Physics
Power and Efficiency
Power is the rate at which work is done or energy is transferred, measured in watts. Efficiency is a measure of how well a device or system converts input energy into useful output energy. It is calculated by dividing the useful output energy by the total input energy and is often expressed as a percentage.
Written by Perlego with AI-assistance
Related key terms
1 of 5
9 Key excerpts on "Power and Efficiency"
eBook - PDF- Donald F. Elger, Barbara A. LeBret, Clayton T. Crowe, John A. Roberson(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
For example, when electrical power is supplied to a motor, the electric current is clas- sified as a work term. Power Power , which expresses a rate of work or energy, is defined by P ≡ quantity of work (or energy) interval of time = lim Δt →0 ΔW Δt = W · (7.2) *This generalized kind of work is sometimes called thermodynamic work to distinguish it from mechanical work. In this text, we use the label work to represent all types of work, including mechanical work. † This definition comes from chemical engineering professor and Nobel Prize winner John Fenn in his book Engines, Energy, and Entropy: A Thermodynamics Primer, p. 5. Return spring Closed check valve Spray (a) Force Piston (b) Torque FIGURE 7.2 (a) For a spray bottle, the force acting through a distance is an example of mechanical work. (b) For the wind turbine, the pressure of the air causes a torque that acts through an angular displacement. This is also an example of mechanical work. Conservation of Energy 187 Eq. (7.2) is defined at an instant in time because power can vary with time. To calculate power, engineers use several different equations. For rectilinear motion, such as a car or bicycle, the amount of work is the product of force and displacement: ∆W = F∆x. Then, power can be found using P = lim Δt →0 FΔx Δt = FV (7.3a) where V is the velocity of the moving body. When a shaft is rotating (Fig. 7.2b), the amount of work is given by the product of torque and angular displacement, ∆W = T∆θ. In this case, the power equation is P = lim Δt →0 TΔθ Δt = Tω (7.3b) where ω is the angular speed. The SI units of angular speed are rad/s. Because power has units of energy per time, the SI unit is a joule/second, which is called a watt. Common units for power are the watt (W), horsepower (hp), and the ft-lbf/s. Some typi- cal values of power include the following: • An incandescent lightbulb can use 60–100 J/s of energy. • A well-conditioned athlete can sustain a power output of about 300 J/s for an hour.
- Prof. Olav Bolland, Prof. Lars O. Nord(Authors)
- 2020(Publication Date)
- Wiley-VCH(Publisher)
7 Power Plant Efficiency CalculationsThere is diversity in the methodology for calculating power plant efficiencies, which causes a lot of uncertainty when comparing plant options. Several terms are used inconsistently, and often with a lack of definition, for the term efficiency. Terms such as ‘efficiency’, ‘thermal efficiency’, ‘cycle efficiency’, ‘process efficiency’, ‘net/gross efficiency’, ‘net plant efficiency’, ‘electrical efficiency’, ‘total efficiency’, ‘exergy efficiency’, ‘second law efficiency’, ‘fuel efficiency’, and ‘fuel utilisation’ are used, some of them are interchangeable. In addition, many publications dealing with efficiencies give insufficient information about the computational assumptions, e.g. pressure drop, heat loss, temperature differences, and component efficiencies. Further, different software is used with various thermodynamic property models. The definition of system boundaries is often omitted. The diversity observed in efficiency calculation methods is not peculiar to power plants with CO2 capture but can be observed for energy conversion process analysis in general. In the following, an attempt is made to clarify efficiency calculations.7.1 General Definition of Efficiency
Efficiency is the ratio between two energy quantities: the numerator being the energy product of the process and the denominator being the energy input to the process.The energy product from a power plant is the power (or electricity) being delivered at a given boundary. It may also be both power and heat in the case of a cogeneration plant. When there is more than one energy product, the efficiency often becomes confusing, as energy products of different thermodynamics and economic values are added together. In some cases, one of the products of the process may be a substance, such as hydrogen or methanol.The energy input
eBook - PDFGeneral Engineering Science in SI Units
In Two Volumes
- G. W. Marr, N. Hiller(Authors)
- 2016(Publication Date)
- Pergamon(Publisher)
Hence efficiency, W 0 P Q t P 0 η Wi Pit P { ' The efficiency may in such cases be measured by the ratio output power input power * The difference between the amounts of input and output energy represents, as we know, energy which is not available for use as required, and from the practical point of view this energy is wasted. 85 GENERAL ENGINEERING SCIENCE IN SI UNITS This waste energy is frequently referred to as the energy loss. It must be remembered that the use of the word loss is not meant to imply that energy has been lost in the sense that the energy has been destroyed, but only that the energy has not been made available as useful output. If w^ = energy wasted or energy loss, then W 0 = W { -W L9 efficiency = — = -^ — = 1- — . Alternatively, since W 0 = W { -W^ then W { = W 0 +W L9 efficiency = -^ ξ ^ . The corresponding formulae in terms of power are efficiency = -^ -= -^ -= 1 -— . The symbol P L represents the rate at which energy is being wasted, and it is frequently referred to as the power loss, a not altogether satisfactory expression. It represents the decrease in power between input and output, but such an expression is rather cumbersome. In practice the efficiency of a machine is not, in general, constant, although it may be approximately so over a considerable range of power output. The fact that efficiency varies with power output should not cause surprise if one bears in mind the fact that the forms in which energy is wasted are not directly related to the form in which the output energy is required. This point will be better appreciated when particular types of machines are con-sidered. EXAMPLE. A pump raises 2 400 litres of water per min to a height of 5 m. Calculate the power output of the pump. 86 POWER AND ENERGY The pump is driven by an electric motor which operates with an efficiency of 70%.
eBook - PDFGeneral Engineering Science in SI Units
The Commonwealth and International Library: Mechanical Engineering Division
- G. W. Marr, N. Hiller(Authors)
- 2013(Publication Date)
- Pergamon(Publisher)
Suppose that the input energy W { to a machine is supplied at a constant rate for a time /. The power input is then P { = WJt, and hence W { = P { t. Similarly, for constant operating conditions during this period, the output energy is W Q = P Q t, where P 0 is the output power. Hence efficiency, W 0 P 0 t = P 0 V W { Pit P-' The efficiency may in such cases be measured by the ratio output power ' input power * The difference between the amounts of input and output energy represents, as we know, energy which is not available for use as required, and from the practical point of view this energy is wasted. 85 GENERAL ENGINEERING SCIENCE IN SI UNITS This waste energy is frequently referred to as the energy loss. It must be remembered that the use of the word loss is not meant to imply that energy has been lost in the sense that the energy has been destroyed, but only that the energy has not been made available as useful output. If W L = energy wasted or energy loss, then W 0 = W-W^, efficiency = — = — ^ — = l -_ . Alternatively, since W 0 = W { -W L , then W { = W 0 +W L , ffi · W ° efficiency = ~w^wl · The corresponding formulae in terms of power are re · P — PL PO Λ PL e f f i c 1 e n c y = -T -= T -^ -= l --. The symbol P L represents the rate at which energy is being wasted, and it is frequently referred to as the power loss, a not altogether satisfactory expression. It represents the decrease in power between input and output, but such an expression is rather cumbersome. In practice the efficiency of a machine is not, in general, constant, although it may be approximately so over a considerable range of power output. The fact that efficiency varies with power output should not cause surprise if one bears in mind the fact that the forms in which energy is wasted are not directly related to the form in which the output energy is required. This point will be better appreciated when particular types of machines are con-sidered.
eBook - PDFApplied Mathematics
Made Simple
- Patrick Murphy(Author)
- 2014(Publication Date)
- Butterworth-Heinemann(Publisher)
Considering the principle of the conservation of energy in the widest sense, we suggest that although energy can be converted from one form to another it can never be destroyed. This means that the sum of all the different energies in a system remains constant. To illustrate this point consider the energy stored in a gallon of petrol. If this is burned under ideal conditions it will release a certain amount of energy, E say, but if we burn it in a car engine we shall not get an output equivalent to E in order to drive the wheels. Suppose, for example, that we are in a car which burns one gallon of petrol and that we travel with a uniform velocity ν in a straight line for a distance s. Then, assum- Work, Energy, and Power 229 ing that the frictional force F i s constant, the work done by the frictional force is Fs. The burning of petrol has given (Fs + imv 2 ) joules say, but we find that Fs + mv 2 Φ E. So it looks at first as though some energy has been lost or destroyed. However, we have forgotten the work / done against frictional forces in the engine, the energy h lost in heat, and the energy η lost in sound. In fact what we should have written down is Fs + imv 2 +f+h + n + b = E where b accounts for energy lost in overcoming some electrical resistance and so on. From this we can see that if the efficiency of an engine is measured by the motion of the car, the engine will never be 100 per cent efficient since so much energy will have been lost to forces which do not contribute to the motion of the car. The efficiency with which one form of energy is converted into another dominates engineering design. The simplest mechanical example is the typical hydroelectric scheme where a lake of water is dammed and the water flow then regulated to feed through tunnels to drive machinery in order to generate electricity. This is a straightforward conversion of the water's potential energy into kinetic energy.
eBook - PDF- Jerry B. Marion(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
Chapter Æ* WORK , ENERGY , AND POWE R We all hav e some intuitiv e notion s abou t th e quantit y tha t is th e centra l topi c of thi s book— energy. We kno w tha t we must bu y gasolin e to suppl y th e energ y tha t run s our automobiles , and we pa y a monthl y bill to th e electri c compan y for th e electri c energ y tha t is delivere d to our homes . We understan d tha t coal, oil, and gas pla y importan t role s in supplyin g th e energ y tha t is necessar y for our everyda y living. But to pursu e our topi c in detai l we need mor e tha n thes e qualitativ e ideas . We need to understan d some of th e basi c physica l principle s tha t govern situation s involvin g energy . Befor e we can begin a meaningfu l discussio n of energ y problems , we mus t establis h th e languag e we will use. Tha t is, we must defin e th e term s and th e unit s tha t ar e necessar y to describ e variou s situation s involvin g energy . We will requir e only a few of th e larg e numbe r of th e term s tha t appl y to physica l quantities—primarily , work, energy, and power. Th e unit s we will use ar e metric units—meters , kilograms , and seconds , as well as a few derive d unit s such as watt s and kilowatt-hours . Thus , we will emplo y only a limite d vocabulary , one designe d to cover only th e situation s of immediat e interest . THE DEFINITION OF WOR K We frequentl y use th e ter m work in ordinar y conversation . We might say, for example , Tha t job require s a grea t dea l of work. Wha t does work reall y mean here ? If you lift a numbe r of heav y boxes from floor level an d plac e them on a high shelf, you will feel tire d afte r th e job is completed—yo u 9 10 2. WORK , ENERGY , AND POWE R will kno w tha t you hav e don e work. This is exactl y right. Gravit y pull s th e boxes downwar d and when you lift th e boxes, you ar e doin g work agains t th e gravitationa l force . In its physica l meaning , work alway s involves overcomin g some opposin g force .
eBook - PDFEngineering Mechanics
Problems and Solutions
- Arshad Noor Siddiquee, Zahid A. Khan, Pankul Goel(Authors)
- 2018(Publication Date)
- Cambridge University Press(Publisher)
13.4. If the particle is infinitesimally displaced by displacement ‘ ds ’ during time ‘ dt ’ then the work done by pushing force will be given by δ δ w F ds w m a ds a dv dt = = = . . . where Substituting the value of a in equation (1), δ δ δ w m dv dt ds w m ds dt dv w m v dv = = = . . . . . . ..... (1) 594 Engineering Mechanics If the particle is finally displaced by distance ‘s’ from position 1 to position 2 (not shown), then work done can be determine by integrating the above equation, δ δ w m v dv w m v dv W m v v 1 2 1 2 1 2 1 2 2 2 1 2 1 2 ∫ ∫ ∫ ∫ = = = -( ) . . . Work done = Change in kinetic energy of the particle Thus according to this principle, the work done on a moving particle is equal to the change in its kinetic energy. This principle is useful when kinetic problems are required to be exclusively dealt with in variation of velocities. 13.6 Power Power is a term which designates the work performed with minimum time. For example, a person wants to travel a distance of 5 km. Suppose he travels the same distance by three different modes, i.e., by walking, bicycle and motor cycle, and takes time 70 min, 25 min, and 8 min, respectively. Thus the work performed in the third case is most meaningful as it is conducted with the least time. Hence power is the capacity of a machine to perform work with respect to time or it is the rate at which work is performed. If a machine performs work W in total time duration t then, the average power of such machine will be given by P W t avg = F mg ds v 1 v 2 Fig. 13.4 Work and Energy 595 If a machine performs work δw for instant time dt then the instantaneous power of machine will be given by P w dt w F ds P F ds dt P F dv inst inst inst = = = = δ δ as . . . Hence, Power P = F. v Power is expressed in watt or joule per second in S.I. units. However, in electrical and mechanical equipment devices like motor and engine, the power is defined in terms of horsepower (hp).
- Paul Anthony Russell(Author)
- 2021(Publication Date)
- Reeds(Publisher)
vertical height is raised mm 0.2342 m G GO GA = - = - = = 309 2 75 234 2 . . work done weight vertical lift of J = × = × = G 1040 0 2342 243 5 . . Ans. (ii) Power POWER is the rate of doing work, or the quantity of work completed in a given time. The unit of power is the watt, which is equal to the rate 1 joule of work being done every second. power J/s Nm/s) force velocity work done (for small ( W F ds = = = × = displacement) power (for small time interval) (i = = F ds dt P Fv nstantaneous velocity ) v 84 • Applied Mechanics When describing the power generated in marine engineering applications, either mechanical, electrical or hydraulic, the kilowatt (kW) is usually a more convenient unit of measure, due to the size of the power that is being generated. Example 4.2. A pump lifts fresh water from one tank to another through an effective height of 12 m. If the mass flow of water is 40 t/h, find the output power of the pump. 40 40 10 9 81 3 3 t kg weight of water lifted per second 40 10 3 = × = × × . 600 9 81 1 N power weight lifted per second height = 40 10 3 = × × × × . 2 3600 1308 W W or 1.308 kW P = MECHANICAL EFFICIENCY is the ratio of power that comes out of a machine compared to the power that is put in, therefore: mechanical efficiency output power input power = This will always give a fraction less than unity; however, it is common practice to multiply the result by 100 and express the efficiency as a percentage. For example, if the input power of the pump in Example 4.2 was 1.75 kW, then the efficiency would be ℑ= = = output power input power or 74.74% 1 308 1 75 0 7474 . . . PRESSURE is defined as the force per unit area. It is measured in units of N/m 2 and is used in calculating power. POWER OF RECIPROCATING ENGINES. When a gas or a liquid acts on a piston in a closed cylinder, the pressure multiplied by the piston area on which the pressure acts gives the total force on the piston.
eBook - PDF- Donald F. Elger, Barbara A. LeBret, Clayton T. Crowe, John A. Roberson(Authors)
- 2022(Publication Date)
- Wiley(Publisher)
Chapter 7: The Energy Equation 260 7.5 MECHANICAL EFFICIENCY Figure 7.6 shows an electric motor connected to a centrifugal pump. Motors, pumps, turbines, and similar devices have energy losses. In pumps and turbines, energy losses are caused by fac- tors such as mechanical friction, viscous dissipation, and leakage. Energy losses are accounted for by using efficiency. Mechanical efficiency is defined as the ratio of power output to power input: η ≡ power output from a machine or system _________________________________ power input to a machine or system = P output _ P input (7.32) The symbol for mechanical efficiency is the Greek letter η, which is pronounced as “eta.” In addition to mechanical efficiency, engineers use thermal efficiency, which is defined using ther- mal energy input into a system. In this text, only mechanical efficiency is used, and we some- times use the label “efficiency” instead of “mechanical efficiency.” EXAMPLE Suppose an electric motor like the one shown in Fig. 7.6 is drawing 1000 W of electrical power from a wall circuit. As shown in Fig. 7.7, the motor provides 750 J/s of power to its output shaft. This power drives the pump, and the pump supplies 450 J/s to the fluid. FIGURE 7.6 CAD drawing of a centrifugal pump and electric motor. (Image courtesy of Ted Kyte; www.ted-kyte.com.) Physics: The head provided by the pump (67.3 m) is balanced by the increase in pressure head (42.3 m) plus the increase in elevation head (20 m) plus the head loss (5 m). 4. Power equation: P = γQ h p = (9810 N / m 3 ) (1.0 m 3 / s) (67.3 m) = 660.2 kW = (660.2 kW) ( 1.0 hp _ 0.746 kW ) = 885 hp Review the Solution and the Process Discussion. The calculated power represents the work/time being done by the pump impeller on the water. The electrical power supplied to the pump would need to be larger than this because of energy losses in the electrical motor and because the pump itself is not 100% efficient.
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
