or disturbance. The higher entropy denotes bigger disordered states, thus more energy loss from the system. Just for a quick review revision on entropy s , we shall already note and are quite familiar with the property s that appears in many charts and tables of properties; and we also have read lines of constant entropy on many graphs. For example, in a T-s diagram, e.g., Figure 1.5, the shaded area or 2 1 T ds represents the heat supply usually denoted with Q . 1.3.3 General Mechanical Energy Equation The General Mechanical Energy Equation is a statement of the conservation of energy principle. It involves energy, heat transfer, and work. Here are some of the Energy Equations in various forms, with relation to common energy applications, and with their respective importance. Energy content per unit mass of a closed system in rate form Applying the energy conservation law, the energy content per unit mass of a closed system can be changed by energy input applied on the system, i.e., heat transfer (Q) and work transfer (W). Therefore, we can write conservation of energy for a closed system, expressed in rate form, as dE system dt = ˙ Q net,in + ˙ W net,in (1.14) ∗ This includes excitation of quantum states at the microscopic level.
eBook - ePubEnergy Demand And Economic Growth
Measurement And Conceptual Issues In Policy Analysis
- Corazon M Siddayao(Author)
- 2021(Publication Date)
- Routledge(Publisher)
1 In fact, the term was intended to take account of the fact that heat and work are interchangeable. Although they are interchangeable, however, a given quantity of heat does not always yield the same quantity of work. Definitional problems thus arise principally because various energy forms have different capacities to do work. Several terms have been used to describe this condition; one of them is thermal efficiency. One might also refer to the problem as that of defining the level of effective energy. In addition, intertemporal considerations and interdependence within a system require recognition of the concept of embodied energy. These and other basic issues are summarized in this section.The most important definitional question concerning energy arises from the vagueness with which the term is used. In most current discussions on the "energy problem," the principal focus tends to be on the heat quality of energy. However, energy is also stored work. The heat it produces may be intense enough to emit light. Heat, light, motive force, and chemical change induced by, or resulting in, electricity are all manifestations of energy. The combustible sources of energy may be transformed into electricity. Mechanical energy and electricity may also be derived from the kinetic energy of a mass of water that moves from one level to another (e.g., a dam, river falls, tides, waves) or from a mass of air that moves from a higher to a lower pressure area. Heat may be produced through combustion or fission of a suitable fuel, compression of a suitable liquid or gaseous medium, from the capture of the sun's rays, from hot rocks below the surface of the earth, from the passage of electricity through an appropriate material, or from certain exothermic chemical processes.2Enthalpy, the heat content of a substance, H, is a thermodynamic property defined as the internal energy, E, plus the product of the pressure, P, multiplied by the volume, V, of that substance:H = E + PVIt contains the units of energy and is usually expressed in calories (or kilocalories) or in British thermal units (Btus).3 (See Appendix 1.1) The joule is the only energy unit recognized by the SystSme International d'Unites (SI ). It was first promulgated as the SI unit of energy in 1946 and then as the SI
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