ONE. The Earth-atmosphere system CHAPTER

Size: px
Start display at page:

Download "ONE. The Earth-atmosphere system CHAPTER"

Transcription

1 CHAPTER ONE The Earth-atmoshere system 1.1 INTRODUCTION The Earth s atmoshere is the gaseous enveloe surrounding the lanet. Like other lanetary atmosheres, it figures centrally in transfers of energy between the sun, the Earth, and dee sace. It also figures in transfers of energy from one region of the globe to another. By maintaining thermal equilibrium, such transfers determine the Earth s climate. However, among neighboring lanets, the Earth s atmoshere is unique because it is related closely to ocean and surface rocesses that, together with the atmoshere, form the basis for life. Because it is a fluid system, the atmoshere is caable of suorting a wide sectrum of motions. These range from turbulent eddies of a few meters to circulations with dimensions of the Earth itself. By rearranging mass, air motion influences other atmosheric comonents such as water vaor, ozone, and cloud, which figure rominently in radiative and chemical rocesses. Such influence makes the atmosheric circulation a key ingredient of the global energy budget Descritions of atmosheric behavior The mobility of a fluid system makes its descrition comlex. Atmosheric motion redistributes mass and constituents into a variety of comlex configurations. Like any fluid system, the atmoshere is governed by the laws of continuum mechanics. They can be derived from the laws of mechanics and thermodynamics that govern a discrete fluid body by generalizing those laws to a continuum of such systems. In the atmoshere, the discrete system to which these laws aly is an infinitesimal fluid element, or air arcel, which is defined by a fixed collection of matter. 1

2 2 The Earth-atmoshere system Two frameworks are used to describe atmosheric behavior. The Eulerian descrition reresents atmosheric behavior in terms of field roerties, such as the instantaneous distributions of temerature, motion, and constituents. Governed by artial differential equations, the field descrition of atmosheric behavior is convenient for numerical alications. The Lagrangian descrition reresents atmosheric behavior in terms of the roerties of individual air arcels (e.g., in terms of their instantaneous ositions, temeratures, and constituent concentrations). Because it focuses on transformations of roerties within an air arcel and on interactions between that system and its environment, the Lagrangian descrition offers concetual as well as certain diagnostic advantages. For this reason, the basic rinciles governing atmosheric behavior are develoed in this text from a Lagrangian ersective. In the Lagrangian framework, the system considered is an individual air arcel moving through the circulation. Although it may change in form through deformation and in comosition through thermodynamic and chemical transformations, this system is uniquely identified by the matter comrising it initially. Mass can be transferred across the boundary of an air arcel through molecular diffusion and turbulent mixing. However, such transfers are slow enough to be ignored for many alications. An individual arcel can then change only through interaction with its environment and through internal transformations that alter its comosition and state Mechanisms influencing atmosheric behavior Of the factors influencing atmosheric behavior, gravity is the single most imortant. Even though it has no uer boundary, the atmoshere is contained by the gravitational field of the Earth, which revents atmosheric mass from escaing to sace. Because it is such a strong body force, gravity determines many atmosheric roerties. Most immediate is the geometry of the atmoshere. Atmosheric mass is concentrated in the lowest 10 km less than 1% of the Earth s radius. Gravitational attraction has comressed the atmoshere into a shallow layer above the Earth s surface in which mass and constituents are stratified vertically: They are layered. Through stratification of mass, gravity imoses a strong kinematic constraint on atmosheric motion. Circulations with dimensions greater than a few tens of kilometers are quasi-horizontal. Vertical dislacements of air are then much smaller than horizontal dislacements. Under these circumstances, constituents such as water vaor and ozone fan out in layers or strata. Vertical dislacements are comarable to horizontal dislacements only in small-scale circulations such as convective cells and fronts, which have horizontal dimensions comarable to the vertical scale of the mass distribution. The comressibility of air comlicates the descrition of atmosheric behavior by enabling the volume of a arcel to change as it exeriences changes in surrounding ressure. Therefore, concentrations of mass and constituents for the arcel can change, even though the number of molecules remains fixed. The concentration of a chemical constituent can also change through internal transformations, which alter the number of a articular tye of molecule. For examle, condensation decreases the abundance of water vaor in an air arcel that asses through a cloud system. Photodissociation of O 2 will increase the abundance of ozone in a arcel that asses through a region of sunlight. Exchanges of energy with its environment and transformations between one form of energy and another likewise alter the roerties of an air arcel. By exanding, an

3 1.2 Comosition and structure 3 air arcel exchanges energy mechanically with its environment through work that it erforms on the surroundings. Heat transfer, as occurs through absortion of radiant energy and conduction with the Earth s surface, reresents a thermal exchange of energy with a arcel s environment. Absortion of water vaor by an air arcel (e.g., through contact with a warm ocean surface) has a similar effect. When the vaor condenses, latent heat of vaorization carried by the vaor is released to the surrounding molecules of dry air that comrise the arcel. If the condensed water then reciitates back to the Earth s surface, this rocess leads to a net transfer of heat from the Earth s surface to the arcel. The Earth s rotation, like gravity, exerts an imortant influence on atmosheric motion and, hence, on distributions of atmosheric roerties. Because the Earth is a noninertial reference frame, the conventional laws of mechanics do not hold; they must be modified to account for its acceleration. Aarent forces introduced by the Earth s rotation are resonsible for roerties of the large-scale circulation, in articular, the flow of air around centers of low and high ressure. Those forces also inhibit meridional, e.g., NS (North-South) motion. Consequently, they inhibit transfers of heat and constituents between the equator and oles. For this reason, rotation tends to stratify roerties meridionally, just as gravity tends to stratify them vertically. The hysical rocesses described in the receding aragrahs do not oerate indeendently. They are interwoven in a comlex fabric of radiation, chemistry, and dynamics that govern the Earth-atmoshere system. Interactions among these can be just as imortant as the individual rocesses themselves. For instance, radiative transfer controls the thermal structure of the atmoshere, which determines the circulation. Transort by the circulation, in turn, influences the distributions of radiatively active comonents such as water vaor, ozone, and cloud. In view of their interdeendence, understanding how one of these rocesses influences behavior requires an understanding of how that rocess interacts with others. This feature makes the study of the Earth-atmoshere system an eclectic one, involving the integration of many different hysical rinciles. This book develos the most fundamental of these. 1.2 COMPOSITION AND STRUCTURE The Earth s atmoshere consists of a mixture of gases, mostly molecular nitrogen (78% by volume) and molecular oxygen (21% by volume); see Table 1.1. Water vaor, carbon dioxide, and ozone, along with other minor constituents, comrise the remaining 1% of the atmoshere. Although resent in very small abundances, trace secies such as water vaor and ozone lay a key role in the energy balance of the Earth through their involvement in radiative rocesses. Because they are created and destroyed in articular regions and are linked to the circulation through transort, these and other minor secies are highly variable. For this reason, trace secies are treated searately from the rimary atmosheric constituents, which are referred to simly as dry air Descrition of air The starting oint for describing atmosheric behavior is the ideal gas law V = nr T = m M R T (1.1) = mrt,

4 4 The Earth-atmoshere system Table 1.1. Atmosheric Comosition. Constituents are listed with volume mixing ratios reresentative of the Trooshere or Stratoshere, how the latter are distributed vertically, and controlling rocesses Troosheric Vertical Distribution Constituent Mixing Ratio (Mixing Ratio) Controlling Processes N Homogeneous Vertical Mixing O Homogeneous Vertical Mixing H 2 O Decreases sharly in Trooshere Evaoration, Condensation, Increases in Stratoshere Transort Highly Variable Production by CH 4 Oxidation Ar.0093 Homogeneous Vertical Mixing CO mv Homogeneous Vertical Mixing Production by Surface and Anthroogenic Processes O 3 10 mv $ Increases sharly in Stratoshere Photochemical Production Highly Variable in Stratoshere; secondarily through ollution in trooshere Destruction at Surface Transort CH mv Homogeneous in Trooshere Production by Surface Processes Decreases in Middle Atmoshere Oxidation Produces H 2 O N 2 O 320 bv Homogeneous in Trooshere Production by Surface and Decreases in Middle Atmoshere Anthroogenic Processes Dissociation in Middle Atmoshere Produces NO Transort CO 70 bv Decreases in Trooshere Production Anthroogenically Increases in Stratoshere and by Oxidation of CH 4 Transort NO 0.1 bv $ Increases Vertically Production by Dissociation of N 2 O Catalytic Destruction of O 3 CFC bv Homogeneous in Trooshere Industrial Production CFC bv Decreases in Stratoshere Mixing in Trooshere HFC 134A 30 t Photo-dissociation in Stratoshere Radiatively active $ Stratosheric value which constitutes the equation of state for a ure (single-comonent) gas. In (1.1),, T,andM denote the ressure, temerature, and molar weight of the gas, and V, m, and n = m refer to the volume, mass, and molar abundance of a fixed collection of M matter (e.g., an air arcel). The secific gas constant R is related to the universal gas constant R through R = R M. (1.2) Equivalent forms of the ideal gas law that do not deend on the dimension of the system are = ρrt v = RT, (1.3) where ρ and v = 1 ρ (also denoted α) are the density and secific volume of the gas.

5 1.2 Comosition and structure 5 Because it is a mixture of gases, air obeys similar relationshis. So do its individual comonents. The artial ressure i of the ith comonent is that ressure the ith comonent would exert in isolation at the same volume and temerature as the mixture. It satisfies the equation of state i V = m i R i T, (1.4.1) where R i is the secific gas constant of the ith comonent. Similarly, the artial volume V i is that volume the ith comonent would occuy in isolation at the same ressure and temerature as the mixture. It satisfies the equation of state V i = m i R i T. (1.4.2) Dalton s law asserts that the ressure of a mixture of gases equals the sum of their artial ressures = i i. (1.5) Likewise, the volume of the mixture equals the sum of the artial volumes 1 V = i V i. (1.6) The equation of state for the mixture can be obtained by summing (1.4) over all of the comonents V = T i m i R i. Then, defining the mean secific gas constant i R = m i R i m yields the equation of state for the mixture (1.7) The mean molar weight of the mixture is defined by V = mrt. (1.8) M = m n. (1.9) Because the molar abundance of the mixture is equal to the sum of the molar abundances of the individual comonents, n = i m i M i, (1.9) may be exressed M = R m ( ). i m R i M i 1 These are among several consequences of the Gibbs-Dalton law, which relates the roerties of a mixture to roerties of the individual comonents (e.g., Keenan, 1970).

6 6 The Earth-atmoshere system Then alying (1.2) for the ith comonent together with (1.7) leads to R = R M. (1.10) Equation (1.10) is analogous to (1.2) for a single-comonent gas. Because of their involvement in radiative and chemical rocesses, variable comonents of air must be quantified. The absolute concentration of the ith secies is measured by its density ρ i or, alternatively, by its number density [i] = ( NA M i ) ρ i (1.11) (also denoted n i ), where N A is Avogadro s number and M i is the molar weight of the secies. Partial ressure i and artial volume V i are other measures of absolute concentration. The comressibility of air makes absolute concentration an ambiguous measure of a constituent s abundance. Even if a constituent is assive, namely if the number of molecules inside an individual arcel is fixed, its absolute concentration can change through changes of volume. For this reason, a constituent s abundance is more faithfully described by the relative concentration, which is referenced to the overall abundance of air or simly dry air. The relative concentration of the ith secies is measured by the molar fraction N i = n i n. (1.12) Dividing (1.4) by (1.8) and alying (1.2) for the ith comonent leads to N i = i = V i V. (1.13) Molar fraction uses as a reference the molar abundance of the mixture, which can vary through changes of individual secies. A more convenient measure of relative concentration is mixing ratio. The mass mixing ratio of the ith secies r i = m i m d, (1.14) where the subscrit d refers to dry air, is dimensionless. It is exressed in g kg 1 for troosheric water vaor and in arts er million by mass (mm, or simly m) for stratosheric ozone. Unlike molar abundance, the reference mass m d is constant for an individual air arcel. If the ith secies is assive, namely if it does not undergo a transformation of hase or a chemical reaction, its mass m i is also constant. The mixing ratio r i is then fixed for an individual air arcel. For a trace secies, such as water vaor or ozone, the mixing ratio is closely related to the molar fraction N i = r i ɛ i, (1.15.1)

7 1.2 Comosition and structure 7 where ɛ i = M i M d, (1.15.2) because the mass of air in the resence of such secies is nearly identical to that of dry air. The volume mixing ratio rovides similar information. It is distinguished from mass mixing ratio by dimensions such as arts er million by volume (mv) for stratosheric ozone (Probs. 1.2, 1.3). From (1.13) and (1.12), it follows that the volume mixing ratio is aroximately equal to the molar fraction. Each measures the relative abundance of molecules of the ith secies. As noted, the mixing ratio of a assive secies is fixed for an individual air arcel. A roerty that is invariant for individual arcels is said to be conserved. Although constant for individual air arcels, a conserved roerty is generally not constant in sace and time. Unless that roerty haens to be homogeneous, its distribution must vary satially and temorally, as arcels with different values exchange ositions. A conserved roerty is a material tracer because articular values track the motion of individual air arcels. Thus, tracking articular values of r i rovides a descrition of how air is rearranged by the circulation and, therefore, of how all conserved secies are redistributed Stratification of mass By confining mass to a shallow layer above the Earth s surface, gravity exerts a rofound influence on atmosheric behavior. If vertical accelerations are ignored, then Newton s second law of motion alied to the column of air between some level at ressure and a level incrementally higher at ressure + d (Fig. 1.1) reduces to a balance between the weight of that column and the net ressure force acting on it da ( + d)da = ρgdv, where g denotes the acceleration of gravity, or d = ρg. (1.16) dz This simle form of mechanical equilibrium is known as hydrostatic balance. It is a good aroximation even if the atmoshere is in motion because, for large-scale circulations, vertical dislacements of air are small. This feature renders vertical acceleration two to three orders of magnitude smaller than the forces in (1.16). Alying the same analysis between the ressure and the to of the atmoshere (where vanishes) illustrates the origin of atmosheric ressure: The ressure at any level must equal the weight of the atmosheric column of unit cross-sectional area above that level. Owing to the comressibility of air, the density in (1.16) is not constant. It deends on the air s ressure through the gas law. Eliminating ρ with (1.3) and integrating from the surface to an altitude z yields = e z dz z H (z ) s, (1.17.1) s

8 8 The Earth-atmoshere system Figure 1.1 Hydrostatic balance for an incremental atmosheric column of cross-sectional area da and height dz, bounded vertically by isobaric surfaces at ressures and + d. where H (z) = RT (z) g (1.17.2) is the ressure scale height and s is the surface ressure. The scale height reresents the characteristic vertical dimension of the mass distribution. A function of altitude, it varies from about 8 km near the Earth s surface to 6 km in very cold regions of the atmoshere. As illustrated by Fig. 1.2, global-mean ressure and density decrease with altitude aroximately exonentially. Pressure decreases from about 1000 hpa or 10 5 Pascals (Pa) at the surface to only 10% of that value at an altitude of 15 km (two scale heights). 2 According to hydrostatic balance, 90% of the atmoshere s mass then lies beneath this level. Pressure decreases by another factor of 10 for each additional 15 km of altitude. Density decreases with altitude at about the same rate, from a surface value of about 1.2 kg m 3. The shar uward decrease of ressure imlies that isobaric surfaces, along which = const, are quasi-horizontal. Deflections of those surfaces introduce comaratively small horizontal variations of ressure that drive atmosheric motion. 2 The historical unit of ressure, millibar (mb), has been relaced by its equivalent in the Standard International (SI) system of units, the hectopascal (hpa), where 1 hpa = 100 Pa = 1mb.See Aendix A for conversions between the SI system of units and others.

9 1.2 Comosition and structure Temerature (K) Altitude (km) Pressure Density Temerature Pressure (hpa) Density (kg m -3 ) Figure 1.2 Global-mean ressure (solid), density (dashed), and temerature (dotted), as functions of altitude. Source: U.S. Standard Atmoshere (1976). Above 100 km, ressure and density also decrease exonentially (Fig. 1.3), but at a rate which differs from that below and which varies gradually with altitude. The distinct change of behavior near 100 km marks a transition in the rocesses that control the stratification of mass and the comosition of air. The mean free ath of molecules is determined by the frequency of collisions. It varies inversely with air density. Consequently, the mean free ath increases exonentially with altitude, from about 10 7 m at the surface to of order 1 m at 100 km. Because it controls molecular diffusion, the mean free ath determines roerties of air such as viscosity and thermal conductivity. Diffusion of momentum and heat suorted by those roerties dissiate atmosheric motion by destroying gradients of velocity and temerature. Below 100 km, the mean free ath is short enough for turbulent eddies in the circulation to be only weakly damed by molecular diffusion. At those altitudes, bulk transort by turbulent air motion dominates diffusive transort of atmosheric constituents. Turbulence stirs different gases with equal efficiency. Mixing ratios of

10 Altitude (km) O 2 O Cambridge University Press 10 The Earth-atmoshere system 300 Temerature (K) M O T Normal Solar 200 He N 2 M T Active Solar O 2 M N He O O 2 M N 2 T He O Pressure (hpa) Number Density (m -3 ) Molar Weight Figure 1.3 Global-mean ressure (bold), temerature (stiled), mean molar weight (solid), and number densities of atmosheric constituents as functions of altitude. Source: U.S. Standard Atmoshere (1976). assive constituents are therefore homogeneous in this region. Those constituents are said to be well mixed. The densities of assive constituents then all decrease with altitude at the same exonential rate. This gives air a homogeneous comosition, with constant mixing ratios r N2 = 0.78, ro2 = 0.21, and the constant gas roerties 3 M d = gmol 1 (1.18.1) N 2 R d = Jkg 1 K 1. (1.18.2) The well-mixed region below 100 km is known as the homoshere. 3 Proerties of dry air are tabulated in Aendix B, along with other thermodynamic constants.

Ideal Gas Law. September 2, 2014

Ideal Gas Law. September 2, 2014 Ideal Gas Law Setember 2, 2014 Thermodynamics deals with internal transformations of the energy of a system and exchanges of energy between that system and its environment. A thermodynamic system refers

More information

4. A Brief Review of Thermodynamics, Part 2

4. A Brief Review of Thermodynamics, Part 2 ATMOSPHERE OCEAN INTERACTIONS :: LECTURE NOTES 4. A Brief Review of Thermodynamics, Part 2 J. S. Wright jswright@tsinghua.edu.cn 4.1 OVERVIEW This chater continues our review of the key thermodynamics

More information

Liquid water static energy page 1/8

Liquid water static energy page 1/8 Liquid water static energy age 1/8 1) Thermodynamics It s a good idea to work with thermodynamic variables that are conserved under a known set of conditions, since they can act as assive tracers and rovide

More information

GEF2200 vår 2017 Løsningsforslag sett 1

GEF2200 vår 2017 Løsningsforslag sett 1 GEF2200 vår 2017 Løsningsforslag sett 1 A.1.T R is the universal gas constant, with value 8.3143JK 1 mol 1. R is the gas constant for a secic gas, given by R R M (1) where M is the molecular weight of

More information

Phase transition. Asaf Pe er Background

Phase transition. Asaf Pe er Background Phase transition Asaf Pe er 1 November 18, 2013 1. Background A hase is a region of sace, throughout which all hysical roerties (density, magnetization, etc.) of a material (or thermodynamic system) are

More information

ESCI 342 Atmospheric Dynamics I Lesson 10 Vertical Motion, Pressure Coordinates

ESCI 342 Atmospheric Dynamics I Lesson 10 Vertical Motion, Pressure Coordinates Reading: Martin, Section 4.1 PRESSURE COORDINATES ESCI 342 Atmosheric Dynamics I Lesson 10 Vertical Motion, Pressure Coordinates Pressure is often a convenient vertical coordinate to use in lace of altitude.

More information

Chapter 1 Fundamentals

Chapter 1 Fundamentals Chater Fundamentals. Overview of Thermodynamics Industrial Revolution brought in large scale automation of many tedious tasks which were earlier being erformed through manual or animal labour. Inventors

More information

Notes on pressure coordinates Robert Lindsay Korty October 1, 2002

Notes on pressure coordinates Robert Lindsay Korty October 1, 2002 Notes on ressure coordinates Robert Lindsay Korty October 1, 2002 Obviously, it makes no difference whether the quasi-geostrohic equations are hrased in height coordinates (where x, y,, t are the indeendent

More information

1. Read the section on stability in Wallace and Hobbs. W&H 3.53

1. Read the section on stability in Wallace and Hobbs. W&H 3.53 Assignment 2 Due Set 5. Questions marked? are otential candidates for resentation 1. Read the section on stability in Wallace and Hobbs. W&H 3.53 2.? Within the context of the Figure, and the 1st law of

More information

R g. o p2. Lecture 2: Buoyancy, stability, convection and gravity waves

R g. o p2. Lecture 2: Buoyancy, stability, convection and gravity waves Lecture : Clarifications of lecture 1: Hydrostatic balance: Under static conditions, only gravity will work on the fluid. Why doesn't all the fluid contract to the ground? Pressure builds u and resists

More information

Atmosphere, Ocean and Climate Dynamics Answers to Chapter 4

Atmosphere, Ocean and Climate Dynamics Answers to Chapter 4 Atmoshere, Ocean and Climate Dynamics Answers to Chater 4 1. Show that the buoyancy frequency, Eq.(4.22), may be written in terms of the environmental temerature rofile thus N 2 = g µ dte T E dz + Γ d

More information

Where: Where: f Wave s frequency (Hz) c Speed of light ( ms -1 ) Wavelength (m)

Where: Where: f Wave s frequency (Hz) c Speed of light ( ms -1 ) Wavelength (m) in a direction to both of the fields as shown in Figure 1. In wave model, the electromagnetic radiation is commonly associated with wavelength and frequency, exressed mathematically as: c f...(1) f Wave

More information

PHYS1001 PHYSICS 1 REGULAR Module 2 Thermal Physics Chapter 17 First Law of Thermodynamics

PHYS1001 PHYSICS 1 REGULAR Module 2 Thermal Physics Chapter 17 First Law of Thermodynamics PHYS1001 PHYSICS 1 REGULAR Module Thermal Physics Chater 17 First Law of Thermodynamics References: 17.1 to 17.9 Examles: 17.1 to 17.7 Checklist Thermodynamic system collection of objects and fields. If

More information

The Second Law: The Machinery

The Second Law: The Machinery The Second Law: The Machinery Chater 5 of Atkins: The Second Law: The Concets Sections 3.7-3.9 8th Ed, 3.3 9th Ed; 3.4 10 Ed.; 3E 11th Ed. Combining First and Second Laws Proerties of the Internal Energy

More information

dn i where we have used the Gibbs equation for the Gibbs energy and the definition of chemical potential

dn i where we have used the Gibbs equation for the Gibbs energy and the definition of chemical potential Chem 467 Sulement to Lectures 33 Phase Equilibrium Chemical Potential Revisited We introduced the chemical otential as the conjugate variable to amount. Briefly reviewing, the total Gibbs energy of a system

More information

First law of thermodynamics (Jan 12, 2016) page 1/7. Here are some comments on the material in Thompkins Chapter 1

First law of thermodynamics (Jan 12, 2016) page 1/7. Here are some comments on the material in Thompkins Chapter 1 First law of thermodynamics (Jan 12, 2016) age 1/7 Here are some comments on the material in Thomkins Chater 1 1) Conservation of energy Adrian Thomkins (eq. 1.9) writes the first law as: du = d q d w

More information

Equilibrium Thermodynamics

Equilibrium Thermodynamics Part I Equilibrium hermodynamics 1 Molecular hermodynamics Perhas the most basic equation in atmosheric thermodynamics is the ideal gas law = rr where is ressure, r is the air density, is temerature, and

More information

MODULE 2: DIFFUSION LECTURE NO. 2

MODULE 2: DIFFUSION LECTURE NO. 2 PTEL Chemical Mass Transfer Oeration MODULE : DIFFUSIO LECTURE O.. STEDY STTE MOLECULR DIFFUSIO I FLUIDS UDER STGT D LMIR FLOW CODITIOS.. Steady state diffusion through a constant area Steady state diffusion

More information

FUGACITY. It is simply a measure of molar Gibbs energy of a real gas.

FUGACITY. It is simply a measure of molar Gibbs energy of a real gas. FUGACITY It is simly a measure of molar Gibbs energy of a real gas. Modifying the simle equation for the chemical otential of an ideal gas by introducing the concet of a fugacity (f). The fugacity is an

More information

rate~ If no additional source of holes were present, the excess

rate~ If no additional source of holes were present, the excess DIFFUSION OF CARRIERS Diffusion currents are resent in semiconductor devices which generate a satially non-uniform distribution of carriers. The most imortant examles are the -n junction and the biolar

More information

THE FIRST LAW OF THERMODYNAMICS

THE FIRST LAW OF THERMODYNAMICS THE FIRST LA OF THERMODYNAMIS 9 9 (a) IDENTIFY and SET UP: The ressure is constant and the volume increases (b) = d Figure 9 Since is constant, = d = ( ) The -diagram is sketched in Figure 9 The roblem

More information

Day 3. Fluid Statics. - pressure - forces

Day 3. Fluid Statics. - pressure - forces Day 3 Fluid Statics - ressure - forces we define fluid article: small body of fluid with finite mass but negligible dimension (note: continuum mechanics must aly, so not too small) we consider a fluid

More information

Synoptic Meteorology I: The Geostrophic Approximation. 30 September, 7 October 2014

Synoptic Meteorology I: The Geostrophic Approximation. 30 September, 7 October 2014 The Equations of Motion Synotic Meteorology I: The Geostrohic Aroimation 30 Setember, 7 October 2014 In their most general form, and resented without formal derivation, the equations of motion alicable

More information

Weather and Climate Laboratory Spring 2009

Weather and Climate Laboratory Spring 2009 MIT OenCourseWare htt://ocw.mit.edu 12.307 Weather and Climate Laboratory Sring 2009 For information about citing these materials or our Terms of Use, visit: htt://ocw.mit.edu/terms. Thermal wind John

More information

2.6 Primitive equations and vertical coordinates

2.6 Primitive equations and vertical coordinates Chater 2. The continuous equations 2.6 Primitive equations and vertical coordinates As Charney (1951) foresaw, most NWP modelers went back to using the rimitive equations, with the hydrostatic aroximation,

More information

The Role of Water Vapor. atmosphere (we will ignore the solid phase here) Refer to the phase diagram in the web notes.

The Role of Water Vapor. atmosphere (we will ignore the solid phase here) Refer to the phase diagram in the web notes. The Role of Water Vaor Water can exist as either a vaor or liquid in the atmoshere (we will ignore the solid hase here) under a variety of Temerature and ressure conditions. Refer to the hase diagram in

More information

HEAT, WORK, AND THE FIRST LAW OF THERMODYNAMICS

HEAT, WORK, AND THE FIRST LAW OF THERMODYNAMICS HET, ORK, ND THE FIRST L OF THERMODYNMIS 8 EXERISES Section 8. The First Law of Thermodynamics 5. INTERPRET e identify the system as the water in the insulated container. The roblem involves calculating

More information

Lecture 28: Kinetics of Oxidation of Metals: Part 1: rusting, corrosion, and

Lecture 28: Kinetics of Oxidation of Metals: Part 1: rusting, corrosion, and Lecture 8: Kinetics of xidation of etals: Part 1: rusting, corrosion, and the surface rotection, all about chemistry Today s toics hemical rocesses of oxidation of metals: the role layed by oxygen. How

More information

Mixture Homogeneous Mixtures (air, sea water ) same composition, no chemical bond components are NOT distinguishable

Mixture Homogeneous Mixtures (air, sea water ) same composition, no chemical bond components are NOT distinguishable BASIC CONCEPTAND DEFINITIONS1 2 THERMODYNAMICS CHAPTER 2 Thermodynamic Concets Lecturer Axel GRONIEWSKY, PhD 11 th of February2019 Thermodynamics study of energy and its transformation describes macroscoic

More information

df da df = force on one side of da due to pressure

df da df = force on one side of da due to pressure I. Review of Fundamental Fluid Mechanics and Thermodynamics 1. 1 Some fundamental aerodynamic variables htt://en.wikiedia.org/wiki/hurricane_ivan_(2004) 1) Pressure: the normal force er unit area exerted

More information

1 atm = 1.01x10 Pa = 760 Torr = 14.7 lb / in

1 atm = 1.01x10 Pa = 760 Torr = 14.7 lb / in Last class we began discussion of ressure in fluids, with ressure defined as, F = ; units N 1 Pa = 1 m 2 There are a number of other ressure units in common use having the following equivalence, 5 2 1

More information

Q ABS (x,t s ) = S o /4 S(x)a p (x,t s ).

Q ABS (x,t s ) = S o /4 S(x)a p (x,t s ). Lecture 14 ICE The feedback of exanding and contracting ice sheets has often been offered as a lausible exlanation for how the contrasting climates of the glacialinterglacial times can be both (relatively)

More information

Week 8 lectures. ρ t +u ρ+ρ u = 0. where µ and λ are viscosity and second viscosity coefficients, respectively and S is the strain tensor:

Week 8 lectures. ρ t +u ρ+ρ u = 0. where µ and λ are viscosity and second viscosity coefficients, respectively and S is the strain tensor: Week 8 lectures. Equations for motion of fluid without incomressible assumtions Recall from week notes, the equations for conservation of mass and momentum, derived generally without any incomressibility

More information

Actual exergy intake to perform the same task

Actual exergy intake to perform the same task CHAPER : PRINCIPLES OF ENERGY CONSERVAION INRODUCION Energy conservation rinciles are based on thermodynamics If we look into the simle and most direct statement of the first law of thermodynamics, we

More information

I have not proofread these notes; so please watch out for typos, anything misleading or just plain wrong.

I have not proofread these notes; so please watch out for typos, anything misleading or just plain wrong. hermodynamics I have not roofread these notes; so lease watch out for tyos, anything misleading or just lain wrong. Please read ages 227 246 in Chater 8 of Kittel and Kroemer and ay attention to the first

More information

2 Dynamical basics, part 1

2 Dynamical basics, part 1 Contents 1 Dynamical basics, art 1 3 1.1 What drives the atmosheric circulation?........................ 7 1.2 Conservation laws..................................... 8 1.3 Large-scale circulation: Basic

More information

Atmospheric Thermodynamics

Atmospheric Thermodynamics Atmospheric Thermodynamics Atmospheric Composition What is the composition of the Earth s atmosphere? Gaseous Constituents of the Earth s atmosphere (dry air) Constituent Molecular Weight Fractional Concentration

More information

ANALYTICAL MODEL FOR THE BYPASS VALVE IN A LOOP HEAT PIPE

ANALYTICAL MODEL FOR THE BYPASS VALVE IN A LOOP HEAT PIPE ANALYTICAL MODEL FOR THE BYPASS ALE IN A LOOP HEAT PIPE Michel Seetjens & Camilo Rindt Laboratory for Energy Technology Mechanical Engineering Deartment Eindhoven University of Technology The Netherlands

More information

12.808: Some Physical Properties of Sea Water or, More than you ever wanted to know about the basic state variables of the ocean

12.808: Some Physical Properties of Sea Water or, More than you ever wanted to know about the basic state variables of the ocean 12.88: Some Physical Proerties of Sea Water or, More than you ever wanted to know about the basic state variables of the ocean Salinity Various salt constituents in 1 m 3 of seawater having (t, S) = (2,

More information

On Gravity Waves on the Surface of Tangential Discontinuity

On Gravity Waves on the Surface of Tangential Discontinuity Alied Physics Research; Vol. 6, No. ; 4 ISSN 96-9639 E-ISSN 96-9647 Published by anadian enter of Science and Education On Gravity Waves on the Surface of Tangential Discontinuity V. G. Kirtskhalia I.

More information

1. Composition and Structure

1. Composition and Structure Atmospheric sciences focuses on understanding the atmosphere of the earth and other planets. The motivations for studying atmospheric sciences are largely: weather forecasting, climate studies, atmospheric

More information

Chapter 20: Exercises: 3, 7, 11, 22, 28, 34 EOC: 40, 43, 46, 58

Chapter 20: Exercises: 3, 7, 11, 22, 28, 34 EOC: 40, 43, 46, 58 Chater 0: Exercises:, 7,,, 8, 4 EOC: 40, 4, 46, 8 E: A gasoline engine takes in.80 0 4 and delivers 800 of work er cycle. The heat is obtained by burning gasoline with a heat of combustion of 4.60 0 4.

More information

whether a process will be spontaneous, it is necessary to know the entropy change in both the

whether a process will be spontaneous, it is necessary to know the entropy change in both the 93 Lecture 16 he entroy is a lovely function because it is all we need to know in order to redict whether a rocess will be sontaneous. However, it is often inconvenient to use, because to redict whether

More information

A SIMPLE PLASTICITY MODEL FOR PREDICTING TRANSVERSE COMPOSITE RESPONSE AND FAILURE

A SIMPLE PLASTICITY MODEL FOR PREDICTING TRANSVERSE COMPOSITE RESPONSE AND FAILURE THE 19 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS A SIMPLE PLASTICITY MODEL FOR PREDICTING TRANSVERSE COMPOSITE RESPONSE AND FAILURE K.W. Gan*, M.R. Wisnom, S.R. Hallett, G. Allegri Advanced Comosites

More information

REVIEW & SUMMARY. Molar Specific Heats The molar specific heat C V of a gas at constant volume is defined as

REVIEW & SUMMARY. Molar Specific Heats The molar specific heat C V of a gas at constant volume is defined as REIEW & SUMMARY 59 PART Kinetic Theory of Gases The kinetic theory of gases relates the macroscoic roerties of gases (for examle, ressure and temerature) to the microscoic roerties of gas molecules (for

More information

not to be republished NCERT STATES OF MATTER UNIT 5 INTRODUCTION

not to be republished NCERT STATES OF MATTER UNIT 5 INTRODUCTION 32 CHEMISRY UNI 5 SAES OF MAER After studying this unit you will be able to exlain the existence of different states of matter in terms of balance between intermolecular forces and thermal energy of articles;

More information

f self = 1/T self (b) With revolution, rotaton period T rot in second and the frequency Ω rot are T yr T yr + T day T rot = T self > f self

f self = 1/T self (b) With revolution, rotaton period T rot in second and the frequency Ω rot are T yr T yr + T day T rot = T self > f self Problem : Units : Q-a Mathematically exress the relationshi between the different units of the hysical variables: i) Temerature: ) Fahrenheit and Celsius; 2) Fahrenheit and Kelvin ii) Length: ) foot and

More information

Chapter 6: Sound Wave Equation

Chapter 6: Sound Wave Equation Lecture notes on OPAC0- ntroduction to Acoustics Dr. Eser OLĞAR, 08 Chater 6: Sound Wave Equation. Sound Waves in a medium the wave equation Just like the eriodic motion of the simle harmonic oscillator,

More information

STATES OF MATTER UNIT 5

STATES OF MATTER UNIT 5 32 32 CHEMISTRY UNIT 5 After studying this unit you will be able to exlain the existence of different states of matter in terms of balance between intermolecular forces and thermal energy of articles;

More information

Lecture 8, the outline

Lecture 8, the outline Lecture, the outline loose end: Debye theory of solids more remarks on the first order hase transition. Bose Einstein condensation as a first order hase transition 4He as Bose Einstein liquid Lecturer:

More information

Compressible Flow Introduction. Afshin J. Ghajar

Compressible Flow Introduction. Afshin J. Ghajar 36 Comressible Flow Afshin J. Ghajar Oklahoma State University 36. Introduction...36-36. he Mach Number and Flow Regimes...36-36.3 Ideal Gas Relations...36-36.4 Isentroic Flow Relations...36-4 36.5 Stagnation

More information

9 The Theory of Special Relativity

9 The Theory of Special Relativity 9 The Theory of Secial Relativity Assign: Read Chater 4 of Carrol and Ostlie (2006) Newtonian hysics is a quantitative descrition of Nature excet under three circumstances: 1. In the realm of the very

More information

What did we learn in Ch. 1? Energy Transfers Link Ch What did we learn in Ch. 3? What did we learn in Ch. 4? Key Combined 1 st +2 nd Law Results

What did we learn in Ch. 1? Energy Transfers Link Ch What did we learn in Ch. 3? What did we learn in Ch. 4? Key Combined 1 st +2 nd Law Results Energy ransfers Link Ch. - Ch. Atmosheric Comosition dry air (N, O, Ar, CO ), Water, (articles) Ch. First and Second Laws Energy Balance (System/Environment) Ch. 3 Stefan-Boltzmann Equation Kirchoff s

More information

Feedback-error control

Feedback-error control Chater 4 Feedback-error control 4.1 Introduction This chater exlains the feedback-error (FBE) control scheme originally described by Kawato [, 87, 8]. FBE is a widely used neural network based controller

More information

Chapter 6. Thermodynamics and the Equations of Motion

Chapter 6. Thermodynamics and the Equations of Motion Chater 6 hermodynamics and the Equations of Motion 6.1 he first law of thermodynamics for a fluid and the equation of state. We noted in chater 4 that the full formulation of the equations of motion required

More information

THERMODYNAMICS. Prepared by Sibaprasad Maity Asst. Prof. in Chemistry For any queries contact at

THERMODYNAMICS. Prepared by Sibaprasad Maity Asst. Prof. in Chemistry For any queries contact at HERMODYNAMIS reared by Sibarasad Maity Asst. rof. in hemistry For any queries contact at 943445393 he word thermo-dynamic, used first by illiam homson (later Lord Kelvin), has Greek origin, and is translated

More information

1/18/2011. Conservation of Momentum Conservation of Mass Conservation of Energy Scaling Analysis ESS227 Prof. Jin-Yi Yu

1/18/2011. Conservation of Momentum Conservation of Mass Conservation of Energy Scaling Analysis ESS227 Prof. Jin-Yi Yu Lecture 2: Basic Conservation Laws Conservation Law of Momentum Newton s 2 nd Law of Momentum = absolute velocity viewed in an inertial system = rate of change of Ua following the motion in an inertial

More information

Homogeneous and Inhomogeneous Model for Flow and Heat Transfer in Porous Materials as High Temperature Solar Air Receivers

Homogeneous and Inhomogeneous Model for Flow and Heat Transfer in Porous Materials as High Temperature Solar Air Receivers Excert from the roceedings of the COMSOL Conference 1 aris Homogeneous and Inhomogeneous Model for Flow and Heat ransfer in orous Materials as High emerature Solar Air Receivers Olena Smirnova 1 *, homas

More information

MET 4302 Midterm Study Guide 19FEB18

MET 4302 Midterm Study Guide 19FEB18 The exam will be 4% short answer and the remainder (6%) longer (1- aragrahs) answer roblems and mathematical derivations. The second section will consists of 6 questions worth 15 oints each. Answer 4.

More information

The thermal wind 1. v g

The thermal wind 1. v g The thermal win The thermal win Introuction The geostrohic win is etermine by the graient of the isobars (on a horizontal surface) or isohyses (on a ressure surface). On a ressure surface the graient of

More information

Internal Energy in terms of Properties

Internal Energy in terms of Properties Lecture #3 Internal Energy in terms of roerties Internal energy is a state function. A change in the state of the system causes a change in its roerties. So, we exress the change in internal energy in

More information

Mathematics as the Language of Physics.

Mathematics as the Language of Physics. Mathematics as the Language of Physics. J. Dunning-Davies Deartment of Physics University of Hull Hull HU6 7RX England. Email: j.dunning-davies@hull.ac.uk Abstract. Courses in mathematical methods for

More information

Chapter 2 Solutions. 2.1 (D) Pressure and temperature are dependent during phase change and independent when in a single phase.

Chapter 2 Solutions. 2.1 (D) Pressure and temperature are dependent during phase change and independent when in a single phase. Chater Solutions.1 (D) Pressure and temerature are deendent during hase change and indeendent when in a single hase.. (B) Sublimation is the direct conversion of a solid to a gas. To observe this rocess,

More information

SELF-SIMILAR FLOW OF A MIXTURE OF A NON-IDEAL GAS AND SMALL SOLID PARTICLES WITH INCREASING ENERGY BEHIND A SHOCK WAVE UNDER A GRAVITATIONAL FIELD

SELF-SIMILAR FLOW OF A MIXTURE OF A NON-IDEAL GAS AND SMALL SOLID PARTICLES WITH INCREASING ENERGY BEHIND A SHOCK WAVE UNDER A GRAVITATIONAL FIELD SELF-SIMILAR FLOW OF A MIXTURE OF A NON-IDEAL GAS AND SMALL SOLID PARTICLES WITH INCREASING ENERGY BEHIND A SHOCK WAVE UNDER A GRAVITATIONAL FIELD Vishwakarma J.P. and Prerana Pathak 1 Deartment of Mathematics

More information

Lecture Thermodynamics 9. Entropy form of the 1 st law. Let us start with the differential form of the 1 st law: du = d Q + d W

Lecture Thermodynamics 9. Entropy form of the 1 st law. Let us start with the differential form of the 1 st law: du = d Q + d W Lecture hermodnamics 9 Entro form of the st law Let us start with the differential form of the st law: du = d Q + d W Consider a hdrostatic sstem. o know the required d Q and d W between two nearb states,

More information

/ p) TA,. Returning to the

/ p) TA,. Returning to the Toic2610 Proerties; Equilibrium and Frozen A given closed system having Gibbs energy G at temerature T, ressure, molecular comosition (organisation ) and affinity for sontaneous change A is described by

More information

Chapter 5. Transient Conduction. Islamic Azad University

Chapter 5. Transient Conduction. Islamic Azad University Chater 5 Transient Conduction Islamic Azad University Karaj Branch 1 Transient Conduction Many heat transfer roblems are time deendent Changes in oerating conditions in a system cause temerature variation

More information

5. PRESSURE AND VELOCITY SPRING Each component of momentum satisfies its own scalar-transport equation. For one cell:

5. PRESSURE AND VELOCITY SPRING Each component of momentum satisfies its own scalar-transport equation. For one cell: 5. PRESSURE AND VELOCITY SPRING 2019 5.1 The momentum equation 5.2 Pressure-velocity couling 5.3 Pressure-correction methods Summary References Examles 5.1 The Momentum Equation Each comonent of momentum

More information

Setting up the Mathematical Model Review of Heat & Material Balances

Setting up the Mathematical Model Review of Heat & Material Balances Setting u the Mathematical Model Review of Heat & Material Balances Toic Summary... Introduction... Conservation Equations... 3 Use of Intrinsic Variables... 4 Well-Mixed Systems... 4 Conservation of Total

More information

Session 5: Review of Classical Astrodynamics

Session 5: Review of Classical Astrodynamics Session 5: Review of Classical Astrodynamics In revious lectures we described in detail the rocess to find the otimal secific imulse for a articular situation. Among the mission requirements that serve

More information

8.7 Associated and Non-associated Flow Rules

8.7 Associated and Non-associated Flow Rules 8.7 Associated and Non-associated Flow Rules Recall the Levy-Mises flow rule, Eqn. 8.4., d ds (8.7.) The lastic multilier can be determined from the hardening rule. Given the hardening rule one can more

More information

1 Entropy 1. 3 Extensivity 4. 5 Convexity 5

1 Entropy 1. 3 Extensivity 4. 5 Convexity 5 Contents CONEX FUNCIONS AND HERMODYNAMIC POENIALS 1 Entroy 1 2 Energy Reresentation 2 3 Etensivity 4 4 Fundamental Equations 4 5 Conveity 5 6 Legendre transforms 6 7 Reservoirs and Legendre transforms

More information

Atmospheric Thermodynamics

Atmospheric Thermodynamics Atmosheric hermodynamics 3 he theory of thermodynamics is one of the cornerstones and crowning glories of classical hysics. It has alications not only in hysics, chemistry, and the Earth sciences, but

More information

Conservation of Mass Conservation of Energy Scaling Analysis. ESS227 Prof. Jin-Yi Yu

Conservation of Mass Conservation of Energy Scaling Analysis. ESS227 Prof. Jin-Yi Yu Lecture 2: Basic Conservation Laws Conservation of Momentum Conservation of Mass Conservation of Energy Scaling Analysis Conservation Law of Momentum Newton s 2 nd Law of Momentum = absolute velocity viewed

More information

Landau Theory of the Fermi Liquid

Landau Theory of the Fermi Liquid Chater 5 Landau Theory of the Fermi Liquid 5. Adiabatic Continuity The results of the revious lectures, which are based on the hysics of noninteracting systems lus lowest orders in erturbation theory,

More information

On the Fluid Dependence of Rock Compressibility: Biot-Gassmann Refined

On the Fluid Dependence of Rock Compressibility: Biot-Gassmann Refined Downloaded 0/9/3 to 99.86.4.8. Redistribution subject to SEG license or coyright; see Terms of Use at htt://library.seg.org/ On the luid Deendence of Rock Comressibility: Biot-Gassmann Refined Leon Thomsen,

More information

SIMULATION OF DIFFUSION PROCESSES IN LABYRINTHIC DOMAINS BY USING CELLULAR AUTOMATA

SIMULATION OF DIFFUSION PROCESSES IN LABYRINTHIC DOMAINS BY USING CELLULAR AUTOMATA SIMULATION OF DIFFUSION PROCESSES IN LABYRINTHIC DOMAINS BY USING CELLULAR AUTOMATA Udo Buschmann and Thorsten Rankel and Wolfgang Wiechert Deartment of Simulation University of Siegen Paul-Bonatz-Str.

More information

ATM The thermal wind Fall, 2016 Fovell

ATM The thermal wind Fall, 2016 Fovell ATM 316 - The thermal wind Fall, 2016 Fovell Reca and isobaric coordinates We have seen that for the synotic time and sace scales, the three leading terms in the horizontal equations of motion are du dt

More information

ATMOSPHERIC THERMODYNAMICS

ATMOSPHERIC THERMODYNAMICS ATMOSPHERIC THERMODYNAMICS 1. Introduction 1.1 The field of thermodynamics Classical thermodynamics deals with energy and the transformations of the nature of energy. To a certain extent, it classifies

More information

Statics and dynamics: some elementary concepts

Statics and dynamics: some elementary concepts 1 Statics and dynamics: some elementary concets Dynamics is the study of the movement through time of variables such as heartbeat, temerature, secies oulation, voltage, roduction, emloyment, rices and

More information

CHAPTER 20. Answer to Checkpoint Questions. 1. all but c 2. (a) all tie; (b) 3, 2, 1

CHAPTER 20. Answer to Checkpoint Questions. 1. all but c 2. (a) all tie; (b) 3, 2, 1 558 CHAPTER 0 THE KINETIC THEORY OF GASES CHAPTER 0 Answer to Checkoint Questions. all but c. (a) all tie; (b) 3,, 3. gas A 4. 5 (greatest change in T ), then tie of,, 3, and 4 5.,, 3 (Q 3 0, Q goes into

More information

6.7 Thermal wind in pressure coordinates

6.7 Thermal wind in pressure coordinates 176 CHAPTER 6. THE EQUATIONS OF FLUID MOTION 6.7 Thermal wind in ressure coordinates The thermal wind relation aroriate to the atmoshere is untidy when exressed with height as a vertical coordinate (because

More information

1. The vertical structure of the atmosphere. Temperature profile.

1. The vertical structure of the atmosphere. Temperature profile. Lecture 4. The structure of the atmosphere. Air in motion. Objectives: 1. The vertical structure of the atmosphere. Temperature profile. 2. Temperature in the lower atmosphere: dry adiabatic lapse rate.

More information

Integrating Lidar and Atmospheric Boundary Layer Measurements to Determine Fluxes and Dynamics of Particulate Emissions from an Agriculture Facility

Integrating Lidar and Atmospheric Boundary Layer Measurements to Determine Fluxes and Dynamics of Particulate Emissions from an Agriculture Facility Integrating Lidar and Atmosheric Boundary Layer Measurements to Determine Fluxes and Dynamics of Particulate Emissions from an Agriculture Facility Lawrence His 1, John H. Prueger 2, Jerry Hatfield 2,

More information

centrifugal acceleration, whose magnitude is r cos, is zero at the poles and maximum at the equator. This distribution of the centrifugal acceleration

centrifugal acceleration, whose magnitude is r cos, is zero at the poles and maximum at the equator. This distribution of the centrifugal acceleration Lecture 10. Equations of Motion Centripetal Acceleration, Gravitation and Gravity The centripetal acceleration of a body located on the Earth's surface at a distance from the center is the force (per unit

More information

Paper C Exact Volume Balance Versus Exact Mass Balance in Compositional Reservoir Simulation

Paper C Exact Volume Balance Versus Exact Mass Balance in Compositional Reservoir Simulation Paer C Exact Volume Balance Versus Exact Mass Balance in Comositional Reservoir Simulation Submitted to Comutational Geosciences, December 2005. Exact Volume Balance Versus Exact Mass Balance in Comositional

More information

ATMOS Lecture 7. The First Law and Its Consequences Pressure-Volume Work Internal Energy Heat Capacity Special Cases of the First Law

ATMOS Lecture 7. The First Law and Its Consequences Pressure-Volume Work Internal Energy Heat Capacity Special Cases of the First Law TMOS 5130 Lecture 7 The First Law and Its Consequences Pressure-Volume Work Internal Energy Heat Caacity Secial Cases of the First Law Pressure-Volume Work Exanding Volume Pressure δw = f & dx δw = F ds

More information

International Journal of Mathematics Trends and Technology- Volume3 Issue4-2012

International Journal of Mathematics Trends and Technology- Volume3 Issue4-2012 Effect of Hall current on Unsteady Flow of a Dusty Conducting Fluid through orous medium between Parallel Porous Plates with Temerature Deendent Viscosity and Thermal Radiation Harshbardhan Singh and Dr.

More information

Mixing and Available Potential Energy in a Boussinesq Ocean*

Mixing and Available Potential Energy in a Boussinesq Ocean* APRIL 998 HUANG 669 Mixing and Available Potential Energy in a Boussinesq Ocean* RUI XIN HUANG Deartment of Physical Oceanograhy, Woods Hole Oceanograhic Institution, Woods Hole, Massachussetts (Manuscrit

More information

Theory of turbomachinery. Chapter 1

Theory of turbomachinery. Chapter 1 Theory of turbomachinery Chater Introduction: Basic Princiles Take your choice of those that can best aid your action. (Shakeseare, Coriolanus) Introduction Definition Turbomachinery describes machines

More information

A compression line for soils with evolving particle and pore size distributions due to particle crushing

A compression line for soils with evolving particle and pore size distributions due to particle crushing Russell, A. R. (2011) Géotechnique Letters 1, 5 9, htt://dx.doi.org/10.1680/geolett.10.00003 A comression line for soils with evolving article and ore size distributions due to article crushing A. R. RUSSELL*

More information

Homework #11. (Due December 5 at the beginning of the class.) Numerical Method Series #6: Engineering applications of Newton-Raphson Method to

Homework #11. (Due December 5 at the beginning of the class.) Numerical Method Series #6: Engineering applications of Newton-Raphson Method to Homework #11 (Due December 5 at the beginning of the class.) Numerical Method Series #6: Engineering alications of Newton-Rahson Method to solving systems of nonlinear equations Goals: 1. Understanding

More information

Modelling heat transfer and fluid flow inside a pressure cooker

Modelling heat transfer and fluid flow inside a pressure cooker 17 th Euroean Symosium on Comuter Aided Process Engineering ESCAPE17 V. Plesu and P.S. Agachi (Editors) 2007 Elsevier B.V. All rights reserved. 1 Modelling heat transfer and fluid flow inside a ressure

More information

Thermodynamics in combustion

Thermodynamics in combustion Thermodynamics in combustion 2nd ste in toolbox Thermodynamics deals with a equilibrium state and how chemical comosition can be calculated for a system with known atomic or molecular comosition if 2 indeendent

More information

ME scope Application Note 16

ME scope Application Note 16 ME scoe Alication Note 16 Integration & Differentiation of FFs and Mode Shaes NOTE: The stes used in this Alication Note can be dulicated using any Package that includes the VES-36 Advanced Signal Processing

More information

The Numerical Simulation of Gas Turbine Inlet-Volute Flow Field

The Numerical Simulation of Gas Turbine Inlet-Volute Flow Field World Journal of Mechanics, 013, 3, 30-35 doi:10.436/wjm.013.3403 Published Online July 013 (htt://www.scir.org/journal/wjm) The Numerical Simulation of Gas Turbine Inlet-Volute Flow Field Tao Jiang 1,

More information

Planetary Atmospheres

Planetary Atmospheres Planetary Atmospheres Structure Composition Meteorology Clouds Photochemistry Atmospheric Escape EAS 4803/8803 - CP 20:1 Cloud formation Saturated Vapor Pressure: Maximum amount of water vapor partial

More information

16. CHARACTERISTICS OF SHOCK-WAVE UNDER LORENTZ FORCE AND ENERGY EXCHANGE

16. CHARACTERISTICS OF SHOCK-WAVE UNDER LORENTZ FORCE AND ENERGY EXCHANGE 16. CHARACTERISTICS OF SHOCK-WAVE UNDER LORENTZ FORCE AND ENERGY EXCHANGE H. Yamasaki, M. Abe and Y. Okuno Graduate School at Nagatsuta, Tokyo Institute of Technology 459, Nagatsuta, Midori-ku, Yokohama,

More information