Glacier Hydrology. Where does the Water Go? Why study water flow? Why study (cont.) Water routes (1/3) Water routes (2/3) Vatnafræði

Size: px
Start display at page:

Download "Glacier Hydrology. Where does the Water Go? Why study water flow? Why study (cont.) Water routes (1/3) Water routes (2/3) Vatnafræði"

Transcription

1 Why study ater flo? Glacer Hydrology Vatnafræð Þröstur Þorstensson Glacer rvers provde much of the ater for: Agrculture (Canadan prares, central Asa) Hydro-electrcal poer producton (Iceland, France, Stzerland, Noray). Glacer run-off has unusual features such as: large durnal varatons maxmum flo occurs durng summer (hen many rvers are dry) storage of ater Why study (cont.) In the Alps and Noray, sub-glacal tunnels drlled to get ater for hydroelectrc plants. Need to kno ater flo at the bed. Sudden dranage of glacer-dammed lakes or of ater stored thn glacers, jökulhlaup Assocated mudflos are also a rsk. Becomes more mportant as ctes and roads move closer and closer to out-flo planes and glacers. Water at bed affects sldng; tll deformaton, sldng, surges Where does the Water Go? Water at the surface of a glacer, that ether fell as ran or melts there, can choose beteen several dfferent routes before reachng the ocean. Belo s a short summary of some of these routes Water routes (1/3) Water routes (2/3) 1. Water n the accumulaton area can percolate through the sno and frn don to the ce layer. 2. Water can flo on the surface, even all the ay to the glacer termnus. 3.a A fracton flos through ens that form at the ntersecton of grans (lqud due to hgher surface tenson) 3.b Most of the ater drans to the bed through moulns. 4.a Water at the bed can flo n tunnels that ncse the ce, so-called R-tunnels. Eskers (malarásar) commonly form n those. 4.b Water at the bed can flo n tunnels that ncse the bed, so-called N-tunnels. 4.c Water at the bed can flo as a thn sheet of ater (W-sheet). Unlkely to be stable. Throstur Thorstensson (ThrosturTh@h.s) 1

2 Water routes (3/3) 4.d Water at the bed can flo as groundater n sedments under the ce. 4.e Water at the bed can flo n cavtes, hch could be lnked. 4.f Water at the bed can flo n a system of broad and shallo canals, at the top of sedments. Water n Glacers Water can also accumulate n sub-glacal lakes. Sub-glacal lakes sometmes dran n catastrophc ay as glacer outburst floods, or jökulhlaup. 5. The ater that emerges at the snout flos to the sea as a glacer rver. Water pathays - schematc Surface ater Wens Surface ater Mouln Some ater flos n channels on the surface, lke rvers, and off to the sdes or the termnus Much dsappears through cracks and vertcal passages, called mouln s. Tunnel Mouln Mouln Form here a stream flos nto a crevasse If crevasse flled th ater e have P gh gh P Mouln do most often form n areas of extenson Throstur Thorstensson (ThrosturTh@h.s) 2

3 Mouln (II) Water system at the BED Melt-ater on the surface of Greenland ce sheet. Photo: Brathate Drect measurement dffcult Durng summer, glacer acts as a reservor (especally early summer) Durng nter mouln s etc close In sprng there s a delay for reopenng Water pressure potental The drecton of ater flo n and under glacers s controlled by the ater pressure potental f, f 0 p z f 0 f p gz s a constant s ater pressure s elevaton Water pressure potental (II) The ater flo s perpendcular to the surfaces of constant f. If e assume, p g( z z) that s ce overburden pressure, e get f f0 gzs ( ) gz s Breðamerkur jökull Breda (II) Surface elevaton and bed topography. Bed goes from 300 m to 1807 m, and surface elevaton ranges from sea level to 2012 m. Pressure potental and drecton of flo f (perpendcular to surfaces of constant p-potental). Throstur Thorstensson (ThrosturTh@h.s) 3

4 Steady flo n a tunnel Tunnels Sze of a condut determned by: Meltng, due to vscous dsspaton and frcton aganst the alls. And f ater above 0 C the release of latent heat Closure by overburden pressure (f greater than ater pressure) Response tme s slo, order of a eek meltng Water pressure Ice deformaton Water flux Closure rate Closure rate due to ce deformaton gven by c dr P ra dt n P p p, n p gz Melt n steady state In steady state the sze of the tunnel must reman constant, that mples that ce melted per unt length M s, dr M 2 r dt P M 2 SA, S r n n 2 TUNNELS Tunnels Q vs p Large tunnels gro snce for ncreasng flux Q the ater pressure p drops. Large tunnels capture ater from small tunnels. Throstur Thorstensson (ThrosturTh@h.s) 4

5 Water at the bed Water at the bed (I) Channels cut upard nto the ce Röthlsberger -, or R-channels Channels n the bedrock Nye-, or N-channels Canals on soft bed, broad and shallo If Q p, so stay small and seperate Cavtes Fnd length by consderng ho long t takes a partcle to travel from A to B. Water at the bed (II) Water at the bed (III) Cavtes Closure and melt rate same as for tunnels Assumng that the length l s much greater than the heght r, then the length s r tv, c m t h l u Cavtes, length of t t v h ru l c m Channels Pcture of a tunnel: R-channel Throstur Thorstensson (ThrosturTh@h.s) 5

6 G. Favre Sss flm team Throstur Thorstensson 6

7 Throstur Thorstensson 7

Physics of Glaciers: Glacier Hydraulics

Physics of Glaciers: Glacier Hydraulics Introduction Theory Examples References Physics of Glaciers: Glacier Hydraulics Mauro A. Werder VAW / ETHZ 27.11.2017 Introduction Theory Examples References Problems Front matters Me: postdoc at VAW specialising

More information

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle

More information

(T > w) F R = T - w. Going up. T - w = ma

(T > w) F R = T - w. Going up. T - w = ma ANSES Suspended Acceleratng-Objects A resultant orce causes a syste to accelerate. he drecton o the acceleraton s n the drecton o the resultant orce. As llustrated belo, hen suspended objects accelerate,

More information

Chapter 7. Potential Energy and Conservation of Energy

Chapter 7. Potential Energy and Conservation of Energy Chapter 7 Potental Energy and Conservaton o Energy 1 Forms o Energy There are many orms o energy, but they can all be put nto two categores Knetc Knetc energy s energy o moton Potental Potental energy

More information

EMU Physics Department

EMU Physics Department Physcs 0 Lecture 8 Potental Energy and Conservaton Assst. Pro. Dr. Al ÖVGÜN EMU Physcs Department www.aovgun.com Denton o Work W q The work, W, done by a constant orce on an object s dened as the product

More information

EN40: Dynamics and Vibrations. Homework 4: Work, Energy and Linear Momentum Due Friday March 1 st

EN40: Dynamics and Vibrations. Homework 4: Work, Energy and Linear Momentum Due Friday March 1 st EN40: Dynamcs and bratons Homework 4: Work, Energy and Lnear Momentum Due Frday March 1 st School of Engneerng Brown Unversty 1. The fgure (from ths publcaton) shows the energy per unt area requred to

More information

First Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force.

First Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force. Secton 1. Dynamcs (Newton s Laws of Moton) Two approaches: 1) Gven all the forces actng on a body, predct the subsequent (changes n) moton. 2) Gven the (changes n) moton of a body, nfer what forces act

More information

Chapter 3 and Chapter 4

Chapter 3 and Chapter 4 Chapter 3 and Chapter 4 Chapter 3 Energy 3. Introducton:Work Work W s energy transerred to or rom an object by means o a orce actng on the object. Energy transerred to the object s postve work, and energy

More information

Math1110 (Spring 2009) Prelim 3 - Solutions

Math1110 (Spring 2009) Prelim 3 - Solutions Math 1110 (Sprng 2009) Solutons to Prelm 3 (04/21/2009) 1 Queston 1. (16 ponts) Short answer. Math1110 (Sprng 2009) Prelm 3 - Solutons x a 1 (a) (4 ponts) Please evaluate lm, where a and b are postve numbers.

More information

Physics 5153 Classical Mechanics. D Alembert s Principle and The Lagrangian-1

Physics 5153 Classical Mechanics. D Alembert s Principle and The Lagrangian-1 P. Guterrez Physcs 5153 Classcal Mechancs D Alembert s Prncple and The Lagrangan 1 Introducton The prncple of vrtual work provdes a method of solvng problems of statc equlbrum wthout havng to consder the

More information

Physics for Scientists and Engineers. Chapter 9 Impulse and Momentum

Physics for Scientists and Engineers. Chapter 9 Impulse and Momentum Physcs or Scentsts and Engneers Chapter 9 Impulse and Momentum Sprng, 008 Ho Jung Pak Lnear Momentum Lnear momentum o an object o mass m movng wth a velocty v s dened to be p mv Momentum and lnear momentum

More information

Physics 5153 Classical Mechanics. Principle of Virtual Work-1

Physics 5153 Classical Mechanics. Principle of Virtual Work-1 P. Guterrez 1 Introducton Physcs 5153 Classcal Mechancs Prncple of Vrtual Work The frst varatonal prncple we encounter n mechancs s the prncple of vrtual work. It establshes the equlbrum condton of a mechancal

More information

Lecture 16. Chapter 11. Energy Dissipation Linear Momentum. Physics I. Department of Physics and Applied Physics

Lecture 16. Chapter 11. Energy Dissipation Linear Momentum. Physics I. Department of Physics and Applied Physics Lecture 16 Chapter 11 Physcs I Energy Dsspaton Lnear Momentum Course webste: http://aculty.uml.edu/andry_danylov/teachng/physcsi Department o Physcs and Appled Physcs IN IN THIS CHAPTER, you wll learn

More information

PHYS 1441 Section 002 Lecture #16

PHYS 1441 Section 002 Lecture #16 PHYS 1441 Secton 00 Lecture #16 Monday, Mar. 4, 008 Potental Energy Conservatve and Non-conservatve Forces Conservaton o Mechancal Energy Power Today s homework s homework #8, due 9pm, Monday, Mar. 31!!

More information

Week 9 Chapter 10 Section 1-5

Week 9 Chapter 10 Section 1-5 Week 9 Chapter 10 Secton 1-5 Rotaton Rgd Object A rgd object s one that s nondeformable The relatve locatons of all partcles makng up the object reman constant All real objects are deformable to some extent,

More information

Spring Force and Power

Spring Force and Power Lecture 13 Chapter 9 Sprng Force and Power Yeah, energy s better than orces. What s net? Course webste: http://aculty.uml.edu/andry_danylov/teachng/physcsi IN THIS CHAPTER, you wll learn how to solve problems

More information

Chapter Seven - Potential Energy and Conservation of Energy

Chapter Seven - Potential Energy and Conservation of Energy Chapter Seven - Potental Energy and Conservaton o Energy 7 1 Potental Energy Potental energy. e wll nd that the potental energy o a system can only be assocated wth specc types o orces actng between members

More information

and Reinforced Soil Structures

and Reinforced Soil Structures Geosynthetcs t and Renforced Sol Structures K. Rajagopal, Professor Department of Cvl Engneerng IIT Madras, Chenna e-mal: gopalkr@tm.ac.n Embankment or Wall? Any slope steeper than 70 s desgned as a retanng

More information

Week 6, Chapter 7 Sect 1-5

Week 6, Chapter 7 Sect 1-5 Week 6, Chapter 7 Sect 1-5 Work and Knetc Energy Lecture Quz The frctonal force of the floor on a large sutcase s least when the sutcase s A.pushed by a force parallel to the floor. B.dragged by a force

More information

Ice Cap Glaciers in the Arctic Region. John Evans Glacier, Ellesmere Island (Robert Bingham, U. Aberdeen)

Ice Cap Glaciers in the Arctic Region. John Evans Glacier, Ellesmere Island (Robert Bingham, U. Aberdeen) Ice Cap Glaciers in the Arctic Region John Evans Glacier, Ellesmere Island (Robert Bingham, U. Aberdeen) Iceland Svalbard Ellesmere and Baffin Islands Severny and Anzhu Islands Topics: Temperate vs non-temperate

More information

ME 300 Exam 2 November 18, :30 p.m. to 7:30 p.m.

ME 300 Exam 2 November 18, :30 p.m. to 7:30 p.m. CICLE YOU LECTUE BELOW: Frst Name Last Name 1:3 a.m. 1:3 p.m. Nak Gore ME 3 Exam November 18, 14 6:3 p.m. to 7:3 p.m. INSTUCTIONS 1. Ths s a closed book and closed notes examnaton. You are provded wth

More information

PHYSICS - CLUTCH CH 28: INDUCTION AND INDUCTANCE.

PHYSICS - CLUTCH CH 28: INDUCTION AND INDUCTANCE. !! www.clutchprep.com CONCEPT: ELECTROMAGNETIC INDUCTION A col of wre wth a VOLTAGE across each end wll have a current n t - Wre doesn t HAVE to have voltage source, voltage can be INDUCED V Common ways

More information

Chapter 07: Kinetic Energy and Work

Chapter 07: Kinetic Energy and Work Chapter 07: Knetc Energy and Work Conservaton o Energy s one o Nature s undamental laws that s not volated. Energy can take on derent orms n a gven system. Ths chapter we wll dscuss work and knetc energy.

More information

Temperature. Chapter Heat Engine

Temperature. Chapter Heat Engine Chapter 3 Temperature In prevous chapters of these notes we ntroduced the Prncple of Maxmum ntropy as a technque for estmatng probablty dstrbutons consstent wth constrants. In Chapter 9 we dscussed the

More information

basal } 0.01 m a -1 Glacier hydrology Glacier hydrology Glacier hydrology Water sources 2nd part: applied glaciology

basal } 0.01 m a -1 Glacier hydrology Glacier hydrology Glacier hydrology Water sources 2nd part: applied glaciology Glacier hydrology GEO 4420, 19.10.2006 Glacier hydrology Relevance: Water resource (climate change scenario) Ice dynamics (sliding, surge, icestreams) Geo-hazards (outburst floods) (Erosion, sediment transport)

More information

CHAPTER 8 Potential Energy and Conservation of Energy

CHAPTER 8 Potential Energy and Conservation of Energy CHAPTER 8 Potental Energy and Conservaton o Energy One orm o energy can be converted nto another orm o energy. Conservatve and non-conservatve orces Physcs 1 Knetc energy: Potental energy: Energy assocated

More information

Modeling of Dynamic Systems

Modeling of Dynamic Systems Modelng of Dynamc Systems Ref: Control System Engneerng Norman Nse : Chapters & 3 Chapter objectves : Revew the Laplace transform Learn how to fnd a mathematcal model, called a transfer functon Learn how

More information

find (x): given element x, return the canonical element of the set containing x;

find (x): given element x, return the canonical element of the set containing x; COS 43 Sprng, 009 Dsjont Set Unon Problem: Mantan a collecton of dsjont sets. Two operatons: fnd the set contanng a gven element; unte two sets nto one (destructvely). Approach: Canoncal element method:

More information

Thermodynamics Second Law Entropy

Thermodynamics Second Law Entropy Thermodynamcs Second Law Entropy Lana Sherdan De Anza College May 8, 2018 Last tme the Boltzmann dstrbuton (dstrbuton of energes) the Maxwell-Boltzmann dstrbuton (dstrbuton of speeds) the Second Law of

More information

Discussion 11 Summary 11/20/2018

Discussion 11 Summary 11/20/2018 Dscusson 11 Summary 11/20/2018 1 Quz 8 1. Prove for any sets A, B that A = A B ff B A. Soluton: There are two drectons we need to prove: (a) A = A B B A, (b) B A A = A B. (a) Frst, we prove A = A B B A.

More information

Modeling of CO 2 Cut in CBM Production

Modeling of CO 2 Cut in CBM Production Modelng of CO Cut n CBM Producton A study by: - Kamal Morad - Davd Dunn - ous Mattar Fekete Assocates Inc. Mult-Component Gas n Coalbed Methane Coalbed Methane has dfferent characterstcs from conventonal

More information

Week 11: Chapter 11. The Vector Product. The Vector Product Defined. The Vector Product and Torque. More About the Vector Product

Week 11: Chapter 11. The Vector Product. The Vector Product Defined. The Vector Product and Torque. More About the Vector Product The Vector Product Week 11: Chapter 11 Angular Momentum There are nstances where the product of two vectors s another vector Earler we saw where the product of two vectors was a scalar Ths was called the

More information

Effect of loading frequency on the settlement of granular layer

Effect of loading frequency on the settlement of granular layer Effect of loadng frequency on the settlement of granular layer Akko KONO Ralway Techncal Research Insttute, Japan Takash Matsushma Tsukuba Unversty, Japan ABSTRACT: Cyclc loadng tests were performed both

More information

Physics 53. Rotational Motion 3. Sir, I have found you an argument, but I am not obliged to find you an understanding.

Physics 53. Rotational Motion 3. Sir, I have found you an argument, but I am not obliged to find you an understanding. Physcs 53 Rotatonal Moton 3 Sr, I have found you an argument, but I am not oblged to fnd you an understandng. Samuel Johnson Angular momentum Wth respect to rotatonal moton of a body, moment of nerta plays

More information

PHYSICS - CLUTCH 1E CH 28: INDUCTION AND INDUCTANCE.

PHYSICS - CLUTCH 1E CH 28: INDUCTION AND INDUCTANCE. !! www.clutchprep.com CONCEPT: ELECTROMAGNETIC INDUCTION A col of wre wth a VOLTAGE across each end wll have a current n t - Wre doesn t HAVE to have voltage source, voltage can be INDUCED V Common ways

More information

A Mechanics-Based Approach for Determining Deflections of Stacked Multi-Storey Wood-Based Shear Walls

A Mechanics-Based Approach for Determining Deflections of Stacked Multi-Storey Wood-Based Shear Walls A Mechancs-Based Approach for Determnng Deflectons of Stacked Mult-Storey Wood-Based Shear Walls FPINNOVATIONS Acknowledgements Ths publcaton was developed by FPInnovatons and the Canadan Wood Councl based

More information

TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES. PHYS 2211, Exam 2 Section 1 Version 1 October 18, 2013 Total Weight: 100 points

TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES. PHYS 2211, Exam 2 Section 1 Version 1 October 18, 2013 Total Weight: 100 points TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS, Exam Secton Verson October 8, 03 Total Weght: 00 ponts. Check your examnaton or completeness pror to startng. There are a total o nne

More information

PHYS 1443 Section 004 Lecture #12 Thursday, Oct. 2, 2014

PHYS 1443 Section 004 Lecture #12 Thursday, Oct. 2, 2014 PHYS 1443 Secton 004 Lecture #1 Thursday, Oct., 014 Work-Knetc Energy Theorem Work under rcton Potental Energy and the Conservatve Force Gravtatonal Potental Energy Elastc Potental Energy Conservaton o

More information

Physics 240: Worksheet 30 Name:

Physics 240: Worksheet 30 Name: (1) One mole of an deal monatomc gas doubles ts temperature and doubles ts volume. What s the change n entropy of the gas? () 1 kg of ce at 0 0 C melts to become water at 0 0 C. What s the change n entropy

More information

Elastic Collisions. Definition: two point masses on which no external forces act collide without losing any energy.

Elastic Collisions. Definition: two point masses on which no external forces act collide without losing any energy. Elastc Collsons Defnton: to pont asses on hch no external forces act collde thout losng any energy v Prerequstes: θ θ collsons n one denson conservaton of oentu and energy occurs frequently n everyday

More information

GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE

GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE Prof. J. N. Mandal Department of cvl engneerng, IIT Bombay, Powa, Mumba 400076, Inda. Tel.022-25767328 emal: cejnm@cvl.tb.ac.n Module - 9 LECTURE - 48

More information

Week 8: Chapter 9. Linear Momentum. Newton Law and Momentum. Linear Momentum, cont. Conservation of Linear Momentum. Conservation of Momentum, 2

Week 8: Chapter 9. Linear Momentum. Newton Law and Momentum. Linear Momentum, cont. Conservation of Linear Momentum. Conservation of Momentum, 2 Lnear omentum Week 8: Chapter 9 Lnear omentum and Collsons The lnear momentum of a partcle, or an object that can be modeled as a partcle, of mass m movng wth a velocty v s defned to be the product of

More information

PHYS 1441 Section 002 Lecture #15

PHYS 1441 Section 002 Lecture #15 PHYS 1441 Secton 00 Lecture #15 Monday, March 18, 013 Work wth rcton Potental Energy Gravtatonal Potental Energy Elastc Potental Energy Mechancal Energy Conservaton Announcements Mdterm comprehensve exam

More information

5. TWO-DIMENSIONAL FLOW OF WATER THROUGH SOILS 5.1 INTRODUCTION

5. TWO-DIMENSIONAL FLOW OF WATER THROUGH SOILS 5.1 INTRODUCTION 5. TWO-DIMENSIONAL FLOW OF WATER TROUG SOILS 5.1 INTRODUCTION In many instances the flo of ater through soils is neither one-dimensional nor uniform over the area perpendicular to flo. It is often necessary

More information

Physics 2A Chapter 3 HW Solutions

Physics 2A Chapter 3 HW Solutions Phscs A Chapter 3 HW Solutons Chapter 3 Conceptual Queston: 4, 6, 8, Problems: 5,, 8, 7, 3, 44, 46, 69, 70, 73 Q3.4. Reason: (a) C = A+ B onl A and B are n the same drecton. Sze does not matter. (b) C

More information

Chapter 8: Potential Energy and The Conservation of Total Energy

Chapter 8: Potential Energy and The Conservation of Total Energy Chapter 8: Potental Energy and The Conservaton o Total Energy Work and knetc energy are energes o moton. K K K mv r v v F dr Potental energy s an energy that depends on locaton. -Dmenson F x d U( x) dx

More information

Problem Set 9 Solutions

Problem Set 9 Solutions Desgn and Analyss of Algorthms May 4, 2015 Massachusetts Insttute of Technology 6.046J/18.410J Profs. Erk Demane, Srn Devadas, and Nancy Lynch Problem Set 9 Solutons Problem Set 9 Solutons Ths problem

More information

Work is the change in energy of a system (neglecting heat transfer). To examine what could

Work is the change in energy of a system (neglecting heat transfer). To examine what could Work Work s the change n energy o a system (neglectng heat transer). To eamne what could cause work, let s look at the dmensons o energy: L ML E M L F L so T T dmensonally energy s equal to a orce tmes

More information

SEDIMENT TRANSPORT PROCESSES IN MOUNTAIN AREA OF KINUGAWA RIVER

SEDIMENT TRANSPORT PROCESSES IN MOUNTAIN AREA OF KINUGAWA RIVER SEDIMENT TRANSPORT PROCESSES IN MOUNTAIN AREA OF KINUGAWA RIVER Catherne G. Jaceldone 1 Supervsors: Atsuhro Yorozuya 2 MEE15625 Shnj Egashra ABSTRACT Ths study ams to develop a sedment transport model

More information

CHAPTER 7 ENERGY BALANCES SYSTEM SYSTEM. * What is energy? * Forms of Energy. - Kinetic energy (KE) - Potential energy (PE) PE = mgz

CHAPTER 7 ENERGY BALANCES SYSTEM SYSTEM. * What is energy? * Forms of Energy. - Kinetic energy (KE) - Potential energy (PE) PE = mgz SYSTM CHAPTR 7 NRGY BALANCS 1 7.1-7. SYSTM nergy & 1st Law of Thermodynamcs * What s energy? * Forms of nergy - Knetc energy (K) K 1 mv - Potental energy (P) P mgz - Internal energy (U) * Total nergy,

More information

Glacier Hydrology. Why should you care?

Glacier Hydrology. Why should you care? Glacier Hydrology Why should you care? Climate Local Meteorology Surface Mass And Energy Exchange Net Mass Balance Dynamic Response Effect on Landscape Changes In Geometry Water Flow PRACTICAL MATTERS:

More information

Limited Dependent Variables

Limited Dependent Variables Lmted Dependent Varables. What f the left-hand sde varable s not a contnuous thng spread from mnus nfnty to plus nfnty? That s, gven a model = f (, β, ε, where a. s bounded below at zero, such as wages

More information

Physics 106a, Caltech 11 October, Lecture 4: Constraints, Virtual Work, etc. Constraints

Physics 106a, Caltech 11 October, Lecture 4: Constraints, Virtual Work, etc. Constraints Physcs 106a, Caltech 11 October, 2018 Lecture 4: Constrants, Vrtual Work, etc. Many, f not all, dynamcal problems we want to solve are constraned: not all of the possble 3 coordnates for M partcles (or

More information

Recitation: Energy, Phys Energies. 1.2 Three stones. 1. Energy. 1. An acorn falling from an oak tree onto the sidewalk.

Recitation: Energy, Phys Energies. 1.2 Three stones. 1. Energy. 1. An acorn falling from an oak tree onto the sidewalk. Rectaton: Energy, Phys 207. Energy. Energes. An acorn fallng from an oak tree onto the sdewalk. The acorn ntal has gravtatonal potental energy. As t falls, t converts ths energy to knetc. When t hts the

More information

Chapter 3 Describing Data Using Numerical Measures

Chapter 3 Describing Data Using Numerical Measures Chapter 3 Student Lecture Notes 3-1 Chapter 3 Descrbng Data Usng Numercal Measures Fall 2006 Fundamentals of Busness Statstcs 1 Chapter Goals To establsh the usefulness of summary measures of data. The

More information

How do glaciers form?

How do glaciers form? Glaciers What is a Glacier? A large mass of moving ice that exists year round is called a glacier. Glaciers are formed when snowfall exceeds snow melt year after year Snow and ice remain on the ground

More information

Thomas P. Phillips CIRES Prof K. Steffen, L. Colgan PhD ABD, D. McGrath MA

Thomas P. Phillips CIRES Prof K. Steffen, L. Colgan PhD ABD, D. McGrath MA Thomas P. Phillips CIRES Prof K. Steffen, L. Colgan PhD ABD, D. McGrath MA Problem: we know very little about the processes happening within the Greenland Ice Sheet. What is the velocity at the base? What

More information

Aerosols, Dust and High Spectral Resolution Remote Sensing

Aerosols, Dust and High Spectral Resolution Remote Sensing Aerosols, Dust and Hgh Spectral Resoluton Remote Sensng Irna N. Sokolk Program n Atmospherc and Oceanc Scences (PAOS) Unversty of Colorado at Boulder rna.sokolk@colorado.edu Goals and challenges MAIN GOALS:

More information

Physics 2A Chapters 6 - Work & Energy Fall 2017

Physics 2A Chapters 6 - Work & Energy Fall 2017 Physcs A Chapters 6 - Work & Energy Fall 017 These notes are eght pages. A quck summary: The work-energy theorem s a combnaton o Chap and Chap 4 equatons. Work s dened as the product o the orce actng on

More information

Friction and Ocean Turbulence Part I

Friction and Ocean Turbulence Part I Frcton and Ocean Trblence Part I L. Goodman General Physcal Oceanography MAR 555 School for Marne Scences and Technology Umass-Dartmoth Frcton and Ocean Trblence Part I 3 Types of Flow Potental Flow No

More information

Important Dates: Post Test: Dec during recitations. If you have taken the post test, don t come to recitation!

Important Dates: Post Test: Dec during recitations. If you have taken the post test, don t come to recitation! Important Dates: Post Test: Dec. 8 0 durng rectatons. If you have taken the post test, don t come to rectaton! Post Test Make-Up Sessons n ARC 03: Sat Dec. 6, 0 AM noon, and Sun Dec. 7, 8 PM 0 PM. Post

More information

EMU Physics Department.

EMU Physics Department. Physcs 0 Lecture 9 Lnear Momentum and Collsons Assst. Pro. Dr. Al ÖVGÜN EMU Physcs Department www.aogun.com Lnear Momentum q Conseraton o Energy q Momentum q Impulse q Conseraton o Momentum q -D Collsons

More information

Physics 207: Lecture 20. Today s Agenda Homework for Monday

Physics 207: Lecture 20. Today s Agenda Homework for Monday Physcs 207: Lecture 20 Today s Agenda Homework for Monday Recap: Systems of Partcles Center of mass Velocty and acceleraton of the center of mass Dynamcs of the center of mass Lnear Momentum Example problems

More information

MTH 263 Practice Test #1 Spring 1999

MTH 263 Practice Test #1 Spring 1999 Pat Ross MTH 6 Practce Test # Sprng 999 Name. Fnd the area of the regon bounded by the graph r =acos (θ). Observe: Ths s a crcle of radus a, for r =acos (θ) r =a ³ x r r =ax x + y =ax x ax + y =0 x ax

More information

Lagrange Multipliers. A Somewhat Silly Example. Monday, 25 September 2013

Lagrange Multipliers. A Somewhat Silly Example. Monday, 25 September 2013 Lagrange Multplers Monday, 5 September 013 Sometmes t s convenent to use redundant coordnates, and to effect the varaton of the acton consstent wth the constrants va the method of Lagrange undetermned

More information

ENGN 40 Dynamics and Vibrations Homework # 7 Due: Friday, April 15

ENGN 40 Dynamics and Vibrations Homework # 7 Due: Friday, April 15 NGN 40 ynamcs and Vbratons Homework # 7 ue: Frday, Aprl 15 1. Consder a concal hostng drum used n the mnng ndustry to host a mass up/down. A cable of dameter d has the mass connected at one end and s wound/unwound

More information

Pattern Classification

Pattern Classification Pattern Classfcaton All materals n these sldes ere taken from Pattern Classfcaton (nd ed) by R. O. Duda, P. E. Hart and D. G. Stork, John Wley & Sons, 000 th the permsson of the authors and the publsher

More information

Class: Life-Science Subject: Physics

Class: Life-Science Subject: Physics Class: Lfe-Scence Subject: Physcs Frst year (6 pts): Graphc desgn of an energy exchange A partcle (B) of ass =g oves on an nclned plane of an nclned angle α = 3 relatve to the horzontal. We want to study

More information

Difference Equations

Difference Equations Dfference Equatons c Jan Vrbk 1 Bascs Suppose a sequence of numbers, say a 0,a 1,a,a 3,... s defned by a certan general relatonshp between, say, three consecutve values of the sequence, e.g. a + +3a +1

More information

Ionization fronts in HII regions

Ionization fronts in HII regions Ionzaton fronts n HII regons Intal expanson of HII onzaton front s supersonc, creatng a shock front. Statonary frame: front advances nto neutral materal In frame where shock front s statonary, neutral

More information

Changing Landscapes: Glaciated Landscapes. How do glaciers move?

Changing Landscapes: Glaciated Landscapes. How do glaciers move? Changing Landscapes: Glaciated Landscapes How do glaciers move? What you need to know Differences between cold-and warm-based glaciers, their locations and rates of movement Glacier ice movement including

More information

Drainage of a glacial lake through an ice spillway

Drainage of a glacial lake through an ice spillway Debris-Covered Glaciers (Proceedings of a workshop held at Seattle, Washington, USA, September 2000). IAHS Publ. no. 264, 2000. 199 Drainage of a glacial lake through an ice spillway CHARLES F. RAYMOND

More information

Physics 141. Lecture 14. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 14, Page 1

Physics 141. Lecture 14. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 14, Page 1 Physcs 141. Lecture 14. Frank L. H. Wolfs Department of Physcs and Astronomy, Unversty of Rochester, Lecture 14, Page 1 Physcs 141. Lecture 14. Course Informaton: Lab report # 3. Exam # 2. Mult-Partcle

More information

How Differential Equations Arise. Newton s Second Law of Motion

How Differential Equations Arise. Newton s Second Law of Motion page 1 CHAPTER 1 Frst-Order Dfferental Equatons Among all of the mathematcal dscplnes the theory of dfferental equatons s the most mportant. It furnshes the explanaton of all those elementary manfestatons

More information

in state i at t i, Initial State E = E i

in state i at t i, Initial State E = E i Physcs 01, Lecture 1 Today s Topcs n More Energy and Work (chapters 7 & 8) n Conservatve Work and Potental Energy n Sprng Force and Sprng (Elastc) Potental Energy n Conservaton of Mechanc Energy n Exercse

More information

Chapter 3. r r. Position, Velocity, and Acceleration Revisited

Chapter 3. r r. Position, Velocity, and Acceleration Revisited Chapter 3 Poston, Velocty, and Acceleraton Revsted The poston vector of a partcle s a vector drawn from the orgn to the locaton of the partcle. In two dmensons: r = x ˆ+ yj ˆ (1) The dsplacement vector

More information

EN40: Dynamics and Vibrations. Homework 7: Rigid Body Kinematics

EN40: Dynamics and Vibrations. Homework 7: Rigid Body Kinematics N40: ynamcs and Vbratons Homewor 7: Rgd Body Knematcs School of ngneerng Brown Unversty 1. In the fgure below, bar AB rotates counterclocwse at 4 rad/s. What are the angular veloctes of bars BC and C?.

More information

#64. ΔS for Isothermal Mixing of Ideal Gases

#64. ΔS for Isothermal Mixing of Ideal Gases #64 Carnot Heat Engne ΔS for Isothermal Mxng of Ideal Gases ds = S dt + S T V V S = P V T T V PV = nrt, P T ds = v T = nr V dv V nr V V = nrln V V = - nrln V V ΔS ΔS ΔS for Isothermal Mxng for Ideal Gases

More information

MAGNETISM MAGNETIC DIPOLES

MAGNETISM MAGNETIC DIPOLES MAGNETISM We now turn to magnetsm. Ths has actually been used for longer than electrcty. People were usng compasses to sal around the Medterranean Sea several hundred years BC. However t was not understood

More information

Physics 101 Lecture 9 Linear Momentum and Collisions

Physics 101 Lecture 9 Linear Momentum and Collisions Physcs 0 Lecture 9 Lnear Momentum and Collsons Dr. Al ÖVGÜN EMU Physcs Department www.aogun.com Lnear Momentum and Collsons q q q q q q q Conseraton o Energy Momentum Impulse Conseraton o Momentum -D Collsons

More information

Newton s Laws of Motion

Newton s Laws of Motion Chapter 4 Newton s Laws of Moton 4.1 Forces and Interactons Fundamental forces. There are four types of fundamental forces: electromagnetc, weak, strong and gravtatonal. The frst two had been successfully

More information

UNIVERSITY OF TORONTO Faculty of Arts and Science. December 2005 Examinations STA437H1F/STA1005HF. Duration - 3 hours

UNIVERSITY OF TORONTO Faculty of Arts and Science. December 2005 Examinations STA437H1F/STA1005HF. Duration - 3 hours UNIVERSITY OF TORONTO Faculty of Arts and Scence December 005 Examnatons STA47HF/STA005HF Duraton - hours AIDS ALLOWED: (to be suppled by the student) Non-programmable calculator One handwrtten 8.5'' x

More information

Introduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law:

Introduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law: CE304, Sprng 2004 Lecture 4 Introducton to Vapor/Lqud Equlbrum, part 2 Raoult s Law: The smplest model that allows us do VLE calculatons s obtaned when we assume that the vapor phase s an deal gas, and

More information

Lecture #4 Capacitors and Inductors Energy Stored in C and L Equivalent Circuits Thevenin Norton

Lecture #4 Capacitors and Inductors Energy Stored in C and L Equivalent Circuits Thevenin Norton EES ntro. electroncs for S Sprng 003 Lecture : 0/03/03 A.R. Neureuther Verson Date 0/0/03 EES ntroducton to Electroncs for omputer Scence Andrew R. Neureuther Lecture # apactors and nductors Energy Stored

More information

CHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS

CHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS CHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS 103 Phy 1 9.1 Lnear Momentum The prncple o energy conervaton can be ued to olve problem that are harder to olve jut ung Newton law. It ued to decrbe moton

More information

If the solution does not follow a logical thought process, it will be assumed in error.

If the solution does not follow a logical thought process, it will be assumed in error. Group # Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS Begn each problem n the space provded

More information

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. ME 270 Sprng 2017 Exam 1 NAME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: Instructor s Name

More information

Estimation Of Long-Term Sediment Loads In The Fitzroy Catchment, Queensland, Australia

Estimation Of Long-Term Sediment Loads In The Fitzroy Catchment, Queensland, Australia Estmaton Of Long-Term Sedment Loads In The Ftzroy Catchment, Queensland, Australa Joo, M., 2 B. Yu, B. Fente and 3 C. Caroll Natural Resources and Mnes, 80 Meers Rd Indoorooplly Qld 4068 Emal: Maranna.Joo@nrm.qld.gov.au

More information

Unit 5: Quadratic Equations & Functions

Unit 5: Quadratic Equations & Functions Date Perod Unt 5: Quadratc Equatons & Functons DAY TOPIC 1 Modelng Data wth Quadratc Functons Factorng Quadratc Epressons 3 Solvng Quadratc Equatons 4 Comple Numbers Smplfcaton, Addton/Subtracton & Multplcaton

More information

On Notation Thermodynamics of Glaciers. Types of Glaciers. Why we care. McCarthy Summer School

On Notation Thermodynamics of Glaciers. Types of Glaciers. Why we care. McCarthy Summer School On Notation Thermodynamics of Glaciers McCarthy Summer School Andy Aschwanden Geophysical nstitute University of Alaska Fairbanks, USA (hopefully) consistent with Continuum Mechanics (Truffer) with lots

More information

27. Running Water I (p ; )

27. Running Water I (p ; ) 27. Running Water I (p. 424-436; 440-444) Hydrosphere How much of the Earth s surface is covered by water? Earth's water is collectively called the and is stored in a number of so-called as follows: 1.

More information

Chapter 8 Potential Energy and Conservation of Energy Important Terms (For chapters 7 and 8)

Chapter 8 Potential Energy and Conservation of Energy Important Terms (For chapters 7 and 8) Pro. Dr. I. Nasser Chapter8_I November 3, 07 Chapter 8 Potental Energy and Conservaton o Energy Important Terms (For chapters 7 and 8) conservatve orce: a orce whch does wor on an object whch s ndependent

More information

Subglacial Control on Glacier Flow in Northern Greenland

Subglacial Control on Glacier Flow in Northern Greenland Subglacial Control on Glacier Flow in Northern Greenland Beáta Csathó (University at Buffalo, SUNY, Buffalo, NY), C.J. van der Veen (U. of Kansas, Lawrence, KS) Ralph van Frese and Tim Leftwich (The Ohio

More information

Simulation of Heat Transfer during Artificial Ground Freezing Combined with Groundwater Flow

Simulation of Heat Transfer during Artificial Ground Freezing Combined with Groundwater Flow Smulaton of Heat Transfer durng Artfcal Ground Freezng Combned th Groundater Flo Ru Hu *1, Quan Lu 1 1 School of Earth Scence and Engneerng, Hoha Unversty, Nanjng, Chna *Correspondng author: No.8 Fochengx

More information

Supplementary Materials for

Supplementary Materials for advances.scencemag.org/cg/content/full/2/7/e1600304/dc1 Supplementary Materals for Interface-drven topologcal Hall effect n SrRuO3-SrIrO3 blayer Jobu Matsuno, Naok Ogawa, Kenj Yasuda, Fumtaka Kagawa, Wataru

More information

Glaciers. (Shaping Earth s Surface, Part 6) Science 330 Summer 2005

Glaciers. (Shaping Earth s Surface, Part 6) Science 330 Summer 2005 Glaciers (Shaping Earth s Surface, Part 6) Science 330 Summer 2005 1 Glaciers Glaciers are parts of two basic cycles Hydrologic cycle Rock cycle Glacier a thick mass of ice that originates on land from

More information

Lecture 12. Transport in Membranes (2)

Lecture 12. Transport in Membranes (2) Lecture 12. Transport n embranes (2) odule Flow Patterns - Perfect mxng - Countercurrent flow - Cocurrent flow - Crossflow embrane Cascades External ass-transfer Resstances Concentraton Polarzaton and

More information

Soil Mechanics Permeability of Soils and Seepage page 1 CHAPITRE 9. PERMEABILITY OF SOILS AND SEEPAGE...1

Soil Mechanics Permeability of Soils and Seepage page 1 CHAPITRE 9. PERMEABILITY OF SOILS AND SEEPAGE...1 Soil Mechanics Permeability of Soils and Seepage page 1 Contents of this chapter : CHAPITRE 9. PERMEABILITY OF SOILS AND SEEPAGE...1 9.1 INTRODUCTION...1 9.2 DARCY S LAW...1 9.2.1 DEFINITION OF HEAD...1

More information

The initiation of the 1996 jôkulhlaup from Lake Grimsvôtn, Vatnajôkull, Iceland

The initiation of the 1996 jôkulhlaup from Lake Grimsvôtn, Vatnajôkull, Iceland Tilt: Extremes of the Extremes: Extraordinary Floods (Proceedings of a symposium held at Reykjavik. Iceland. July 2000). I AI IS Publ. no. 271. 2002. 57 The initiation of the 1996 jôkulhlaup from Lake

More information

CE 4780 Hurricane Engineering II. Section on Flooding Protection: Earth Retaining Structures and Slope Stability. Table of Content

CE 4780 Hurricane Engineering II. Section on Flooding Protection: Earth Retaining Structures and Slope Stability. Table of Content CE 4780 Hurrcane Engneerng II Secton on Floodng Protecton: Earth Retanng Structures and Slope Stablty Dante Fratta Fall 2002 Table of Content Introducton Shear Strength of Sols Seepage Analyss Methods

More information