EAS44600 Groundwater Hydrology Lecture 8: Storage Properties of Aquifers Dr. Pengfei Zhang
|
|
- Janice Simon
- 7 years ago
- Views:
Transcription
1 EAS44600 Groundatr Hydrology Lctur 8: Storag Proprtis of Aquifrs Dr. Pngfi Zhang Moistur Contnt Rcall that th porosity (n) of arth matrials is th ratio of th volum of th voids (V v ) to th total volum (V ) of th sampl. h volum of th voids may b furthr dividd into th volum of th atr (V ) and th volum of th air (V a ). h volumtric moistur contnt θ is dfind as: V = V θ (8-1) For saturatd zons V = V v and θ = n; for unsaturatd zons V < V v and θ < n. Watr abl A atr tabl is dfind as th surfac on hich th fluid prssur in th pors of a porous mdium is xactly atmosphric. W commonly think that th atr tabl is th boundary btn th unsaturatd zon and th saturatd zon. Hovr, a saturatd capillary fring oftn xistd abov th atr tabl (Figur 8-1). h capillary fring is diffrnt from th typical saturatd zon in that its prssur is lss than on atmosphr. hrfor, a hydrologic systm is oftn dividd into thr zons: an unsaturatd zon, a capillary fring (somtims also calld tnsion-saturatd zon), and a saturatd zon (Figur 8-1). Figur 8-1. A hydrologic systm consists of an unsaturatd zon, a capillary fring and a saturatd zon (Frz and Chrry). If on placs a ll a f ft or so blo th atr tabl, th atr in that ll ill ris to th lvation of th atr tabl at th location of th ll (abl 8-1). h prssur hydraulic had 8-1
2 (h p ) on th atr tabl is zro sinc th prssur on th atr tabl is xactly atmosphric. Rcall that th total hydraulic had (h) is th sum of th lvation had (z) and th prssur had (h p ). hrfor, th total hydraulic had at any point on th atr tabl must b qual to th lvation had (i.., h = z). On figurs th position of th atr tabl is oftn indicatd by a small invrtd triangl, as in Figur 8-1. h atr tabl oftn follos topography, although th rlif of th atr tabl is lss than th topography (Figur 8-2). Groundatr gnrally flos from topographic highs to topographic los, and dischargs at th topographic lo spots. Figur 8-2. Unconfind, or atr tabl aquifr (Fttr). Aquifr An aquifr is a gologic unit that can stor and transmit atr at sufficint rats to supply lls. his rquirs an intrinsic prmability of 10-2 darcy and abov. A confining layr is a gologic unit that has lo to no intrinsic prmability (.g., 10-2 darcy or lss), such as in clays and till. Confining layrs ar subdividd into aquifugs (absolutly imprmabl) and aquitards (imprmabl rlativ to th adjacnt units). Watr tabl aquifrs, thos ith no confining layr abov, ar calld unconfind aquifrs (Figur 8-2). Aquifrs ovrlain by a confining layr ar calld confind aquifrs (Figur 8-3). Whn you think about it, th aquifr insid th pip usd in Darcy s xprimnt as a confind aquifr. h pip itslf as a confining layr. Bcaus this aquifr as confind, any atr that as introducd to th pip fastr than it as rlasd causd prssur in th pip. Natural confind aquifrs act th sam ay. As atr rchargs th confind aquifr, prssur may build up in th aquifr. If on r to drill a ll in a prssurd confind aquifr, th atr 8-2
3 lvl in th ll (pizomtr) might ris far abov th aquifr. An artsian ll is a ll in hich th atr riss abov th top of th aquifr. In som cass th atr lvl may ris abov th ground surfac, in hich cas th ll is calld as a floing ll (Figur 8-4). Rcharg Confining Layr Confind Aquifr Figur 8-3. Confind aquifr (Fttr). Figur 8-4. Artsian and floing ll in confind aquifr (Fttr). Whr do aquifrs gt thir atr? In th cas of an unconfind aquifr, th atr largly coms dirctly from prcipitation sinc thr is no obstruction prvnting infiltrating atr from raching th atr tabl. You can imagin thn that th atr tabl may fluctuat significantly through th sasons bcaus of changs in prcipitation and vapotranspiration that srv to add and rmov atr from th subsurfac. h cas of th confind aquifr is lss straightforard, sinc thr is a confining layr atop th aquifr; its rcharg must com from mans othr than from dirct infiltration. An important mans of rcharg to confind aquifrs is by infiltration of prcipitation into portions of th aquifr that outcrop at th surfac (Figur 8-3). For xampl, 8-3
4 confind aquifrs in intrmontan basins may ris latrally ith th topography, and actually outcrop in th adjacnt foothills. Hnc, th outcrops in th foothills catch prcipitation and thn transmit th atr to lor lvation in th aquifr hr it bcoms confind. Potntiomtric surfac If th atr lvls in lls tappd in a confind aquifr ar plottd on a map and contourd, th rsulting surfac, hich is actually a map of th hydraulic had in th aquifr, is rfrrd to as a potntiomtric surfac (Figurs 8-5 and 8-6). If th aquifr is unconfind, th contour map is rfrrd to as th map of th atr tabl. Groundatr ill flo in th gnral dirction that th potntiomtric surfac is sloping, i.., from highr hydraulic had to lor hydraulic had (Figur 8-6). Figur 8-5. Unconfind aquifr and its atr tabl; confind aquifr and its potntiomtric surfac (Fttr). Figur 8-6. Potntiomtric surfac of th Dakota Sandston (Darton, 1909). 8-4
5 Comprssibility of Watr Fluids ar comprssibl,.g., an incras in prssur dp ill lad to a dcras in th volum of a givn mass of atr (V ). h comprssibility of atr (β) is dfind as: dv / V β = (8-2) dp hr dv is th chang in th volum of th atr, V is th original volum of th atr, and dp is th chang in prssur. h ngativ sign is ncssary to nsur a positiv β. Effctiv Strss h ight of ovrlying rock and atr crats a donard strss (σ ) on a saturatd aquifr (Figur 8-7). his strss is born by th granular sklton of th porous mdium and th fluid prssur p of th atr in th por spacs (Figur 8-7). Mathmatically spaking, hav: σ = σ p (8-3) + hr σ is th ffctiv strss, th portion of th total strss that is born by th granular sklton. In trms of th changs in ths paramtrs, hav: = dp (8-4) + hr is th chang in total strss, is th chang in ffctiv strss, and dp is th chang in fluid prssur. otal Strss σ p Fluid Prssur σ Effctiv Strss Figur 8-7. otal strss, ffctiv strss, and fluid prssur on an arbitrary plan through a saturatd porous mdium (Frz and Chrry). 8-5
6 At a givn point of th saturatd porous mdium, th ight of th ovrlying rock and atr rmains ssntially th sam ovr tim. In such cass, th chang in th total strss = 0, and = dp (8-5) In plain ords, quation 8-5 stats that if th fluid prssur incrass, th ffctiv strss dcrass by an qual amount; and if th fluid prssur dcrass, th ffctiv strss incrass by an qual amount. Rcall that p = ρgh, hr ρ is th dnsity of th fluid and g is th p gravitational constant. Also rcall that h = h p + z, hr h is th total hydraulic had and z is th lvation had. hrfor, th fluid prssur can b xprssd in trms of th hydraulic had as: Sinc z is a constant, diffrntiating quation 8-6 givs Substituting quation 8-7 into quation 8-5 yilds: p = ρ ghp = ρg( h z) (8-6) dp = ρ gdhp = ρgd( h z) = ρgdh (8-7) = ρgdh (8-8) Equation 8-8 stats that th chang in th ffctiv strss ( ) at a givn point in a saturatd aquifr is govrnd by th chang in th hydraulic had at that point. Comprssibility of a Porous Mdium h comprssibility of a porous mdium, α, is dfind as α dv / V = (8-9) hr V is th total volum of th porous mdium, dv is th chang in th volum of th porous mdium, and is th chang in ffctiv strss. Rcall that V = V s + V v, hr V s is th volum of th solids and V v is th volum of th atrsaturatd voids. An incras in ffctiv strss lads to a rduction dv in th total volum of th porous mdium. In granular matrials th rduction in th total volum of th porous mdium is almost ntirly du to grain rarrangmnt. In gnral, dv = dvs + dvv ; but th volum chang for individual grains du to th chang in ffctiv strss is ngligibl (in othr ords, individual grains ar almost incomprssibl). hrfor, can assum dv = dv (8-10) v 8-6
7 Equation 8-10 stats that th chang in th total volum of a porous mdium is qual to th chang in th volum of voids (or porosity) du to th rarrangmnt of th grains undr incrasd ffctiv strss. Aquifr Comprssibility Pumping from a ll ill rduc th prssur had in a saturatd aquifr, lading to incrasd ffctiv strss (quation 8-8). h aquifr sklton may consolidat or compact du to this incrasd ffctiv strss by th rarrangmnt of th grains (Figur 8-8). Aquifr comprssibility is dfind as db / b α = (8-11) hr α is th aquifr comprssibility, db is th chang in aquifr thicknss, b is th original aquifr thicknss, and is th chang in ffctiv strss (Figur 8-8). h ngativ sign indicats that th aquifr thicknss rducs as th ffctiv strss incrass. Figur 8-8. Aquifr compaction causd by groundatr pumping (Frz and Chrry). Sinc as = dp (quation 8-5) and dp = ρgdh (quation 8-7), quation 8-11 can also b rittn db / b db / b α = = (8-12) dp ρgdh Spcific Storag h spcific storag (S s ) of a saturatd aquifr is dfind as th volum of atr rlasd from th storag pr unit volum of th aquifr pr unit dclin in hydraulic had. As discussd arlir, a dcras in hydraulic had h ill lad to a dcras in fluid prssur p and an incras in ffctiv strss σ. A dcras in fluid prssur ill caus th fluid to xpand; and an incras in ffctiv strss ill caus th compaction of th aquifr. hrfor, th atr rlasd from 8-7
8 th storag du to a dcras in h is producd by to mchanisms: 1) th xpansion of th atr causd by dcrasing p, and 2) th compaction of th aquifr causd by incrasing σ. h volum of atr producd (dv ) by th xpansion of th atr can b drivd from quation 8-2: dv = βv dp (8-13) Rcall that for a saturatd aquifr V = V v = nv, hr n is th porosity. With V = 1 (unit volum of aquifr), dp = ρgdh (quation 8-7), and dh = -1 (unit dclin in hydraulic had), quation 8-13 bcoms dv = β ( nv )( ρgdh) = βnρg (8-14) h volum of atr xplld (dv ) from th unit volum of aquifr during compaction is qual to th rduction in volum of th aquifr (dv ). From quation 8-9, hav: dv = αv (8-15) Rcall that dv = dv v (quation 8-10), and V = V v for a saturatd aquifr. hrfor, dv = (8-16) dv h ngativ sign is addd sinc th volumtric rduction dv is ngativ, but th amount of atr producd dv is positiv. Combining quations 8-15 and 8-16, hav: dv = dv = αv (8-17) For V = 1 (unit volum of aquifr), dh = -1 (unit dclin in hydraulic had), and (quation 8-8), quation 8-16 bcoms: = ρgdh dv = αρg (8-18) h spcific storag S s is th sum of th to trms givn by quations 8-14 and 8-18: S s = ρg( α + nβ ) (8-19) ransmissivity and Storativity of a Confind Aquifr W hav mntiond transmissivity () and storativity (S) arlir in th cours. For a confind aquifr of thicknss b, th transmissivity is dfind as = bk (8-20) 8-8
9 hr K is th hydraulic conductivity, and th storativity (or storag cofficint) S is dfind as Substituting quation 8-19 into quation 8-21 givs: S = S s b (8-21) S = ρgb( α + nβ ) (8-22) In plain ords, th storativity of a confind aquifr of thicknss b is th volum of atr rlasd from th storag pr unit surfac ara of th aquifr pr unit dclin in hydraulic had or potntiomtric surfac (Figur 8-9). Figur 8-9. Diagrams illustrating th concpt of storativity in (a) an unconfind aquifr and (b) a confind aquifr (Domnico and Schartz). ransmissivity and Spcific Yild in an Unconfind Aquifr In an unconfind aquifr, th transmissivity is dfind by th sam quation (8-20) but b is th saturatd thicknss of th aquifr or th hight of th atr tabl abov th top of th undrlying confining aquifr. In an unconfind aquifr, th rlas of atr from storag is primary du to th datring of th por spacs. his datring is dirctly rlatd to th spcific yild S y of th aquifr matrials. Watr may also b rlasd in an unconfind aquifr du to th scondary ffcts of atr xpansion and aquifr compaction. hrfor, th storativity of an unconfind aquifr is dfind as S = S S b (8-23) y + s 8-9
10 For an unconfind aquifr th valu of S y is typically svral ordrs of magnitud gratr than th valu of S s b, and th storativity is oftn takn to b qual to S y. h volum of atr draind from an aquifr du to th drop in hydraulic had can b stimatd from th formula V = SA h (8-24) hr V is th volum of atr draind, S is th storativity, A is th surfac ara ovrlying th draind aquifr, and h is th dclin in hydraulic had. Storativity valus for confind aquifrs rang from to 0.005; storativity valus for unconfind aquifrs ar much highr, ranging from 0.02 to hrfor, for th sam dclin in hydraulic had, th volum of atr rlasd from an unconfind aquifr ill b much gratr than th volum of atr rlasd from a confind aquifr. 8-10
Lecture 3: Diffusion: Fick s first law
Lctur 3: Diffusion: Fick s first law Today s topics What is diffusion? What drivs diffusion to occur? Undrstand why diffusion can surprisingly occur against th concntration gradint? Larn how to dduc th
More informationQuestion 3: How do you find the relative extrema of a function?
ustion 3: How do you find th rlativ trma of a function? Th stratgy for tracking th sign of th drivativ is usful for mor than dtrmining whr a function is incrasing or dcrasing. It is also usful for locating
More informationForeign Exchange Markets and Exchange Rates
Microconomics Topic 1: Explain why xchang rats indicat th pric of intrnational currncis and how xchang rats ar dtrmind by supply and dmand for currncis in intrnational markts. Rfrnc: Grgory Mankiw s Principls
More informationBasis risk. When speaking about forward or futures contracts, basis risk is the market
Basis risk Whn spaking about forward or futurs contracts, basis risk is th markt risk mismatch btwn a position in th spot asst and th corrsponding futurs contract. Mor broadly spaking, basis risk (also
More informationQUANTITATIVE METHODS CLASSES WEEK SEVEN
QUANTITATIVE METHODS CLASSES WEEK SEVEN Th rgrssion modls studid in prvious classs assum that th rspons variabl is quantitativ. Oftn, howvr, w wish to study social procsss that lad to two diffrnt outcoms.
More informationby John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia
Studnt Nots Cost Volum Profit Analysis by John Donald, Lcturr, School of Accounting, Economics and Financ, Dakin Univrsity, Australia As mntiond in th last st of Studnt Nots, th ability to catgoris costs
More informationNew Basis Functions. Section 8. Complex Fourier Series
Nw Basis Functions Sction 8 Complx Fourir Sris Th complx Fourir sris is prsntd first with priod 2, thn with gnral priod. Th connction with th ral-valud Fourir sris is xplaind and formula ar givn for convrting
More informationEcon 371: Answer Key for Problem Set 1 (Chapter 12-13)
con 37: Answr Ky for Problm St (Chaptr 2-3) Instructor: Kanda Naknoi Sptmbr 4, 2005. (2 points) Is it possibl for a country to hav a currnt account dficit at th sam tim and has a surplus in its balanc
More informationEFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS
25 Vol. 3 () January-March, pp.37-5/tripathi EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS *Shilpa Tripathi Dpartmnt of Chmical Enginring, Indor Institut
More informationME 612 Metal Forming and Theory of Plasticity. 6. Strain
Mtal Forming and Thory of Plasticity -mail: azsnalp@gyt.du.tr Makin Mühndisliği Bölümü Gbz Yüksk Tknoloji Enstitüsü 6.1. Uniaxial Strain Figur 6.1 Dfinition of th uniaxial strain (a) Tnsil and (b) Comprssiv.
More informationMathematics. Mathematics 3. hsn.uk.net. Higher HSN23000
hsn uknt Highr Mathmatics UNIT Mathmatics HSN000 This documnt was producd spcially for th HSNuknt wbsit, and w rquir that any copis or drivativ works attribut th work to Highr Still Nots For mor dtails
More informationLecture 20: Emitter Follower and Differential Amplifiers
Whits, EE 3 Lctur 0 Pag of 8 Lctur 0: Emittr Followr and Diffrntial Amplifirs Th nxt two amplifir circuits w will discuss ar ry important to lctrical nginring in gnral, and to th NorCal 40A spcifically.
More informationSection 7.4: Exponential Growth and Decay
1 Sction 7.4: Exponntial Growth and Dcay Practic HW from Stwart Txtbook (not to hand in) p. 532 # 1-17 odd In th nxt two ction, w xamin how population growth can b modld uing diffrntial quation. W tart
More informationIntroduction to Finite Element Modeling
Introduction to Finit Elmnt Modling Enginring analysis of mchanical systms hav bn addrssd by driving diffrntial quations rlating th variabls of through basic physical principls such as quilibrium, consrvation
More informationhttp://www.wwnorton.com/chemistry/tutorials/ch14.htm Repulsive Force
ctivation nrgis http://www.wwnorton.com/chmistry/tutorials/ch14.htm (back to collision thory...) Potntial and Kintic nrgy during a collision + + ngativly chargd lctron cloud Rpulsiv Forc ngativly chargd
More informationCPS 220 Theory of Computation REGULAR LANGUAGES. Regular expressions
CPS 22 Thory of Computation REGULAR LANGUAGES Rgular xprssions Lik mathmatical xprssion (5+3) * 4. Rgular xprssion ar built using rgular oprations. (By th way, rgular xprssions show up in various languags:
More informationLong run: Law of one price Purchasing Power Parity. Short run: Market for foreign exchange Factors affecting the market for foreign exchange
Lctur 6: Th Forign xchang Markt xchang Rats in th long run CON 34 Mony and Banking Profssor Yamin Ahmad xchang Rats in th Short Run Intrst Parity Big Concpts Long run: Law of on pric Purchasing Powr Parity
More informationIrrigating With High Salinity Water 1
BUL322 Irrigating With High Watr 1 Dorota Z. Haman 2 In humid aras such as Florida, salinity concrns ar diffrnt than in arid aras sinc larg amounts of rainfall will wash out salts concntrating in th soil
More informationTraffic Flow Analysis (2)
Traffic Flow Analysis () Statistical Proprtis. Flow rat distributions. Hadway distributions. Spd distributions by Dr. Gang-Ln Chang, Profssor Dirctor of Traffic safty and Oprations Lab. Univrsity of Maryland,
More informationVan der Waals Forces Between Atoms
Van dr Waals Forcs twn tos Michal Fowlr /8/7 Introduction Th prfct gas quation of stat PV = NkT is anifstly incapabl of dscribing actual gass at low tpraturs, sinc thy undrgo a discontinuous chang of volu
More informationAP Calculus AB 2008 Scoring Guidelines
AP Calculus AB 8 Scoring Guidlins Th Collg Board: Conncting Studnts to Collg Succss Th Collg Board is a not-for-profit mmbrship association whos mission is to connct studnts to collg succss and opportunity.
More informationFundamentals: NATURE OF HEAT, TEMPERATURE, AND ENERGY
Fundamntals: NATURE OF HEAT, TEMPERATURE, AND ENERGY DEFINITIONS: Quantum Mchanics study of individual intractions within atoms and molculs of particl associatd with occupid quantum stat of a singl particl
More information81-1-ISD Economic Considerations of Heat Transfer on Sheet Metal Duct
Air Handling Systms Enginring & chnical Bulltin 81-1-ISD Economic Considrations of Hat ransfr on Sht Mtal Duct Othr bulltins hav dmonstratd th nd to add insulation to cooling/hating ducts in ordr to achiv
More informationThe Hall Plot Analysis of a Water Injection Test Affected by Geothermal Reservoir Response
Procdings World Gothrmal Congrss 25 Antalya, Turky, 24-29 April 25 Th Hall Plot Analysis of a Watr Injction Tst Affctd by Gothrmal Rsrvoir Rspons I. Mtin Mihcakan,* Elif I. Altinay,* and Ibrahim Kasap**
More information5.4 Exponential Functions: Differentiation and Integration TOOTLIFTST:
.4 Eponntial Functions: Diffrntiation an Intgration TOOTLIFTST: Eponntial functions ar of th form f ( ) Ab. W will, in this sction, look at a spcific typ of ponntial function whr th bas, b, is.78.... This
More informationVector Network Analyzer
Cours on Microwav Masurmnts Vctor Ntwork Analyzr Prof. Luca Prrgrini Dpt. of Elctrical, Computr and Biomdical Enginring Univrsity of Pavia -mail: luca.prrgrini@unipv.it wb: microwav.unipv.it Microwav Masurmnts
More informationFinancial Mathematics
Financial Mathatics A ractical Guid for Actuaris and othr Businss rofssionals B Chris Ruckan, FSA & Jo Francis, FSA, CFA ublishd b B rofssional Education Solutions to practic qustions Chaptr 7 Solution
More informationA Note on Approximating. the Normal Distribution Function
Applid Mathmatical Scincs, Vol, 00, no 9, 45-49 A Not on Approimating th Normal Distribution Function K M Aludaat and M T Alodat Dpartmnt of Statistics Yarmouk Univrsity, Jordan Aludaatkm@hotmailcom and
More informationIncreasing Net Debt as a percentage of Average Equalized ValuaOon
City of Orang Township Warning Trnd: Incrasing Nt Dbt as a prcntag of avrag qualizd valuation Nt Dbt 3 yr. Avg. qualizd Valuation Incrasing Nt Dbt as a prcntag of Avrag Equalizd ValuaOon rc 1.20% 1.00%
More informationInternational Association of Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research)
Intrnational Association of Scintific Innovation and Rsarch (IASIR) (An Association Unifing th Scincs, Enginring, and Applid Rsarch) ISSN (Print): 79-000 ISSN (Onlin): 79-009 Intrnational Journal of Enginring,
More informationEconomic Analysis of Floating Exchange Rate Systems
Economic Analysis of Floating Rat Systms Th businss sction of any nwspapr will hav a tabl of spot s. Ths ar th s at which a prson could hav bought othr currncis or forign, such as th English Pound, Frnch
More informationCPU. Rasterization. Per Vertex Operations & Primitive Assembly. Polynomial Evaluator. Frame Buffer. Per Fragment. Display List.
Elmntary Rndring Elmntary rastr algorithms for fast rndring Gomtric Primitivs Lin procssing Polygon procssing Managing OpnGL Stat OpnGL uffrs OpnGL Gomtric Primitivs ll gomtric primitivs ar spcifid by
More informationParallel and Distributed Programming. Performance Metrics
Paralll and Distributd Programming Prformanc! wo main goals to b achivd with th dsign of aralll alications ar:! Prformanc: th caacity to rduc th tim to solv th roblm whn th comuting rsourcs incras;! Scalability:
More informationPerformance Evaluation
Prformanc Evaluation ( ) Contnts lists availabl at ScincDirct Prformanc Evaluation journal hompag: www.lsvir.com/locat/pva Modling Bay-lik rputation systms: Analysis, charactrization and insuranc mchanism
More information(Analytic Formula for the European Normal Black Scholes Formula)
(Analytic Formula for th Europan Normal Black Schols Formula) by Kazuhiro Iwasawa Dcmbr 2, 2001 In this short summary papr, a brif summary of Black Schols typ formula for Normal modl will b givn. Usually
More informationFactorials! Stirling s formula
Author s not: This articl may us idas you havn t larnd yt, and might sm ovrly complicatd. It is not. Undrstanding Stirling s formula is not for th faint of hart, and rquirs concntrating on a sustaind mathmatical
More informationIntermediate Macroeconomic Theory / Macroeconomic Analysis (ECON 3560/5040) Final Exam (Answers)
Intrmdiat Macroconomic Thory / Macroconomic Analysis (ECON 3560/5040) Final Exam (Answrs) Part A (5 points) Stat whthr you think ach of th following qustions is tru (T), fals (F), or uncrtain (U) and brifly
More informationSPECIAL VOWEL SOUNDS
SPECIAL VOWEL SOUNDS Plas consult th appropriat supplmnt for th corrsponding computr softwar lsson. Rfr to th 42 Sounds Postr for ach of th Spcial Vowl Sounds. TEACHER INFORMATION: Spcial Vowl Sounds (SVS)
More informationNoise Power Ratio (NPR) A 65-Year Old Telephone System Specification Finds New Life in Modern Wireless Applications.
TUTORIL ois Powr Ratio (PR) 65-Yar Old Tlphon Systm Spcification Finds w Lif in Modrn Wirlss pplications ITRODUTIO by Walt Kstr Th concpt of ois Powr Ratio (PR) has bn around sinc th arly days of frquncy
More informationChapter 7. Fastenings. Contents. Lawrence A. Soltis
Fastnings Lawrnc A. Soltis Chaptr 7 Contnts Nails 7 Withdrawal Rsistanc 7 Latral Rsistanc 7 5 Spiks 7 8 Stapls 7 8 Drift Bolts 7 9 Wood Scrws 7 9 Withdrawal Rsistanc 7 9 Latral Rsistanc 7 1 Lag Scrws 7
More informationThe example is taken from Sect. 1.2 of Vol. 1 of the CPN book.
Rsourc Allocation Abstract This is a small toy xampl which is wll-suitd as a first introduction to Cnts. Th CN modl is dscribd in grat dtail, xplaining th basic concpts of C-nts. Hnc, it can b rad by popl
More informationCIRCUITS AND ELECTRONICS. Basic Circuit Analysis Method (KVL and KCL method)
6. CIRCUITS AND ELECTRONICS Basic Circuit Analysis Mthod (KVL and KCL mthod) Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur Rviw Lumpd
More informationCurrent and Resistance
Chaptr 6 Currnt and Rsistanc 6.1 Elctric Currnt...6-6.1.1 Currnt Dnsity...6-6. Ohm s Law...6-4 6.3 Elctrical Enrgy and Powr...6-7 6.4 Summary...6-8 6.5 Solvd Problms...6-9 6.5.1 Rsistivity of a Cabl...6-9
More informationCHAPTER 4c. ROOTS OF EQUATIONS
CHAPTER c. ROOTS OF EQUATIONS A. J. Clark School o Enginring Dpartmnt o Civil and Environmntal Enginring by Dr. Ibrahim A. Aakka Spring 00 ENCE 03 - Computation Mthod in Civil Enginring II Dpartmnt o Civil
More informationAdverse Selection and Moral Hazard in a Model With 2 States of the World
Advrs Slction and Moral Hazard in a Modl With 2 Stats of th World A modl of a risky situation with two discrt stats of th world has th advantag that it can b natly rprsntd using indiffrnc curv diagrams,
More information5 2 index. e e. Prime numbers. Prime factors and factor trees. Powers. worked example 10. base. power
Prim numbrs W giv spcial nams to numbrs dpnding on how many factors thy hav. A prim numbr has xactly two factors: itslf and 1. A composit numbr has mor than two factors. 1 is a spcial numbr nithr prim
More information1.72, Groundwater Hydrology Prof. Charles Harvey Lecture Packet #2: Aquifers, Porosity, and Darcy s Law. Lake (Exposed Water Table)
1.72, Groundwater Hydrology Prof. Charles Harvey Lecture Packet #2: Aquifers, Porosity, and Darcy s Law Precipitation Infiltration Lake (Exposed Water Table) River Water table Saturated zone - Aquifer
More informationLG has introduced the NeON 2, with newly developed Cello Technology which improves performance and reliability. Up to 320W 300W
Cllo Tchnology LG has introducd th NON 2, with nwly dvlopd Cllo Tchnology which improvs prformanc and rliability. Up to 320W 300W Cllo Tchnology Cll Connction Elctrically Low Loss Low Strss Optical Absorption
More informationHost Country: Czech Republic Other parties: Denmark Expected ERUs in 2008 2012: ~ 1,250,000 tco 2
Projct CZ1000033: Nitrous Oxid Emission Rductions at Lovochmi Host Country: Czch Rpublic Othr partis: Dnmark Expctd ERUs in 2008 2012: ~ 1,250,000 tco 2 Th projct at Lovochmi in th Czch Rpublic aims to
More informationLecture notes: 160B revised 9/28/06 Lecture 1: Exchange Rates and the Foreign Exchange Market FT chapter 13
Lctur nots: 160B rvisd 9/28/06 Lctur 1: xchang Rats and th Forign xchang Markt FT chaptr 13 Topics: xchang Rats Forign xchang markt Asst approach to xchang rats Intrst Rat Parity Conditions 1) Dfinitions
More informationDevelopment of Financial Management Reporting in MPLS
1 Dvlopmnt of Financial Managmnt Rporting in MPLS 1. Aim Our currnt financial rports ar structurd to dlivr an ovrall financial pictur of th dpartmnt in it s ntirty, and thr is no attmpt to provid ithr
More informationVersion 1.0. General Certificate of Education (A-level) January 2012. Mathematics MPC3. (Specification 6360) Pure Core 3. Final.
Vrsion.0 Gnral Crtificat of Education (A-lvl) January 0 Mathmatics MPC (Spcification 660) Pur Cor Final Mark Schm Mark schms ar prpard by th Principal Eaminr and considrd, togthr with th rlvant qustions,
More informationEntity-Relationship Model
Entity-Rlationship Modl Kuang-hua Chn Dpartmnt of Library and Information Scinc National Taiwan Univrsity A Company Databas Kps track of a company s mploys, dpartmnts and projcts Aftr th rquirmnts collction
More informationBASIC DEFINITIONS AND TERMINOLOGY OF SOILS
1 BASIC DEFINITIONS AND TERMINOLOGY OF SOILS Soil i a thr pha atrial hich coit of olid particl hich ak up th oil klto ad void hich ay b full of atr if th oil i aturatd, ay b full of air if th oil i dry,
More informationOn the moments of the aggregate discounted claims with dependence introduced by a FGM copula
On th momnts of th aggrgat discountd claims with dpndnc introducd by a FGM copula - Mathiu BARGES Univrsité Lyon, Laboratoir SAF, Univrsité Laval - Hélèn COSSETTE Ecol Actuariat, Univrsité Laval, Québc,
More informationTHE FUNDAMENTALS OF CURRENT SENSE TRANSFORMER DESIGN. Patrick A. Cattermole, Senior Applications Engineer MMG 10 Vansco Road, Toronto Ontario Canada
, Snior Alications nginr MMG 10 Vansco Road, Toronto Ontario Canada Abstract Th following ar will first rviw th basic rincils of oration of a Currnt Sns Transformr and thn follow a simlifid dsign rocdur.
More information[ ] These are the motor parameters that are needed: Motor voltage constant. J total (lb-in-sec^2)
MEASURING MOOR PARAMEERS Fil: Motor paramtrs hs ar th motor paramtrs that ar ndd: Motor voltag constant (volts-sc/rad Motor torqu constant (lb-in/amp Motor rsistanc R a (ohms Motor inductanc L a (Hnris
More informationPhysics 106 Lecture 12. Oscillations II. Recap: SHM using phasors (uniform circular motion) music structural and mechanical engineering waves
Physics 6 Lctur Oscillations II SJ 7 th Ed.: Chap 5.4, Rad only 5.6 & 5.7 Rcap: SHM using phasors (unifor circular otion) Physical pndulu xapl apd haronic oscillations Forcd oscillations and rsonanc. Rsonanc
More informationAdsorption of Malachite Green Dye onto Activated Carbon Derived from Durian Peel
Adsorption of Malachit Grn Dy onto Activatd Carbon Drivd from Durian Pl SARAWUT SRIKHUN, SAMORN HIRUNPRADITKUN, KAMCHAI NUITHITIKUL* Dpartmnt of Chmical Enginring King Mongkut s Univrsity of Tchnology
More informationIncomplete 2-Port Vector Network Analyzer Calibration Methods
Incomplt -Port Vctor Ntwork nalyzr Calibration Mthods. Hnz, N. Tmpon, G. Monastrios, H. ilva 4 RF Mtrology Laboratory Instituto Nacional d Tcnología Industrial (INTI) Bunos irs, rgntina ahnz@inti.gov.ar
More informationProduction Costing (Chapter 8 of W&W)
Production Costing (Chaptr 8 of W&W).0 Introduction Production costs rfr to th oprational costs associatd with producing lctric nrgy. Th most significant componnt of production costs ar th ful costs ncssary
More informationTheoretical aspects of investment demand for gold
Victor Sazonov (Russia), Dmitry Nikolav (Russia) Thortical aspcts of invstmnt dmand for gold Abstract Th main objctiv of this articl is construction of a thortical modl of invstmnt in gold. Our modl is
More informationGovernment Spending or Tax Cuts for Education in Taylor County, Texas
Govrnmnt Spnding or Tax Cuts for Education in Taylor County, Txas Ian Shphrd Abiln Christian Univrsity D Ann Shphrd Abiln Christian Univrsity On Fbruary 17, 2009, Prsidnt Barack Obama signd into law th
More informationHigh Interest Rates In Ghana,
NO. 27 IEA MONOGRAPH High Intrst Rats In Ghana, A Critical Analysis IEA Ghana THE INSTITUTE OF ECONOMIC AFFAIRS A Public Policy Institut High Intrst Rats In Ghana, A Critical Analysis 1 by DR. J. K. KWAKYE
More informationEthanolic Extraction of Soybean Oil: Oil Solubility Equilibria and Kinetic Studies
Ethanolic Extraction of Soyban Oil: Oil Solubility Equilibria and Kintic Studis Christiann E. C. Rodrigus*, Natália M. Longo, Cibl C. Silva, Kila K.. Aracava, Bruna R. Garavazo Sparation Enginring Laboratory
More informationAnalyzing the Economic Efficiency of ebaylike Online Reputation Reporting Mechanisms
A rsarch and ducation initiativ at th MIT Sloan School of Managmnt Analyzing th Economic Efficincy of Baylik Onlin Rputation Rporting Mchanisms Papr Chrysanthos Dllarocas July For mor information, plas
More informationAP Calculus Multiple-Choice Question Collection 1969 1998. connect to college success www.collegeboard.com
AP Calculus Multipl-Choic Qustion Collction 969 998 connct to collg succss www.collgboard.com Th Collg Board: Conncting Studnts to Collg Succss Th Collg Board is a not-for-profit mmbrship association whos
More informationESCI 241 Meteorology Lesson 6 Humidity
ESCI 41 Mtorology Lsson 6 Humiity Raing: MT Chatr 5 PARTIAL PRESSURE In a mixtur of gass, ach gas scis contributs to th total rssur. ο Th rssur xrt by a singl gas scis is known as th artial rssur for that
More informationA Theoretical Model of Public Response to the Homeland Security Advisory System
A Thortical Modl of Public Rspons to th Homland Scurity Advisory Systm Amy (Wnxuan) Ding Dpartmnt of Information and Dcision Scincs Univrsity of Illinois Chicago, IL 60607 wxding@uicdu Using a diffrntial
More informationRemember you can apply online. It s quick and easy. Go to www.gov.uk/advancedlearningloans. Title. Forename(s) Surname. Sex. Male Date of birth D
24+ Advancd Larning Loan Application form Rmmbr you can apply onlin. It s quick and asy. Go to www.gov.uk/advancdlarningloans About this form Complt this form if: you r studying an ligibl cours at an approvd
More informationFACULTY SALARIES FALL 2004. NKU CUPA Data Compared To Published National Data
FACULTY SALARIES FALL 2004 NKU CUPA Data Compard To Publishd National Data May 2005 Fall 2004 NKU Faculty Salaris Compard To Fall 2004 Publishd CUPA Data In th fall 2004 Northrn Kntucky Univrsity was among
More informationThe international Internet site of the geoviticulture MCC system Le site Internet international du système CCM géoviticole
Th intrnational Intrnt sit of th goviticultur MCC systm L sit Intrnt intrnational du systèm CCM géoviticol Flávio BELLO FIALHO 1 and Jorg TONIETTO 1 1 Rsarchr, Embrapa Uva Vinho, Caixa Postal 130, 95700-000
More informationConstraint-Based Analysis of Gene Deletion in a Metabolic Network
Constraint-Basd Analysis of Gn Dltion in a Mtabolic Ntwork Abdlhalim Larhlimi and Alxandr Bockmayr DFG-Rsarch Cntr Mathon, FB Mathmatik und Informatik, Fri Univrsität Brlin, Arnimall, 3, 14195 Brlin, Grmany
More informationSTATEMENT OF INSOLVENCY PRACTICE 3.2
STATEMENT OF INSOLVENCY PRACTICE 3.2 COMPANY VOLUNTARY ARRANGEMENTS INTRODUCTION 1 A Company Voluntary Arrangmnt (CVA) is a statutory contract twn a company and its crditors undr which an insolvncy practitionr
More informationCARE QUALITY COMMISSION ESSENTIAL STANDARDS OF QUALITY AND SAFETY. Outcome 10 Regulation 11 Safety and Suitability of Premises
CARE QUALITY COMMISSION ESSENTIAL STANDARDS OF QUALITY AND SAFETY Outcom 10 Rgulation 11 Safty and Suitability of Prmiss CQC Rf 10A 10A(1) Lad Dirctor / Lad Officr Rspons Impact Liklihood Lvl of Concrn
More informationCUTTING METHODS AND CARTESIAN ROBOTS KESME YÖNTEMLERİ VE KARTEZYEN ROBOTLAR
ournal of Naval Scinc and Enginring 2009, Vol. 5, No.2, pp. 35-42 CUTTING METHODS AND CARTESIAN ROBOTS Asst. Prof. Ugur SIMSIR, Lt.Cdr. Turkish Naval Acady Mchanical Enginring Dpartnt Tuzla, Istanbul,Turkiy
More informationSPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM
RESEARCH PAPERS IN MANAGEMENT STUDIES SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM M.A.H. Dmpstr & S.S.G. Hong WP 26/2000 Th Judg Institut of Managmnt Trumpington Strt Cambridg CB2 1AG Ths paprs
More informationWORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769
08-16-85 WORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769 Summary of Dutis : Dtrmins City accptanc of workrs' compnsation cass for injurd mploys; authorizs appropriat tratmnt
More informationFredy Vélez. Centro Tecnológico CARTIF, Valladolid, España. frevel@cartif.es
Slcting working fluids in an organic Rankin cycl for powr gnration from low tmpratur hat sourcs Frdy Vélz Cntro Tcnológico CARTIF, Valladolid, España. frvl@cartif.s Rcivd: January 21th, d 2014. Rcivd in
More informationGold versus stock investment: An econometric analysis
Intrnational Journal of Dvlopmnt and Sustainability Onlin ISSN: 268-8662 www.isdsnt.com/ijds Volum Numbr, Jun 202, Pag -7 ISDS Articl ID: IJDS20300 Gold vrsus stock invstmnt: An conomtric analysis Martin
More informationElectric power can be transmitted or dis
64 64 Principls of Powr Systm CHAPTER CHAPTER Unrgroun Cabls. Unrgroun Cabls. Construction of Cabls.3 Insulating Matrials for Cabls.4 Classification of Cabls.5 Cabls for 3-Phas Srvic.6 Laying of Unrgroun
More informationDiskussionspapiere der DFG- Forschergruppe (Nr.: 3468269275): Heterogene Arbeit: Positive und Normative Aspekte der Qualifikationsstruktur der Arbeit
Rchts-, Wirtschafts- und Vrwaltungswissnschaftlich Sktion Fachbrich Wirtschaftswissnschaftn Diskussionspapir dr DFG- Forschrgrupp (Nr.: 3468269275): Htrogn Arbit: Positiv und Normativ Aspkt dr Qualifikationsstruktur
More informationCapacitance and Dielectrics
Chaptr 5 Capacitanc and Dilctrics 5.1 Introduction...5-3 5. Calculation of Capacitanc...5-4 Exampl 5.1: Paralll-Plat Capacitor...5-4 Intractiv Simulation 5.1: Paralll-Plat Capacitor...5-6 Exampl 5.: Cylindrical
More informationThe Coverage Analysis for Low Earth Orbiting Satellites at Low Elevation
(IJACSA) Intrnational Journal of Advancd Computr Scinc and Applications, Vol. 5, No. 6, 14 Th Covrag Analysis for Low Earth Orbiting Satllits at Low Elvation Shklzn Cakaj 1, Bxht Kamo 1, Algnti Lala 1,
More informationI. INTRODUCTION. Figure 1, The Input Display II. DESIGN PROCEDURE
Ballast Dsign Softwar Ptr Grn, Snior ighting Systms Enginr, Intrnational Rctifir, ighting Group, 101S Spulvda Boulvard, El Sgundo, CA, 9045-438 as prsntd at PCIM Europ 0 Abstract: W hav dvlopd a Windows
More informationWage Inflation and the Distribution of Output Gaps in Europe: Insiders vs. Outsiders
Economtric Rsarch and Spcial Studis Dpartmnt Wag Inflation and th Distribution of Output Gaps in Europ: Insidrs vs. Outsidrs M. Dmrtzis and A. Hughs Halltt Rsarch Mmorandum WO&E no. 631 Sptmbr 2000 D Ndrlandsch
More informationNew Concepts and Methods in Information Aggregation
Nw Concpts and Mthods in Information Aggrgation János Fodor 1, Imr J. Rudas John von Numann Faculty of Informatics, Budapst Tch Bécsi út 96/B, H-1034 Budapst, Hungary E-mail: {Fodor, Rudas}@bmf.hu Abstract:
More informationCHARACTERISTICS OF ELECTROMAGNETIC WAVE PROPAGATION THROUGH A MAGNETISED PLASMA SLAB WITH LINEARLY VARYING ELECTRON DEN- SITY
Progrss In Elctromagntics Rsarch B, Vol. 21, 385 398, 2010 CHARACTERISTICS OF ELECTROMAGNETIC WAVE PROPAGATION THROUGH A MAGNETISED PLASMA SLAB WITH LINEARLY VARYING ELECTRON DEN- SITY Ç. S. Gürl Dpartmnt
More informationChapter 19: Permanent Magnet DC Motor Characteristics
Chaptr 19: Prmannt Magnt DC Motor Charactristics 19.1: ntroduction Dirct currnt (DC) motors compris on of th most common typs of actuator dsignd into lctromchanical systms. hy ar a vry straightforward
More informationTIME MANAGEMENT. 1 The Process for Effective Time Management 2 Barriers to Time Management 3 SMART Goals 4 The POWER Model e. Section 1.
Prsonal Dvlopmnt Track Sction 1 TIME MANAGEMENT Ky Points 1 Th Procss for Effctiv Tim Managmnt 2 Barrirs to Tim Managmnt 3 SMART Goals 4 Th POWER Modl In th Army, w spak of rsourcs in trms of th thr M
More informationFleet vehicles opportunities for carbon management
Flt vhicls opportunitis for carbon managmnt Authors: Kith Robrtson 1 Dr. Kristian Stl 2 Dr. Christoph Hamlmann 3 Alksandra Krukar 4 Tdla Mzmir 5 1 Snior Sustainability Consultant & Lad Analyst, Arup 2
More informationDENTAL CAD MADE IN GERMANY MODULAR ARCHITECTURE BACKWARD PLANNING CUTBACK FUNCTION BIOARTICULATOR INTUITIVE USAGE OPEN INTERFACE. www.smartoptics.
DENTAL CAD MADE IN GERMANY MODULAR ARCHITECTURE BACKWARD PLANNING CUTBACK FUNCTION BIOARTICULATOR INTUITIVE USAGE OPEN INTERFACE www.smartoptics.d dntprogrss an b rsion c v o m d ss.d! A fr ntprog.d w
More informationHardware Modules of the RSA Algorithm
SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol. 11, No. 1, Fbruary 2014, 121-131 UDC: 004.3`142:621.394.14 DOI: 10.2298/SJEE140114011S Hardwar Moduls of th RSA Algorithm Vlibor Škobić 1, Branko Dokić 1,
More informationHigher. Exponentials and Logarithms 160
hsn uknt Highr Mthmtics UNIT UTCME Eponntils nd Logrithms Contnts Eponntils nd Logrithms 6 Eponntils 6 Logrithms 6 Lws of Logrithms 6 Eponntils nd Logrithms to th Bs 65 5 Eponntil nd Logrithmic Equtions
More informationWho uses our services? We have a growing customer base. with institutions all around the globe.
not taking xpr Srvic Guid 2013 / 2014 NTE i an affordabl option for audio to txt convrion. Our rvic includ not or dirct trancription rvic from prviouly rcordd audio fil. Our rvic appal pcially to tudnt
More informationArchitecture of the proposed standard
Architctur of th proposd standard Introduction Th goal of th nw standardisation projct is th dvlopmnt of a standard dscribing building srvics (.g.hvac) product catalogus basd on th xprincs mad with th
More informationChapter 4: Biochemical redox reactions
Chaptr 4: Biochmical ractions 4.1 Introduction 4.2 Biochmical half-ractions, th Faraday conststant and th uction potntial 4.2.1 Dfining th uction potntial: 4.2.2 Th standard uction potntial is also th
More informationEffect of Design Parameter on the Performance of Lithium Ion Battery
Aadil Ahmad, Mohd. Parvz / Intrnational Journal of Enginring Rarch and Application Vol. 3, Iu 4, Jul-Aug 2013, pp.1196-1201 Effct of Dign Paramtr on th Prformanc of Lithium Ion Battry Aadil Ahmad 1, Mohd.
More informationUser-Perceived Quality of Service in Hybrid Broadcast and Telecommunication Networks
Usr-Prcivd Quality of Srvic in Hybrid Broadcast and Tlcommunication Ntworks Michal Galtzka Fraunhofr Institut for Intgratd Circuits Branch Lab Dsign Automation, Drsdn, Grmany Michal.Galtzka@as.iis.fhg.d
More information