Advanced Rail Energy Storage (ARES)
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												Energy Literacy Essential Principles and Fundamental Concepts for Energy Education
Energy Literacy Essential Principles and Fundamental Concepts for Energy Education A Framework for Energy Education for Learners of All Ages About This Guide Energy Literacy: Essential Principles and Intended use of this document as a guide includes, Fundamental Concepts for Energy Education but is not limited to, formal and informal energy presents energy concepts that, if understood and education, standards development, curriculum applied, will help individuals and communities design, assessment development, make informed energy decisions. and educator trainings. Energy is an inherently interdisciplinary topic. Development of this guide began at a workshop Concepts fundamental to understanding energy sponsored by the Department of Energy (DOE) arise in nearly all, if not all, academic disciplines. and the American Association for the Advancement This guide is intended to be used across of Science (AAAS) in the fall of 2010. Multiple disciplines. Both an integrated and systems-based federal agencies, non-governmental organizations, approach to understanding energy are strongly and numerous individuals contributed to the encouraged. development through an extensive review and comment process. Discussion and information Energy Literacy: Essential Principles and gathered at AAAS, WestEd, and DOE-sponsored Fundamental Concepts for Energy Education Energy Literacy workshops in the spring of 2011 identifies seven Essential Principles and a set of contributed substantially to the refinement of Fundamental Concepts to support each principle. the guide. This guide does not seek to identify all areas of energy understanding, but rather to focus on those To download this guide and related documents, that are essential for all citizens. The Fundamental visit www.globalchange.gov. Concepts have been drawn, in part, from existing education standards and benchmarks. - 
												
												Energetics of a Turbulent Ocean
Energetics of a Turbulent Ocean Raffaele Ferrari January 12, 2009 1 Energetics of a Turbulent Ocean One of the earliest theoretical investigations of ocean circulation was by Count Rumford. He proposed that the meridional overturning circulation was driven by temperature gradients. The ocean cools at the poles and is heated in the tropics, so Rumford speculated that large scale convection was responsible for the ocean currents. This idea was the precursor of the thermohaline circulation, which postulates that the evaporation of water and the subsequent increase in salinity also helps drive the circulation. These theories compare the oceans to a heat engine whose energy is derived from solar radiation through some convective process. In the 1800s James Croll noted that the currents in the Atlantic ocean had a tendency to be in the same direction as the prevailing winds. For example the trade winds blow westward across the mid-Atlantic and drive the Gulf Stream. Croll believed that the surface winds were responsible for mechanically driving the ocean currents, in contrast to convection. Although both Croll and Rumford used simple theories of fluid dynamics to develop their ideas, important qualitative features of their work are present in modern theories of ocean circulation. Modern physical oceanography has developed a far more sophisticated picture of the physics of ocean circulation, and modern theories include the effects of phenomena on a wide range of length scales. Scientists are interested in understanding the forces governing the ocean circulation, and one way to do this is to derive energy constraints on the differ- ent processes in the ocean. - 
												
												STARS in HYDROSTATIC EQUILIBRIUM Gravitational Energy
STARS IN HYDROSTATIC EQUILIBRIUM Gravitational energy and hydrostatic equilibrium We shall consider stars in a hydrostatic equilibrium, but not necessarily in a thermal equilibrium. Let us define some terms: U = kinetic, or in general internal energy density [ erg cm −3], (eql.1a) U u ≡ erg g −1 , (eql.1b) ρ R M 2 Eth ≡ U4πr dr = u dMr = thermal energy of a star, [erg], (eql.1c) Z Z 0 0 M GM dM Ω= − r r = gravitational energy of a star, [erg], (eql.1d) Z r 0 Etot = Eth +Ω = total energy of a star , [erg] . (eql.1e) We shall use the equation of hydrostatic equilibrium dP GM = − r ρ, (eql.2) dr r and the relation between the mass and radius dM r =4πr2ρ, (eql.3) dr to find a relations between thermal and gravitational energy of a star. As we shall be changing variables many times we shall adopt a convention of using ”c” as a symbol of a stellar center and the lower limit of an integral, and ”s” as a symbol of a stellar surface and the upper limit of an integral. We shall be transforming an integral formula (eql.1d) so, as to relate it to (eql.1c) : s s s GM dM GM GM ρ Ω= − r r = − r 4πr2ρdr = − r 4πr3dr = (eql.4) Z r Z r Z r2 c c c s s s dP s 4πr3dr = 4πr3dP =4πr3P − 12πr2P dr = Z dr Z c Z c c c s −3 P 4πr2dr =Ω. Z c Our final result: gravitational energy of a star in a hydrostatic equilibrium is equal to three times the integral of pressure within the star over its entire volume. - 
												
												Energy Conservation in a Spring
Part II: Energy Conservation in a Spring Activity 4 Title: Forces and Energy in a Spring Summary: Students will use the “Masses and Springs” simulation from PhET to investigate the relationship between gravitational potential energy, spring potential energy, and mass. Standard: PS2 (Ext) - 5 Students demonstrate an understanding of energy by… 5aa Identifying, measuring, calculating and analyzing qualitative and quantitative relationships associated with energy transfer or energy transformation. Specific Learning Goals: 1. Understand how to calculate the force constant of a spring using the formula F = -k ∆x 2. Understand that even though energy is transformed during the oscillation of a spring among gravitational potential energy, elastic potential energy, and kinetic energy, the total energy in the system remains constant. 3. Understand how to calculate the gravitational potential energy for a mass which is lifted to a height above a table. 4. Understand how to calculate the elastic potential energy for a spring which has been displaced by a certain distance. Prior Knowledge: 1. The restoring force that a spring exerts on a mass is proportional to the displacement of the spring and the spring constant and is in a direction opposite the displacement: F = -k ∆x 2. Gravitational potential energy is calculated by the formula: PEg = mgΔh 2 3. Elastic potential energy is calculated by the formula: PEs = ½ k ∆x 4. In a mass and spring system at equilibrium, the restoring force is equal to the gravitational force on the suspended mass (Fg = mg) Schedule: 40-50 minutes Materials: “Masses and Springs 2.02 PhET” Engage: Three different masses are suspended from a spring. - 
												
												Work and Energy Summary Sheet Chapter 6
Work and Energy Summary Sheet Chapter 6 Work: work is done when a force is applied to a mass through a displacement or W=Fd. The force and the displacement must be parallel to one another in order for work to be done. F (N) W =(Fcosθ)d F If the force is not parallel to The area of a force vs. the displacement, then the displacement graph + W component of the force that represents the work θ d (m) is parallel must be found. done by the varying - W d force. Signs and Units for Work Work is a scalar but it can be positive or negative. Units of Work F d W = + (Ex: pitcher throwing ball) 1 N•m = 1 J (Joule) F d W = - (Ex. catcher catching ball) Note: N = kg m/s2 • Work – Energy Principle Hooke’s Law x The work done on an object is equal to its change F = kx in kinetic energy. F F is the applied force. 2 2 x W = ΔEk = ½ mvf – ½ mvi x is the change in length. k is the spring constant. F Energy Defined Units Energy is the ability to do work. Same as work: 1 N•m = 1 J (Joule) Kinetic Energy Potential Energy Potential energy is stored energy due to a system’s shape, position, or Kinetic energy is the energy of state. motion. If a mass has velocity, Gravitational PE Elastic (Spring) PE then it has KE 2 Mass with height Stretch/compress elastic material Ek = ½ mv 2 EG = mgh EE = ½ kx To measure the change in KE Change in E use: G Change in ES 2 2 2 2 ΔEk = ½ mvf – ½ mvi ΔEG = mghf – mghi ΔEE = ½ kxf – ½ kxi Conservation of Energy “The total energy is neither increased nor decreased in any process. - 
												
												Potential Energy
Potential Energy • So far: Considered all forces equal, calculate work done by net force only => Change in kinetic energy. – Analogy: Pure Cash Economy • But: Some forces seem to be able to “store” the work for you (when they do negative work) and “give back” the same amount (when they do positive work). – Analogy: Bank Account. You pay money in (ending up with less cash) - the money is stored for you - you can withdraw it again (get cash back) • These forces are called “conservative” (they conserve your work/money for you) Potential Energy - Example • Car moving up ramp: Weight does negative work ΔW(grav) = -mgΔh • Depends only on initial and final position • Can be retrieved as positive work on the way back down • Two ways to describe it: 1) No net work done on car on way up F Pull 2) Pulling force does positive F Normal y work that is stored as gravitational x potential energy ΔU = -ΔW(grav) α F Weight Total Mechanical Energy • Dimension: Same as Work Unit: Nm = J (Joule) Symbol: E = K.E. + U 1) Specify all external *) forces acting on a system 2) Multiply displacement in the direction of the net external force with that force: ΔWext = F Δs cosφ 3) Set equal to change in total energy: m 2 m 2 ΔE = /2vf - /2vi + ΔU = ΔWext ΔU = -Wint *) We consider all non-conservative forces as external, plus all forces that we don’t want to include in the system. Example: Gravitational Potential Energy *) • I. Motion in vertical (y-) direction only: "U = #Wgrav = mg"y • External force: Lift mass m from height y i to height y f (without increasing velocity) => Work gets stored as gravitational potential energy ΔU = mg (yf -yi)= mg Δy ! • Free fall (no external force): Total energy conserved, change in kinetic energy compensated by change in m 2 potential energy ΔK.E. - 
												
												How Long Would the Sun Shine? Fuel = Gravitational Energy? Fuel
How long would the Sun shine? Fuel = Gravitational Energy? • The mass of the Sun is M = 2 x 1030 kg. • The Sun needs fuel to shine. – The amount of the fuel should be related to the amount of – The Sun shines by consuming the fuel -- it generates energy mass. from the fuel. • Gravity can generate energy. • The lifetime of the Sun is determined by – A falling body acquires velocity from gravity. – How fast the Sun consumes the fuel, and – Gravitational energy = (3/5)GM2/R – How much fuel the Sun contains. – The radius of the Sun: R = 700 million m • How fast does the Sun consume the fuel? – Gravitational energy of the Sun = 2.3 x 1041 Joules. – Energy radiated per second is called the “luminosity”, which • How long could the Sun shine on gravitational energy? is in units of watts. – Lifetime = (Amount of Fuel)/(How Fast the Fuel is – The solar luminosity is about 3.8 x 1026 Watts. Consumed) 41 26 • Watts = Joules per second – Lifetime = (2.3 x 10 Joules)/(3.8 x 10 Joules per second) = 0.6 x 1015 seconds. • Compare it with a light bulb! – Therefore, the Sun lasts for 20 million years (Helmholtz in • What is the fuel?? 1854; Kelvin in 1887), if gravity is the fuel. Fuel = Nuclear Energy Burning Hydrogen: p-p chain • Einstein’s Energy Formula: E=Mc2 1 1 2 + – The mass itself can be the source of energy. • H + H -> H + e + !e 2 1 3 • If the Sun could convert all of its mass into energy by • H + H -> He + " E=Mc2… • 3He + 3He -> 4He + 1H + 1H – Mass energy = 1.8 x 1047 Joules. - 
												
												Innovation Insights Brief | 2020
FIVE STEPS TO ENERGY STORAGE Innovation Insights Brief | 2020 In collaboration with the California Independent System Operator (CAISO) ABOUT THE WORLD ENERGY COUNCIL ABOUT THIS INSIGHTS BRIEF The World Energy Council is the principal impartial This Innovation Insights brief on energy storage is part network of energy leaders and practitioners promoting of a series of publications by the World Energy Council an affordable, stable and environmentally sensitive focused on Innovation. In a fast-paced era of disruptive energy system for the greatest benefit of all. changes, this brief aims at facilitating strategic sharing of knowledge between the Council’s members and the Formed in 1923, the Council is the premiere global other energy stakeholders and policy shapers. energy body, representing the entire energy spectrum, with over 3,000 member organisations in over 90 countries, drawn from governments, private and state corporations, academia, NGOs and energy stakeholders. We inform global, regional and national energy strategies by hosting high-level events including the World Energy Congress and publishing authoritative studies, and work through our extensive member network to facilitate the world’s energy policy dialogue. Further details at www.worldenergy.org and @WECouncil Published by the World Energy Council 2020 Copyright © 2020 World Energy Council. All rights reserved. All or part of this publication may be used or reproduced as long as the following citation is included on each copy or transmission: ‘Used by permission of the World - 
												
												Gravitational Potential Energy
An easy way for numerical calculations • How long does it take for the Sun to go around the galaxy? • The Sun is travelling at v=220 km/s in a mostly circular orbit, of radius r=8 kpc REVISION Use another system of Units: u Assume G=1 Somak Raychaudhury u Unit of distance = 1kpc www.sr.bham.ac.uk/~somak/Y3FEG/ u Unit of velocity= 1 km/s u Then Unit of time becomes 109 yr •Course resources 5 • Website u And Unit of Mass becomes 2.3 × 10 M¤ • Books: nd • Sparke and Gallagher, 2 Edition So the time taken is 2πr/v = 2π × 8 /220 time units • Carroll and Ostlie, 2nd Edition Gravitational potential energy 1 Measuring the mass of a galaxy cluster The Virial theorem 2 T + V = 0 Virial theorem Newton’s shell theorems 2 Potential-density pairs Potential-density pairs Effective potential Bertrand’s theorem 3 Spiral arms To establish the existence of SMBHs are caused by density waves • Stellar kinematics in the core of the galaxy that sweep • Optical spectra: the width of the spectral line from around the broad emission lines Galaxy. • X-ray spectra: The iron Kα line is seen is clearly seen in some AGN spectra • The bolometric luminosities of the central regions of The Winding some galaxies is much larger than the Eddington Paradox (dilemma) luminosity is that if galaxies • Variability in X-rays: Causality demands that the rotated like this, the spiral structure scale of variability corresponds to an upper limit to would be quickly the light-travel time erased. - 
												
												Hydroelectric Power -- What Is It? It=S a Form of Energy … a Renewable Resource
INTRODUCTION Hydroelectric Power -- what is it? It=s a form of energy … a renewable resource. Hydropower provides about 96 percent of the renewable energy in the United States. Other renewable resources include geothermal, wave power, tidal power, wind power, and solar power. Hydroelectric powerplants do not use up resources to create electricity nor do they pollute the air, land, or water, as other powerplants may. Hydroelectric power has played an important part in the development of this Nation's electric power industry. Both small and large hydroelectric power developments were instrumental in the early expansion of the electric power industry. Hydroelectric power comes from flowing water … winter and spring runoff from mountain streams and clear lakes. Water, when it is falling by the force of gravity, can be used to turn turbines and generators that produce electricity. Hydroelectric power is important to our Nation. Growing populations and modern technologies require vast amounts of electricity for creating, building, and expanding. In the 1920's, hydroelectric plants supplied as much as 40 percent of the electric energy produced. Although the amount of energy produced by this means has steadily increased, the amount produced by other types of powerplants has increased at a faster rate and hydroelectric power presently supplies about 10 percent of the electrical generating capacity of the United States. Hydropower is an essential contributor in the national power grid because of its ability to respond quickly to rapidly varying loads or system disturbances, which base load plants with steam systems powered by combustion or nuclear processes cannot accommodate. Reclamation=s 58 powerplants throughout the Western United States produce an average of 42 billion kWh (kilowatt-hours) per year, enough to meet the residential needs of more than 14 million people. - 
												
												Gravitational Potential and Energy of Homogeneous Rectangular
View metadata, citationGravitational and similar papers potential at core.ac.uk and energy of homogeneous rectangular parallelepipedbrought to you by CORE provided by CERN Document Server Zakir F. Seidov, P.I. Skvirsky Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel Gravitational potential and gravitational energy are presented in analytical form for homogeneous right parallelepiped. PACS numbers: 01.55.+b, 45.20.Dd, 96.35.Fs Keywords: Newtonian mechanics; mass, size, gravitational fields I. INTRODUCTION: BASIC FORMULAE As it is well known, Newtonian gravitational potential, of homogeneous body with constant density ρ,atpoint (X,Y,Z) is defined as triple integral over the body's volume: ZZZ U(X; Y; Z)=Gρ u(X; Y; Z; x; y; z) dxdydz (1) with −1=2 u(X; Y; Z; x; y; z)=[(x − X)2 +(y − Y )2 +(z − Z)2] ;(2) here G stands for Newtonian constant of gravitation. In spite of almost 400-year-long attempts since Isaac Newton' times, the integral (1) is known in closed form (not in the series!) in quite a few cases [1]: a) a piece of straight line, b) a sphere, c) an ellipsoid; note that both cases a) and b) may be considered as particular cases of c). As to serial solution, the integral (1) is expressed in terms of the various kinds of series for external points outside the minimal sphere containing the whole body (non-necessary homogeneous), as well as for inner points close to the origin of co-ordinates. However in this note we do not touch the problem of serial solution and are only interested in exact analytical solution of (1). - 
												
												Hydropower Technologies Program — Harnessing America’S Abundant Natural Resources for Clean Power Generation
U.S. Department of Energy — Energy Efficiency and Renewable Energy Wind & Hydropower Technologies Program — Harnessing America’s abundant natural resources for clean power generation. Contents Hydropower Today ......................................... 1 Enhancing Generation and Environmental Performance ......... 6 Large Turbine Field-Testing ............................... 9 Providing Safe Passage for Fish ........................... 9 Improving Mitigation Practices .......................... 11 From the Laboratories to the Hydropower Communities ..... 12 Hydropower Tomorrow .................................... 14 Developing the Next Generation of Hydropower ............ 15 Integrating Wind and Hydropower Technologies ............ 16 Optimizing Project Operations ........................... 17 The Federal Wind and Hydropower Technologies Program ..... 19 Mission and Goals ...................................... 20 2003 Hydropower Research Highlights Alden Research Center completes prototype turbine tests at their facility in Holden, MA . 9 Laboratories form partnerships to develop and test new sensor arrays and computer models . 10 DOE hosts Workshop on Turbulence at Hydroelectric Power Plants in Atlanta . 11 New retrofit aeration system designed to increase the dissolved oxygen content of water discharged from the turbines of the Osage Project in Missouri . 11 Low head/low power resource assessments completed for conventional turbines, unconventional systems, and micro hydropower . 15 Wind and hydropower integration activities in 2003 aim to identify potential sites and partners . 17 Cover photo: To harness undeveloped hydropower resources without using a dam as part of the system that produces electricity, researchers are developing technologies that extract energy from free flowing water sources like this stream in West Virginia. ii HYDROPOWER TODAY Water power — it can cut deep canyons, chisel majestic mountains, quench parched lands, and transport tons — and it can generate enough electricity to light up millions of homes and businesses around the world.