Control of the grain size distribution of the raw material mixture in the production of iron sinter

Size: px
Start display at page:

Download "Control of the grain size distribution of the raw material mixture in the production of iron sinter"

Transcription

1 SAIMM_57-64:Templte Joul 6/9/08 11:55 AM Pge 293 Cotol of the gi size distibutio of the w mteil mixtue i the poductio of io site by E. Lwmb* d A.M. Gbes-Cig* Bckgoud T s c t i o Syopsis The im of this study ws to exmie the effect of gi size distibutio cotol of the w mteil mixtue o the pemebility of the gee site bed d the popeties of the poduced site. This ws chieved by evlutig the gultio chcteistics of the site mixtue (moistue cotet, gultio time d me gule dimete) i tems of its gee bed pemebility, d evlutig the poductivity of the site bed, the coke te, tumble idex (TI), bsio idex (AI), eductio disitegtio idex (RDI) d educibility (RI) of the poduced site. The w site mixtues cotied combitios of Thbzimbi io oe, Sishe io oe, coke, lime d etu fies. The gi size distibutios wee cotolled by emovig the 0.5 mm size fctios of the etu fies d coke, d the 1 mm size fctio of lime. Of the exmied mixtues, mixtue of 20 mss% Thbzimbi io oe, 80 mss% Sishe io oe d fluxes whee the coke, lime d etu fies wee ll sized hd the highest gultio effectiveess d pemebility. The siteig popeties of the mixtues i which the gi size distibutios wee cotolled, wee vey simil fo ll the mixtues, but supeio to the bse cse mixtue i which the gi size distibutio ws ot cotolled. Keywods: Thbzimbi io oe; Sishe io oe; gultio, pemebility, gi size distibutio; site. Itoductio I the mjoity of poductio pocesses, the pticle size distibutios of the w mteils ifluece the popeties of the poduct. This lso petis to io site, which is costituted of mixtue of w mteils (io oe, coke beeze, limestoe, lime, dolomite, etu fies) ll of which hve vious size distibutios. Although AceloMittl Vdebijlpk hs fixed specifictios o the physicl d chemicl popeties of the poduced site fo optiml blst fuce pefomce, the pticle size distibutio of thei site mixtue hs ot yet bee optimized. The mi pupose of this study ws theefoe to exmie the effect of pticle size distibutio cotol of the w mteil mixtue o the qulity of the poduced site. Oly limited mout of fie io oe pticles c be diectly chged to the blst fuce, s they e detimetl to the pemebility d gs flow distibutio i the blst fuce, d c eve be lost i the off-gs1. Fie oes theefoe udego iitil gglometio though siteig o pelletiztio, befoe beig chged to the blst fuce. Duig gglometio though siteig, the w mteil mixtue fist goes though gultio pocess. I this pocess the io oe fies, coke beeze, limestoe d etu site e mixed with wte d tumbled i oty dum. Itemedite d fie pticles (the dheig pticles) the cot the cose pticles (the ucleus pticles), though ite-pticle dhesio vi wte bidges, wheeby lge gules o qusi-pticles fom. These qusipticles e lge i size d owe i size ge th the oigil feed2,3. A potio of these qusi-pticles lso educe i size, due to bekge d ttitio. The oute shell of the qusi-pticle is theefoe ctive duig gultio, s it is costtly bekig dow d e-depositig4,5. Vious uthos defie the sizes of the ucleus d dheig pticles diffeetly: ccodig to Begstd et l.6 the ucleusfomig pticles e typiclly +1 mm, while the dheig pticles e -0.5 mm i size, while Khos d Muel7 epoted the dheig size fctio to be -0.1 mm. Fomoso et l.8 defied the ucleus of the qusi-pticle s beig +0.7 mm, with the dheig fies s mm. The ole of pticles i the itemedite size ge is still ot completely udestood: Liste d Wtes showed tht icesig * Deptmet of Mteils Sciece d Metllugicl Egieeig, Uivesity of Petoi, Petoi. The Southe Afic Istitute of Miig d Metllugy, SA ISSN X/ Ppe eceived Nov. 2007; evised ppe eceived M P p e The Joul of The Southe Afic Istitute of Miig d Metllugy VOLUME 108 REFEREED PAPER MAY

2 SAIMM_57-64:Templte Joul 6/9/08 11:55 AM Pge 294 Cotol of the gi size distibutio popotios of dheig mteil deceses the gultio effectiveess, but decesig the size of the dheig pticles iceses it9. Loo d Pey howeve, showed tht eplcemet of oe by oe tht cotis highe level of itemedite pticles ( mm) c impove pemebility10. Wte dditio, pticle size distibutio, oe poosity, sufce popeties of the io oe d wettbility of the io oe by wte e the most impott fctos tht ffect the gultio efficiecy d pemebility of the gee site bed The pemebility of the site bed i tu cotols the poductivity of the site plt, s well s the micostuctue d popeties of the poduced site, s the gs flow te though the bed goves the tempetue pofile though the bed. The pocess i which qusi-pticles fom is vey stogly iflueced by moistue tht is vilble fo gultio13. Sub-optiml moistue dditio deteiotes gee bed pemebility pidly6. The mout of moistue equied fo gultio vies widely with oe type10,11,14. Khos d Muel foud tht the optimum moistue could be descibed ccutely by kowig the SiO 2, LOIT d Al 2 O 3 ( 1 mm) cotet of the oe, s well s the 0.15 mm d pecetge of itemedite ( mm) size fctios7. Fo most io oes, icese i pticle size close to the 0.1 mm size ge hs the getest effect o educig pemebility d icesig the mout of moistue tht is equied fo gultio7. The use of diffeet size fctios of coke beeze d flux i site mixes hve bee studied15 17 s well s the use of cose io oe pticles10,18,19. Bhgt et l.15 epoted tht the micopoosity of the site d its educibility icesed with decese i the size ge of the coke beeze. The eductio disitegtio idex (RDI) decesed, the educibility decesed mgilly d the poductivity icesed whe the size ge of the flux ws owed dow fom 3 mm to mm. Hosoti et l. epoted tht the simulteous emovl of the 1 mm limestoe fctio d the 0.5 mm coke beeze fctio impoves the gultio idex d pemebility of the gee site bed16. This led to suppessio i the shikge of the site cke, icese i siteig te (d theefoe poductivity), s well s impoved educibility due to icese i the umbe of fie poes. Ksi et l.17 exmied the ifluece of the use of usized d sized coke fies d limestoe o the peigitio pemebility s well s the pemebility of the bed duig siteig. They foud tht the use of lge pticles of coke d limestoe esulted i impoved pemebility befoe d duig siteig. The pemebility of the poduced site cke lso depeded lgely o the pe-igitio pemebility. This idictes tht some spect of the stuctue of bed of gulted site feed is coseved duig siteig. Teo et l.4 epoted tht lge coke (+1.0 mm) d flux (limestoe d sepetie) pticles did ot ppe to pick up fie pticles well. Fie coke pticles c oly be icopoted ito the dheig fies lye whe thee is ledy dheig lye peset fo them to imbed i. They hypothesized tht coke is poo gultig mteil, eve i the uclei size fctio (+1 mm), due to its hydophobic sufce popeties4. Loo d Pey10 epoted tht cose, poous io oe bsobed wte d educed the level of fee wte vilble fo gultio, but impoved the pticle size distibutio of the gulted mix. Two-stge cotig gultio pocesses hve lso bee ivestigted with the itet of impovig poductivity d educibility of the site4,20,21. I these pocesses ceti tget qusi-pticle stuctue ws chieved though divided flux dditios, usig two gultio dums. These pocesses did ot lwys dd beefits to the popeties of the poduced site. Expeimetl Rw mteils The w mteils used i the siteig expeimets wee Thbzimbi io oe, Sishe io oe, etu fies, coke, lime, qutz, wte d feic chloide (FeCl 3 ). The followig bbevitios e used to descibe the exmied smples: 20 d 80 (50 d 50) with fluxes: mixtue of 20 mss pe cet Thbzimbi io oe, 80 mss pe cet Sishe io oe (50 mss pe cet Thbzimbi io oe, 50 mss pe cet Sishe io oe) with fluxes ot sized (C d L): coke beeze d lime sized (C d L d R.F): coke beeze, lime d etu fies sized. The pticle size distibutios of the lime d coke beeze tht wee used e give i Tble I. The etu fies wee sized by emovig the 0.5 mm size fctio. Gultio d pemebility The ifluece of moistue cotet d gultio time o the pemebility d me gule dimete ws studied i the ges of espectively 2 8 mss pe cet d 2 10 miutes. A dum, with dimete of 51.5 cm, height of 50 cm, t costt ottiol speed of 26 ottios pe miute, ws used. Te smples of 10 kg (dy bsis) of ech w mteil mixtue wee used. The pocedue ivolved vyig the moistue cotet of the mixtue while keepig the time costt (5 smples), fte which the effect of gultio time o pemebility t optimum moistue cotet (5 smples) ws exmied. Afte gultio pt of the gulted smple (ppoximtely 4 kg) ws used fo pemebility test. A test pptus, m i height d m i iside dimete, ws used to mesue the pemebility, which ws expessed i tems of the Jpese Pemebility Uit (JPU) ccodig to¹¹: whee: V: iflow te (Nm3/mi) A: e (m2) H: height of the bed (mm) ΔP: suctio pplied coss the bed (mmh 2 O) Tble I Pticle size distibutios of the coke beeze d lime (mss %) mm mm mm Coke beeze Lime MAY 2008 VOLUME 108 REFEREED PAPER The Joul of The Southe Afic Istitute of Miig d Metllugy

3 SAIMM_57-64:Templte Joul 6/9/08 11:55 AM Pge 295 Cotol of the gi size distibutio The pemebility ws clculted by tkig the vege of 3 mesuemets of pessue dop fo diffeet flow tes t the vetui, t the top d t the bottom of the test pptus. Sieve lysis A potio of gulted smple ws foze with liquid itoge, i ode to pefom sieve lysis o the gules, wheeby the mteil tsfe betwee gulometic clsses (by compig the size distibutio befoe d fte gultio) ws studied. This ws doe by plcig g of gulted mixtue o metllic ty, fte which liquid itoge (-200 C) ws poued o the gulted smple d o the scee. The gulted smple ws cooled togethe with the scee i ode to void deteiotio of the gules duig sievig. The gule size distibutio ws detemied by weighig the cooled fctios etied oto diffeet scees fte 5 miutes of sceeig. The esults obtied e peseted o semi logithmic gphs, whee the odite (ithmetic scle) shows the gi o loss s pecetge of the totl smple weight, d the bsciss (logithmic scle) shows the gultio clss. Ech poit epesets the diffeece betwee the qutities of mteil befoe d fte gultio fo ech gulometic clss. The followig pmetes wee detemied22: X: The size limit betwee the educed d icesed gulometic fctio duig the gultio pocess expessed i mm, cosideig tht the educed d icesed gulometic fctios e the fctios whose eltive pecetges espectively educe o icese fte gultio. The vlue of X is obtied fom the itesectio of ech cuve with the x-xis of the semi logithmic gph. S: The level of mteil tsfe betwee the educed d icesed gulometic fctios, expessed s pecetge of the totl weight of the smple. Ex: The efficiecy of elimitio of the fctio smlle th X mm, duig the gultio pocess. S d Ex e clculted fom: S = (%<X mm) BG - (%<X mm) AG = (%>X mm) AG - (%>X mm) BG Ex = 100*S/S, whee S = (%<X mm) BG, d (%<X mm) BG = the weight fctio of gis less th X mm i the mixtue befoe gultio, d (%>X mm) BG = the coespodig weight fctio bove X mm. (%<X mm) AG = the weight fctio of gis less th X mm i the mixtue fte gultio, d (%>X mm) AG = the coespodig weight fctio bove X mm. Siteig Site tests wee cied out t Kumb Io Oe pilot plt i site pot with coss-sectiol gte e of 0.16 m2. Fou site mixtues, idetified s the optiml mixtues fte gultio, wee ivestigted: Mixtue I: 50 d 50 (C d L d R.F), with 5.5 mss pe cet moistue Mixtue II: 20 d 80 (C d L d R.F), with 4.5 mss pe cet moistue Mixtue III: 20 d 80 (C d L), with 4.5 mss pe cet moistue Mixtue IV: 50 d 50 (C d L), with 5.5 mss pe cet moistue. The compositios of these 4 mixtues e give i Tbles II d III. T s c t i o P p e Tble II Compositio of mixtue I (mss %) Rw mteil Mixtue I Thbzimbi io oe Sishe io oe Retu fies Coke beeze Lime Dolomite Silic Wte Feic chloide Tble III Compositio of mixtues II IV (mss %) Rw mteil Mixtue II Mixtue III Mixtue IV Thbzimbi io oe Sishe io oe Retu fies Coke beeze Lime Dolomite Silic Wte Feic chloide The Joul of The Southe Afic Istitute of Miig d Metllugy VOLUME 108 REFEREED PAPER MAY

4 SAIMM_57-64:Templte Joul 6/9/08 11:55 AM Pge 296 Cotol of the gi size distibutio Expeimetl esults Gultio d pemebility The pemebility of both the 20 mss pe cet Thbzimbi io oe: 80 mss pe cet Sishe io oe mixtue, d the 50 mss pe cet Thbzimbi io oe: 50 mss pe cet Sishe io oe mixtues icesed s sized fluxes eplced the usized fluxes, d eched mximum whe ll the fluxes (coke beeze, lime d etu fies) wee sized (Figues 1 d 2). Whe the moistue cotet i the gulted mixtue ws vied, while keepig the gultio time costt t 6 miutes, mximum pemebility of 49 JPU ws chieved fo the 20 mss pe cet Thbzimbi io oe: 80 mss pe cet Sishe io oe, sized coke beeze, lime d etu fies mixtue, t 4.5 mss pe cet moistue. Whe the ifluece of gultio time ws exmied t optimum moistue cotets, the pemebility of the 20 mss pe cet Thbzimbi io oe: 80 mss pe cet Sishe io oe, sized coke beeze, lime d etu fies mixtue ws icesed to 51 JPU whe the gultio time ws decesed to 4 miutes. The optimum moistue cotet d gultio time fo the 50 mss pe cet Thbzimbi io oe: 50 mss pe cet Sishe io oe, sized coke beeze, lime d etu fies mixtue wee espectively 5.5 mss pe cet d 6 miutes (Figues 1 d 2). The sme ted ws obseved fo the me gule dimete (Figue 3): The biggest gules fomed whe the mixtue 20 mss pe cet Thbzimbi io oe: 80 mss pe cet Sishe, with sized coke beeze, lime d etu fies wee gulted. The vege me gule dimete of the mixtue 20 mss pe cet Thbzimbi io oe: 80 mss pe cet Sishe io oe chged fom 2.4 mm befoe gultio to 4.4 mm fte gultio whe oly the coke d lime wee sized, d fom 3.0 mm to 4.8 mm whe ll the fluxes (coke, lime d etu fies) wee sized. Vitio i mteil tsfe betwee gulometic clsses The vitio i mteil tsfe of the w mteil mixtue with fluxes betwee gulometic clsses, fo diffeet moistue levels t 6 miutes of gultio e illustted i Figues 4 to 9. I the mixtue 50 mss pe cet Thbzimbi io oe: 50 mss pe cet Sishe io oe with fluxes ot sized, fie pticles hve dimetes smlle th 0.48 mm d cose pticles hve dimetes lge th 1.8 mm (Figue 4). Whe the coke d lime wee sized, the dimetes of the fie pticles wee smlle th 1 mm, d the cose Pemebility (JPU) Me dimete (mm) Time (miutes) Figue 2 Ifluece of gultio time o pemebility (moistue cotet fo 20 d 80 mixtues is 4.5 mss pe cet; moistue cotet fo 50 d 50 mixtues is 5.5 mss pe cet) Moistue (%) Figue 3 Ifluece of moistue cotet o the me gule dimete of the diffeet io oe mixtues with fluxes (gultio time of 6 miutes) Pemebility (JPU) Loss o gi (%) Fctio (mm) Moistue (%) Figue 1 Ifluece of moistue cotet o pemebility of the diffeet io oe mixtues with fluxes Figue 4 Vitio i mteil tsfe betwee gulometic clsses fo the mixtue 50% Thbzimbi d 50% Sishe with fluxes ot sized. (H = moistue cotet) 296 MAY 2008 VOLUME 108 REFEREED PAPER The Joul of The Southe Afic Istitute of Miig d Metllugy

5 SAIMM_57-64:Templte Joul 6/9/08 11:55 AM Pge 297 Cotol of the gi size distibutio pticles lge th 2.9 mm (Figue 5). Howeve, whe ll the fluxes whee sized, fie pticles hve dimetes smlle th 2 mm d cose pticle hve dimetes lge th 3.35 mm (Figue 6). I the mixtue 20 mss pe cet Thbzimbi io oe d 80 mss pe cet Sishe io oe with fluxes ot sized, fie pticles hve dimetes smlle th 0.9 mm d cose pticles hve dimetes lge th 2.9 mm (Figue 7). Whe the coke d lime wee sized, fie pticles hve dimetes smlle th 1.4 mm d cose pticle hve dimetes lge th 3.35 mm (Figue 8). Whe coke, lime d etu fies wee ll sized, fie pticles hve dimetes smlle th 2.4 mm d cose pticle hve dimetes lge th 3.35 mm (Figue 9). Gultio potetils of mixtues of Thbzimbi d Sishe io oes d fluxes The esults o the gultio potetil of Thbzimbi d Sishe io oes d thei mixtues e summized i Tbles IV to IX. The gultio potetil of give io oe mixtue is bette th othe oe if its pemebility d the mout of mteil tsfe (Ex) is highe t optimum moistue cotets, d lso if its moistue cotet (H) is less. The vlue of S idictes the mout of mteil tsfe i mss pecetge d the vlue of Ex shows which fies e elimited effectively. D(B.G.) d D(A.G.) e espectively the me dimete befoe gultio d fte gultio, expessed i mm. I compig the gultio potetils of mixtues cotiig 50 mss pe cet Thbzimbi io oe d 50 mss pe cet Sishe io oe, the mixtue whee the coke d lime wee sized (Tble V) peset bette site mixtue th the mixtue whee the coke, lime d etu fies wee sized (Tble VI) d whee the fluxes wee ot sized (Tble IV). Although its pemebility is slightly less th tht of the mixtue whee the coke, lime d etu fies wee sized (44 vs. 45 JPU), it pesets highe Loss o gi (%) Fctio (mm) Figue 7 Vitio i mteil tsfe betwee gulometic clsses fo the mixtue 20% Thbzimbi d 80% Sishe with fluxes, ot sized. (H = moistue cotet) T s c t i o P p e Loss o gi (%) Fctio (mm) Figue 5 Vitio i mteil tsfe betwee gulometic clsses fo the mixtue 50% Thbzimbi d 50% Sishe with oly, coke d lime sized. (H = moistue cotet) Loss o gi (%) Loss o gi (%) Loss o gi (%) Fctio (mm) Figue 8 Vitio i mteil tsfe betwee gulometic clsses fo the mixtue 20% Thbzimbi d 80% Sishe with coke d lime sized. (H = moistue cotet) Fctio (mm) Fctio (mm) Figue 6 Vitio i mteil tsfe betwee gulometic clsses fo the mixtue 50% Thbzimbi d 50% Sishe with coke, lime d etu fies sized. (H = moistue cotet) Figue 9 Vitio i mteil tsfe betwee gulometic clsses fo the mixtue 20% Thbzimbi d 80% Sishe with fluxes, coke, lime, d etu fies sized. (H = moistue cotet) The Joul of The Southe Afic Istitute of Miig d Metllugy VOLUME 108 REFEREED PAPER MAY

6 SAIMM_57-64:Templte Joul 6/9/08 11:55 AM Pge 298 Cotol of the gi size distibutio Tble IV Gultio potetil of mixtue 50 mss pe cet Thbzimbi, 50 mss pe cet Sishe with fluxes ot sized Smple Smple Smple Smple Tble V Gultio potetil of mixtue: 50 mss pe cet Thbzimbi, 50 mss pe cet Sishe with coke d lime sized Smple Smple Smple Smple Tble VI Gultio potetil of mixtue: 50 mss pe cet Thbzimbi, 50 mss pe cet Sishe with coke, lime d etu fies sized Smple Smple Smple Smple Smple Tble VII Gultio potetil of mixtue 20 mss pe cet Thbzimbi, 80 mss pe cet Sishe with fluxes ot sized Smple Smple Smple Smple Tble VIII Gultio potetil of mixtue: 20 mss pe cet Thbzimbi, 80 mss pe cet Sishe with fluxes, coke d lime sized Smple Smple Smple Smple efficiecy of elimitio of fie pticles (Ex = 76.2% vs. 59.7%). The gultio potetil of the mixtue with 20 mss pe cet Thbzimbi io oe d 80 mss pe cet Sishe io oe with fluxes whee the coke, lime, d etu fies wee sized (Tble IX) ws the highest with pemebility of 49 JPU, high efficiecy of elimitio of fies (Ex = 86%), d high level of tsfe of fie pticles to cose pticles (S = 50%). Siteig The qulity of the poduced sites wee evluted d comped with the cuetly poduced site (clled the Bse Cse ) i which the site mixtue cosists of 50 mss pe cet Thbzimbi io oe, 50 mss pe cet Sishe io oe d usized fluxes, to which 5.25 mss pe cet moistue is dded duig gultio (Tble X). The site popeties of 298 MAY 2008 VOLUME 108 REFEREED PAPER The Joul of The Southe Afic Istitute of Miig d Metllugy

7 SAIMM_57-64:Templte Joul 6/9/08 11:55 AM Pge 299 Cotol of the gi size distibutio Tble IX Gultio potetil of mixtue: 20 mss pe cet Thbzimbi, 80 mss pe cet Sishe with fluxes, coke, lime d etu fies sized Smple Smple Smple Smple Tble X Compiso of the site popeties of Mixtues I IV with those of the Bse Cse site Mixtue I Mixtue II Mixtue III Mixtue IV Bse Cse Poductivity.(t/24 h/m2) Coke te. (kg/t.site) Yield (%) Siteig time (miutes) TI (% mm) TI (% mm) AI (% -0.5 mm) RDI (% mm) RDI (% mm) RDI (% mm) RI (%/mi) T s c t i o P p e Mixtues I IV wee foud to be vey simil, d supeio to the Bse Cse site, with the exceptio of the TI (% mm) d the RDI(%-0.5 mm) i cse of Mixtues II d III. The poductivity d yield ws impoved whe sized fluxes wee dded to the site mixtue, while the coke te, siteig time d AI(% -0.5 mm) wee educed. Noe of the sites (icludig the Bse Cse site) cofomed to the citei of RDI (% mm) i excess of 70% d RDI (% -0.5 mm) of less th 5%. All the exmied sites cofomed to the equiemets of TI (% mm) > 70 pe cet d RI 1 pe cet pe miute. Site Mixtue IV hd the shotest siteig time (20.1 mi.), the highest poductivity (33.8 t/24 h/m2), good RI (1.2%/mi.), the highest RDI (% mm) (66.7%) d the lowest RDI (% mm) (5%), d is cosideed to be the best of the exmied sites. Mixtue II hs the highest yield (83.93%) d lowest coke te (79.4 kg/t.site), d is cosideed to be the secod best site mixtue to Mixtue IV. Coclusios The pemebility ws the best t y gultio time fo the mixtue tht cotied 20 mss pe cet Thbzimbi io oe, 80 mss pe cet Sishe io oe d fluxes whee the coke, lime d etu fies wee ll sized Whe ll the fluxes wee sized, lge gules wee fomed comped to whe oly the coke beeze d lime wee sized As wte dditio icesed, the pemebility icesed d the gultio effectiveess impoved, esultig i the fomtio of lge pticles. Howeve, whe wte dditio ws icesed beyod the optimum vlue, bed pemebility d gultio deteioted The gowth i me gule dimete duig gultio is fuctio of the iitil me dimete befoe gultio, the mout of moistue, d the gultio time. As the time icesed, the me gule dimete icesed up to ceti vlue d the stted to decese The emovl of the -0.5 mm size fctio of coke beeze, -0.5 mm size fctio of etu fies d -1 mm size fctio of limestoe, s well s the use of highe popotios of Sishe io oe, icesed the size limit (X) betwee the educed d icesed gulometic fctios The me gule dimete does ot pedict the pemebility of the bed The mixtue of 20 mss pe cet Thbzimbi io oe, 80 mss pe cet Sishe io oe with fluxes whee the coke, lime d etu fies wee sized d the mixtue 50 mss pe cet Thbzimbi, 50 mss pe cet Sishe with fluxes whee oly the coke d lime whee sized hve the best gultio potetils The site popeties of the fou sites, i which the gi size distibutios wee cotolled, e simil, but bette th the bse cse site i which the fluxes wee ot sized. Site popeties theefoe beefit fom gi size distibutio cotol of the w site mixtue. Refeeces 1. BISWAS, A.K. Piciples of Blst Fuce Iomkig, Uivesity of Queesld, Bisbe, Austli, p VENKATARAMANA, R., GUPTA, S.S., d KAPUR, P.C. A combied model fo gule size distibutio d cold bed pemebility i the wet stge of io oe siteig pocess. It. J. Mie. Pocess., vol. 57, 1999, pp RANKIN, W.J. d ROLLER, P.W. The mesuemet of void fctio i beds of gulted io oe site feed. Ts. ISIJ, vol. 25, 1985, pp The Joul of The Southe Afic Istitute of Miig d Metllugy VOLUME 108 REFEREED PAPER MAY

8 SAIMM_57-64:Templte Joul 6/9/08 11:55 AM Pge 300 Cotol of the gi size distibutio 4. TEO, C.S., MIKKA, R.A., d LOO, C.E. Positioig coke pticles i io oe siteig, ISIJ It., vol. 32, o. 10, 1992, pp LITSTER, J.D. d WATERS, A.D. Kietics of io oe site feed gultio, Powde Techology, vol. 62, 1990, pp BERGSTRAND, R., KHOSA, J., WATERS, A., d GARDEN, J. The effect of M Mmb oe dditio o the gultio chcteistics of pisolite bsed d hemtite bsed site bleds, ISIJ It., vol. 45, o. 4, 2005, pp KHOSA, J. d MANUEL, J. Pedictig gultig behviou of io oes bsed o size distibutio d compositio, ISIJ It., vol. 47, o. 7, 2007, pp FORMOSO, A., MORO, A., PELLO, G.F., MENENDEZ, J.L., MUNIZ, M., d CORES, A. Ifluece of tue d pticle size distibutio o gultio of io oe mixtues used i site std, Iomkig d Steelmkig, vol. 30, o. 6, 2003, pp LITSTER, J.D. d WATERS, A.G. Ifluece of the mteil popeties of io oe site feed o gultio effectiveess. Powde Techology, vol. 55, 1988, pp LOO, C.E. d PENNY, G.C. Gultio behviou of io oe bleds cotiig cose, poous oe, Tsctios of the Istitutio of Miig d Metllugy, Sectio C (UK), vol. 107, Sept. Dec. 1998, pp. C111 C ELLIS, B.G., LOO, C.E., d WITCHARD, D. Effect of oe popeties o site bed pemebility d stegth, Iomkig & Steelmkig, vol. 34, o. 2, 2007, pp XU, J.Q., ZOU, R.P., d YU, A.B. Qutifictio of the mechisms goveig the pckig of io oe fies, Powde Techology, vol. 169, 2006, pp MAEDA, T., FUKUMOTO, C., MATSUMURA, T., NISHIOKA, K., d SHIMIZU, M. Effect of ddig moistue d wettbility o gultio of io oe, ISIJ It., vol. 45, o. 4, 2005, pp MAY 2008 VOLUME 108 REFEREED PAPER 14. LITSTER, J.D. d WATERS, A.D. Ifluece of the mteil popeties of io oe site feed o gultio effectiveess, Powde Techology, vol. 55, 1988, pp BHAGAT, R.P., CHATTORAJ, U.S., GOSWAMI, M.C., SINGH, D.P., d SIL, S.K. Effect of size pmetes of mix igediets o the poosity d eductio chcteistics of site, Steel Resech It., vol. 78, o. 6, 2007, pp HOSOTANI, Y., KONNO, N., YAMAGUCHI, K., ORIMOTO, T., d INAZUMI, T. Reductio popeties of site with fie dispesed poes t high tempetues of 1273K d bove, ISIJ It., vol. 36, o. 12, 1996, pp KASAI, E., RANKIN, W.J., d GANNON, J.F. The effect of w mixtue popeties o bed pemebility duig siteig, ISIJ It., vol. 29, o. 1, 1989, pp OTOMO, T., TAKASAKI, Y., d KAWAGUCHI, T. Popeties of coe oe i qusipticle equied fo lge mouts usge of limoitic oes i io oe siteig pocess, ISIJ It., vol. 45, o. 4, 2005, pp KAMIJO, C., MATSUMURA, M., d KAWAGUCHI, T. Siteig behviou of w mteil bed plcig lge pticles, ISIJ It., vol. 45, o. 4, 2005, pp OYAMA, N., SATO, H., TAKEDA, K., ARIYAMA, T., MASUMOTO, S., JINNO, T., d FUJII, N. Developmet of cotig gultio pocess t commecil siteig plt fo impovig poductivity d educibility, ISIJ It., vol. 45, o. 6, 2005, pp VENKATARAMANA, R., KAPUR, P.C., d GUPTA, S.S. Modellig of gultio by twostge uto-lyeig mechism i cotiuous idustil dums, Chem. Eg. Sciece, vol. 57, 2002, pp HSIEH, L.-H. Effect of w mteil compositio o the siteig popeties. ISIJ It., vol. 45, o. 4, 2005, pp The Joul of The Southe Afic Istitute of Miig d Metllugy

Marketing Logistics: Opportunities and Limitations

Marketing Logistics: Opportunities and Limitations Mketig Logistics: Oppotuities d Limittios Pethip Vdhsidhu 1, Ugul Lpted 2 1 Gdute School, MBA i Itetiol Busiess, The Uivesity of the Thi Chmbe of Commece Vibhvdee-Rgsit Rod, Dideg, Bgkok, 10400, Thild

More information

N V V L. R a L I. Transformer Equation Notes

N V V L. R a L I. Transformer Equation Notes Tnsfome Eqution otes This file conts moe etile eivtion of the tnsfome equtions thn the notes o the expeiment 3 wite-up. t will help you to unestn wht ssumptions wee neee while eivg the iel tnsfome equtions

More information

The preparation of activated carbon from South African coal

The preparation of activated carbon from South African coal The peption of ctivted cbon fom South Aficn col by Q.P. Cmpbell*, J. R. Bunt*, H. Ksini, nd D.J. Kuge* J o u n l Synopsis Activted cbons used in the pecious metls extction industy e chcteized by lge intenl

More information

(1) continuity equation: 0. momentum equation: u v g (2) u x. 1 a

(1) continuity equation: 0. momentum equation: u v g (2) u x. 1 a Comment on The effect of vible viscosity on mied convection het tnsfe long veticl moving sufce by M. Ali [Intentionl Jounl of Theml Sciences, 006, Vol. 45, pp. 60-69] Asteios Pntoktos Associte Pofesso

More information

Sulphuric acid leaching of zinc and copper from Nigerian Complex Sulphide Ore in the presence of hydrogen peroxide

Sulphuric acid leaching of zinc and copper from Nigerian Complex Sulphide Ore in the presence of hydrogen peroxide Syopsis Sulphuic cid lechig of zic d coppe fom Nigei Complex Sulphide Oe i the pesece of hydoge peoxide by P.A. Olubmbi*, J.O. Boode, d S. Ndlovu* The lechig of zic d coppe fom Nigei bulk sulphide oe with

More information

(Ch. 22.5) 2. What is the magnitude (in pc) of a point charge whose electric field 50 cm away has a magnitude of 2V/m?

(Ch. 22.5) 2. What is the magnitude (in pc) of a point charge whose electric field 50 cm away has a magnitude of 2V/m? Em I Solutions PHY049 Summe 0 (Ch..5). Two smll, positively chged sphees hve combined chge of 50 μc. If ech sphee is epelled fom the othe by n electosttic foce of N when the sphees e.0 m pt, wht is the

More information

A. Description: A simple queueing system is shown in Fig. 16-1. Customers arrive randomly at an average rate of

A. Description: A simple queueing system is shown in Fig. 16-1. Customers arrive randomly at an average rate of Queueig Theory INTRODUCTION Queueig theory dels with the study of queues (witig lies). Queues boud i rcticl situtios. The erliest use of queueig theory ws i the desig of telehoe system. Alictios of queueig

More information

VI.F CURRENT TRANSFORMERS. Originally Issued: 2/99 DMS #84474 Page 1 of 19 Revised:

VI.F CURRENT TRANSFORMERS. Originally Issued: 2/99 DMS #84474 Page 1 of 19 Revised: V.F CURRENT TRANSFORMERS DMS #84474 Pge of 9 Revised: GUDE FOR DETERMNATON OF CURRENT TRANSFORMER RATNGS PJM NTERCONNECTON Heitge MAAC Goup A tsk foce of the Tsmissio d Substtio Subcommittee R. W. Muley

More information

16. Mean Square Estimation

16. Mean Square Estimation 6 Me Sque stmto Gve some fomto tht s elted to uow qutty of teest the poblem s to obt good estmte fo the uow tems of the obseved dt Suppose epeset sequece of dom vbles bout whom oe set of obsevtos e vlble

More information

Periodic Review Probabilistic Multi-Item Inventory System with Zero Lead Time under Constraints and Varying Order Cost

Periodic Review Probabilistic Multi-Item Inventory System with Zero Lead Time under Constraints and Varying Order Cost Ameica Joual of Applied Scieces (8: 3-7, 005 ISS 546-939 005 Sciece Publicatios Peiodic Review Pobabilistic Multi-Item Ivetoy System with Zeo Lead Time ude Costaits ad Vayig Ode Cost Hala A. Fegay Lectue

More information

Understanding Financial Management: A Practical Guide Guideline Answers to the Concept Check Questions

Understanding Financial Management: A Practical Guide Guideline Answers to the Concept Check Questions Udestadig Fiacial Maagemet: A Pactical Guide Guidelie Aswes to the Cocept Check Questios Chapte 4 The Time Value of Moey Cocept Check 4.. What is the meaig of the tems isk-etu tadeoff ad time value of

More information

MATHEMATICS FOR ENGINEERING BASIC ALGEBRA

MATHEMATICS FOR ENGINEERING BASIC ALGEBRA MATHEMATICS FOR ENGINEERING BASIC ALGEBRA TUTORIAL - INDICES, LOGARITHMS AND FUNCTION This is the oe of series of bsic tutorils i mthemtics imed t begiers or yoe wtig to refresh themselves o fudmetls.

More information

Exam in physics, El-grunder (Electromagnetism), 2014-03-26, kl 9.00-15.00

Exam in physics, El-grunder (Electromagnetism), 2014-03-26, kl 9.00-15.00 Umeå Univesitet, Fysik 1 Vitly Bychkov Em in physics, El-gunde (Electomgnetism, 14--6, kl 9.-15. Hjälpmedel: Students my use ny book(s. Mino notes in the books e lso llowed. Students my not use thei lectue

More information

Multicriteria selection for an aluminacement plant location in East Azerbaijan province of Iran

Multicriteria selection for an aluminacement plant location in East Azerbaijan province of Iran Syopsis Multicitei selectio fo lumicemet plt loctio i Est Azebij povice of I by M. Atei* Oe of the most impott fctos ledig to the success of cemet plt is its loctio. A multicitei decisio-mkig method is

More information

Money Math for Teens. Introduction to Earning Interest: 11th and 12th Grades Version

Money Math for Teens. Introduction to Earning Interest: 11th and 12th Grades Version Moey Math fo Tees Itoductio to Eaig Iteest: 11th ad 12th Gades Vesio This Moey Math fo Tees lesso is pat of a seies ceated by Geeatio Moey, a multimedia fiacial liteacy iitiative of the FINRA Ivesto Educatio

More information

Intro to Circle Geometry By Raymond Cheong

Intro to Circle Geometry By Raymond Cheong Into to Cicle Geomety By Rymond Cheong Mny poblems involving cicles cn be solved by constucting ight tingles then using the Pythgoen Theoem. The min chllenge is identifying whee to constuct the ight tingle.

More information

Empirical correlation of mineral commodity prices with exchange-traded mining stock prices

Empirical correlation of mineral commodity prices with exchange-traded mining stock prices text:templte Joul 8/8/11 11:50 Pge 459 Syopsis Empiicl coeltio of miel commodity pices with exchge-tded miig stock pices by C. Ngolo* d C. Musigwii* Miel commodity pices compise oe of the key citei i the

More information

Summary: Vectors. This theorem is used to find any points (or position vectors) on a given line (direction vector). Two ways RT can be applied:

Summary: Vectors. This theorem is used to find any points (or position vectors) on a given line (direction vector). Two ways RT can be applied: Summ: Vectos ) Rtio Theoem (RT) This theoem is used to find n points (o position vectos) on given line (diection vecto). Two ws RT cn e pplied: Cse : If the point lies BETWEEN two known position vectos

More information

Maximum Entropy, Parallel Computation and Lotteries

Maximum Entropy, Parallel Computation and Lotteries Maximum Etopy, Paallel Computatio ad Lotteies S.J. Cox Depatmet of Electoics ad Compute Sciece, Uivesity of Southampto, UK. G.J. Daiell Depatmet of Physics ad Astoomy, Uivesity of Southampto, UK. D.A.

More information

Repeated multiplication is represented using exponential notation, for example:

Repeated multiplication is represented using exponential notation, for example: Appedix A: The Lws of Expoets Expoets re short-hd ottio used to represet my fctors multiplied together All of the rules for mipultig expoets my be deduced from the lws of multiplictio d divisio tht you

More information

Screentrade Car Insurance Policy Summary

Screentrade Car Insurance Policy Summary Sceentde C Insunce Policy Summy This is summy of the policy nd does not contin the full tems nd conditions of the cove, which cn be found in the policy booklet nd schedule. It is impotnt tht you ed the

More information

r (1+cos(θ)) sin(θ) C θ 2 r cos θ 2

r (1+cos(θ)) sin(θ) C θ 2 r cos θ 2 icles xmple 66: Rounding one ssume we hve cone of ngle θ, nd we ound it off with cuve of dius, how f wy fom the cone does the ound stt? nd wht is the chod length? (1+cos(θ)) sin(θ) θ 2 cos θ 2 xmple 67:

More information

Orbits and Kepler s Laws

Orbits and Kepler s Laws Obits nd Keple s Lws This web pge intoduces some of the bsic ides of obitl dynmics. It stts by descibing the bsic foce due to gvity, then consides the ntue nd shpe of obits. The next section consides how

More information

The strategic and tactical value of a 3D geotechnical model for mining optimization, Anglo Platinum, Sandsloot open pit

The strategic and tactical value of a 3D geotechnical model for mining optimization, Anglo Platinum, Sandsloot open pit The sttegic nd tcticl vlue of 3D geotechnicl model fo mining optimiztion, Anglo Pltinum, Sndsloot open pit by A. Bye* J o u n l Synopsis Sndsloot open pit is situted on the nothen limb of the Bushveld

More information

Two degree of freedom systems. Equations of motion for forced vibration Free vibration analysis of an undamped system

Two degree of freedom systems. Equations of motion for forced vibration Free vibration analysis of an undamped system wo degee of feedom systems Equatios of motio fo foced vibatio Fee vibatio aalysis of a udamped system Itoductio Systems that equie two idepedet d coodiates to descibe thei motio ae called two degee of

More information

2.016 Hydrodynamics Prof. A.H. Techet

2.016 Hydrodynamics Prof. A.H. Techet .016 Hydodynmics Reding #5.016 Hydodynmics Po. A.H. Techet Fluid Foces on Bodies 1. Stedy Flow In ode to design oshoe stuctues, suce vessels nd undewte vehicles, n undestnding o the bsic luid oces cting

More information

Curvature. (Com S 477/577 Notes) Yan-Bin Jia. Oct 8, 2015

Curvature. (Com S 477/577 Notes) Yan-Bin Jia. Oct 8, 2015 Cuvtue Com S 477/577 Notes Yn-Bin Ji Oct 8, 205 We wnt to find mesue of how cuved cuve is. Since this cuvtue should depend only on the shpe of the cuve, it should not be chnged when the cuve is epmetized.

More information

Derivation of Annuity and Perpetuity Formulae. A. Present Value of an Annuity (Deferred Payment or Ordinary Annuity)

Derivation of Annuity and Perpetuity Formulae. A. Present Value of an Annuity (Deferred Payment or Ordinary Annuity) Aity Deivatios 4/4/ Deivatio of Aity ad Pepetity Fomlae A. Peset Vale of a Aity (Defeed Paymet o Odiay Aity 3 4 We have i the show i the lecte otes ad i ompodi ad Discoti that the peset vale of a set of

More information

Annuities and loan. repayments. Syllabus reference Financial mathematics 5 Annuities and loan. repayments

Annuities and loan. repayments. Syllabus reference Financial mathematics 5 Annuities and loan. repayments 8 8A Futue value of a auity 8B Peset value of a auity 8C Futue ad peset value tables 8D Loa epaymets Auities ad loa epaymets Syllabus efeece Fiacial mathematics 5 Auities ad loa epaymets Supeauatio (othewise

More information

INVESTIGATION OF PARAMETERS OF ACCUMULATOR TRANSMISSION OF SELF- MOVING MACHINE

INVESTIGATION OF PARAMETERS OF ACCUMULATOR TRANSMISSION OF SELF- MOVING MACHINE ENGINEEING FO UL DEVELOENT Jelgv, 28.-29.05.2009. INVESTIGTION OF ETES OF CCUULTO TNSISSION OF SELF- OVING CHINE leksdrs Kirk Lithui Uiversity of griculture, Kus leksdrs.kirk@lzuu.lt.lt bstrct. Uder the

More information

Summation Notation The sum of the first n terms of a sequence is represented by the summation notation i the index of summation

Summation Notation The sum of the first n terms of a sequence is represented by the summation notation i the index of summation Lesso 0.: Sequeces d Summtio Nottio Def. of Sequece A ifiite sequece is fuctio whose domi is the set of positive rel itegers (turl umers). The fuctio vlues or terms of the sequece re represeted y, 2, 3,...,....

More information

I. Supplementary and Relevant Information

I. Supplementary and Relevant Information hte 9 Bod d Note Vlutio d Relted Iteest Rte Fouls witte fo Ecooics 04 Ficil Ecooics by Pofesso Gy R. Evs Fist editio 2008, this editio Octobe 28, 203 Gy R. Evs The iy uose of this docuet is to show d justify

More information

Breakeven Holding Periods for Tax Advantaged Savings Accounts with Early Withdrawal Penalties

Breakeven Holding Periods for Tax Advantaged Savings Accounts with Early Withdrawal Penalties Beakeve Holdig Peiods fo Tax Advataged Savigs Accouts with Ealy Withdawal Pealties Stephe M. Hoa Depatmet of Fiace St. Boavetue Uivesity St. Boavetue, New Yok 4778 Phoe: 76-375-209 Fax: 76-375-29 e-mail:

More information

between Modern Degree Model Logistics Industry in Gansu Province 2. Measurement Model 1. Introduction 2.1 Synergetic Degree

between Modern Degree Model Logistics Industry in Gansu Province 2. Measurement Model 1. Introduction 2.1 Synergetic Degree www.ijcsi.og 385 Calculatio adaalysis alysis of the Syegetic Degee Model betwee Mode Logistics ad Taspotatio Idusty i Gasu Povice Ya Ya 1, Yogsheg Qia, Yogzhog Yag 3,Juwei Zeg 4 ad Mi Wag 5 1 School of

More information

Finance Practice Problems

Finance Practice Problems Iteest Fiace Pactice Poblems Iteest is the cost of boowig moey. A iteest ate is the cost stated as a pecet of the amout boowed pe peiod of time, usually oe yea. The pevailig maket ate is composed of: 1.

More information

Learning Objectives. Chapter 2 Pricing of Bonds. Future Value (FV)

Learning Objectives. Chapter 2 Pricing of Bonds. Future Value (FV) Leaig Objectives Chapte 2 Picig of Bods time value of moey Calculate the pice of a bod estimate the expected cash flows detemie the yield to discout Bod pice chages evesely with the yield 2-1 2-2 Leaig

More information

Reducing accidents in the mining industry an integrated approach

Reducing accidents in the mining industry an integrated approach Syopi Reducig ccidet i the miig iduty itegted ppoch by J.C. Je* d A.C. Bet* The pltium miig iduty h expeieced igifict icee i ftl ccidet. Mie ccidet e i piciple pevetble, d thee i eomou peue o employe to

More information

The Handbook of Essential Mathematics

The Handbook of Essential Mathematics Fo Puic Relese: Distiutio Ulimited The Ai Foce Resech Lotoy The Hdook of Essetil Mthemtics Fomuls, Pocesses, d Tles Plus Applictios i Pesol Fice X Y Y XY Y X X XY X Y X XY Y Compiltio d Epltios: Joh C.

More information

Chapter 04.05 System of Equations

Chapter 04.05 System of Equations hpter 04.05 System of Equtios After redig th chpter, you should be ble to:. setup simulteous lier equtios i mtrix form d vice-vers,. uderstd the cocept of the iverse of mtrix, 3. kow the differece betwee

More information

The Casino Experience. Let us entertain you

The Casino Experience. Let us entertain you The Csio Expeiee Let us eteti you The Csio Expeiee If you e lookig fo get ight out, Csio Expeiee is just fo you. 10 The Stight Flush Expeiee 25 pe peso This is get itodutio to gmig tht sves you moey Kik

More information

Random Variables and Distribution Functions

Random Variables and Distribution Functions Topic 7 Rndom Vibles nd Distibution Functions 7.1 Intoduction Fom the univese of possible infomtion, we sk question. To ddess this question, we might collect quntittive dt nd ognize it, fo emple, using

More information

PREMIUMS CALCULATION FOR LIFE INSURANCE

PREMIUMS CALCULATION FOR LIFE INSURANCE ls of the Uiversity of etroşi, Ecoomics, 2(3), 202, 97-204 97 REIUS CLCULTIO FOR LIFE ISURCE RE, RI GÎRBCI * BSTRCT: The pper presets the techiques d the formuls used o itertiol prctice for estblishig

More information

Innovative materials and methods for ground support, consolidation and water sealing for the mining industry

Innovative materials and methods for ground support, consolidation and water sealing for the mining industry Innovtive mteils nd methods fo gound suppot, consolidtion nd wte seling fo the mining industy by I.W. Nothcoft* J o u n l Synopsis UGC Intentionl, now pt of BASF the wold s lgest chemicl compny, hs developed

More information

Characteristics of an effective selfdirected work team in the gold-mining industry

Characteristics of an effective selfdirected work team in the gold-mining industry Chcteistics of n effective selfdiected wok tem in the gold-mining industy by A. Nel* nd J. Pien* J o u n l Synopsis The gold mining industy in South Afic stnds to benefit much fom the implementtion of

More information

MATHEMATICS SYLLABUS SECONDARY 7th YEAR

MATHEMATICS SYLLABUS SECONDARY 7th YEAR Europe Schools Office of the Secretry-Geerl Pedgogicl developmet Uit Ref.: 2011-01-D-41-e-2 Orig.: DE MATHEMATICS SYLLABUS SECONDARY 7th YEAR Stdrd level 5 period/week course Approved y the Joit Techig

More information

The dinner table problem: the rectangular case

The dinner table problem: the rectangular case The ie table poblem: the ectagula case axiv:math/009v [mathco] Jul 00 Itouctio Robeto Tauaso Dipatimeto i Matematica Uivesità i Roma To Vegata 00 Roma, Italy tauaso@matuiomait Decembe, 0 Assume that people

More information

A perspective of marine mining within De Beers

A perspective of marine mining within De Beers Syopsis A pespective of mie miig withi De Bees by K. Richdso* Although the De Bees goup hs log histoy of plce miig o ld, the goup oly becme ctively ivolved i deep wte mie dimod explotio d miig i 1983 with

More information

by K.-H. Rutsch*, P.J. Viljoen*, and H. Steyn* The need for systematic project portfolio selection

by K.-H. Rutsch*, P.J. Viljoen*, and H. Steyn* The need for systematic project portfolio selection An investigtion into the cuent pctice of poject potfolio selection in esech nd development division of the South Aficn minels nd enegy industy by K.-H. Rutsch*, P.J. Viljoen*, nd H. Steyn* J o u n l Synopsis

More information

Valuation of Floating Rate Bonds 1

Valuation of Floating Rate Bonds 1 Valuation of Floating Rate onds 1 Joge uz Lopez us 316: Deivative Secuities his note explains how to value plain vanilla floating ate bonds. he pupose of this note is to link the concepts that you leaned

More information

GRAVITATION 1. BASIC FORCES IN NATURE

GRAVITATION 1. BASIC FORCES IN NATURE GRAVITATION. BASIC ORCES IN NATURE POINTS TO REMEMBER. Bsing on the ntue nd eltive stength the bsic foces in ntue e clssified into fou ctegoies. They e ) Gvittionl foce ) Electomgnetic foce 3) Stong Nucle

More information

Development of Customer Value Model for Healthcare Services

Development of Customer Value Model for Healthcare Services 96 Developmet of Custome Value Model fo Healthcae Sevices Developmet of Custome Value Model fo Healthcae Sevices Wa-I Lee ad Bih-Yaw Shih Depatmet of Maetig ad Distibutio Maagemet, Natioal Kaohsiug Fist,

More information

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.-7. find the vecto defined

More information

An Introduction to Omega

An Introduction to Omega An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei isk-ewad chaacteistics? The Finance Development Cente 2002 1 Fom

More information

Application: Volume. 6.1 Overture. Cylinders

Application: Volume. 6.1 Overture. Cylinders Applictio: Volume 61 Overture I this chpter we preset other pplictio of the defiite itegrl, this time to fid volumes of certi solids As importt s this prticulr pplictio is, more importt is to recogize

More information

Long-Term Trend Analysis of Online Trading --A Stochastic Order Switching Model

Long-Term Trend Analysis of Online Trading --A Stochastic Order Switching Model Asia Pacific Maagemet Review (24) 9(5), 893-924 Log-Tem Ted Aalysis of Olie Tadig --A Stochastic Ode Switchig Model Shalig Li * ad Zili Ouyag ** Abstact Olie bokeages ae eplacig bokes ad telephoes with

More information

Introduction to Fluid Mechanics

Introduction to Fluid Mechanics Chapte 1 1 1.6. Solved Examples Example 1.1 Dimensions and Units A body weighs 1 Ibf when exposed to a standad eath gavity g = 3.174 ft/s. (a) What is its mass in kg? (b) What will the weight of this body

More information

Streamline Compositional Simulation of Gas Injections Dacun Li, University of Texas of the Permian Basin

Streamline Compositional Simulation of Gas Injections Dacun Li, University of Texas of the Permian Basin Abstact Steamlie Comositioal Simulatio of Gas jectios Dacu L Uivesity of Texas of the Pemia Basi Whe esevoi temeatues ae lowe tha o F ad essue is lowe tha 5sia, gas ijectios, esecially whe ijectats iclude

More information

tools for Web data extraction

tools for Web data extraction HTML-we tools fo Web dt extction Thesis pesenttion 1 Student: Xvie Azg Supeviso: Andes Tho Tble of contents Intoduction Dt Extction Pocess Dt Extction Tools Relized tests Futue Wok 2 Intoduction We e going

More information

n Using the formula we get a confidence interval of 80±1.64

n Using the formula we get a confidence interval of 80±1.64 9.52 The professor of sttistics oticed tht the rks i his course re orlly distributed. He hs lso oticed tht his orig clss verge is 73% with stdrd devitio of 12% o their fil exs. His fteroo clsses verge

More information

Formulas and Units. Transmission technical calculations Main Formulas. Size designations and units according to the SI-units.

Formulas and Units. Transmission technical calculations Main Formulas. Size designations and units according to the SI-units. Fomuls nd Units Tnsmission technicl clcultions Min Fomuls Size designtions nd units ccoding to the SI-units Line movement: s v = m/s t s = v t m s = t m v = m/s t P = F v W F = m N Rottion ω = π f d/s

More information

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,

More information

Chapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere.

Chapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere. Chapte.3 What is the magnitude of a point chage whose electic field 5 cm away has the magnitude of.n/c. E E 5.56 1 11 C.5 An atom of plutonium-39 has a nuclea adius of 6.64 fm and atomic numbe Z94. Assuming

More information

In-stope bolting for a safer working environment

In-stope bolting for a safer working environment text:templte Jounl 2/3/10 9:34 AM Pge 47 In-stope bolting fo sfe woking envionment by P. Henning* nd P. Feei* J o u n l Synopsis Rock fll ccidents continue to be the min cuse of ftl nd seious injuies in

More information

Present and future value formulae for uneven cash flow Based on performance of a Business

Present and future value formulae for uneven cash flow Based on performance of a Business Advces i Mgemet & Applied Ecoomics, vol., o., 20, 93-09 ISSN: 792-7544 (prit versio), 792-7552 (olie) Itertiol Scietific Press, 20 Preset d future vlue formule for ueve csh flow Bsed o performce of Busiess

More information

We will begin this chapter with a quick refresher of what an exponent is.

We will begin this chapter with a quick refresher of what an exponent is. .1 Exoets We will egi this chter with quick refresher of wht exoet is. Recll: So, exoet is how we rereset reeted ultilictio. We wt to tke closer look t the exoet. We will egi with wht the roerties re for

More information

Notes on Power System Load Flow Analysis using an Excel Workbook

Notes on Power System Load Flow Analysis using an Excel Workbook Notes o owe System Load Flow Aalysis usig a Excel Woboo Abstact These otes descibe the featues of a MS-Excel Woboo which illustates fou methods of powe system load flow aalysis. Iteative techiques ae epeseted

More information

Review: Classification Outline

Review: Classification Outline Data Miig CS 341, Sprig 2007 Decisio Trees Neural etworks Review: Lecture 6: Classificatio issues, regressio, bayesia classificatio Pretice Hall 2 Data Miig Core Techiques Classificatio Clusterig Associatio

More information

Paper SD-07. Key words: upper tolerance limit, macros, order statistics, sample size, confidence, coverage, binomial

Paper SD-07. Key words: upper tolerance limit, macros, order statistics, sample size, confidence, coverage, binomial SESUG 212 Pae SD-7 Samle Size Detemiatio fo a Noaametic Ue Toleace Limit fo ay Ode Statistic D. Deis Beal, Sciece Alicatios Iteatioal Cooatio, Oak Ridge, Teessee ABSTRACT A oaametic ue toleace limit (UTL)

More information

Adaptive Control of a Production and Maintenance System with Unknown Deterioration and Obsolescence Rates

Adaptive Control of a Production and Maintenance System with Unknown Deterioration and Obsolescence Rates Int J of Mthemtic Sciences nd Appictions, Vo, No 3, Septembe Copyight Mind Rede Pubictions wwwjounshubcom Adptive Conto of Poduction nd Mintennce System with Unknown Deteiotion nd Obsoescence Rtes Fwzy

More information

Experiment 6: Centripetal Force

Experiment 6: Centripetal Force Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee

More information

ANNUITIES SOFTWARE ASSIGNMENT TABLE OF CONTENTS... 1 ANNUITIES SOFTWARE ASSIGNMENT... 2 WHAT IS AN ANNUITY?... 2 EXAMPLE 1... 2 QUESTIONS...

ANNUITIES SOFTWARE ASSIGNMENT TABLE OF CONTENTS... 1 ANNUITIES SOFTWARE ASSIGNMENT... 2 WHAT IS AN ANNUITY?... 2 EXAMPLE 1... 2 QUESTIONS... ANNUITIES SOFTWARE ASSIGNMENT TABLE OF CONTENTS ANNUITIES SOFTWARE ASSIGNMENT TABLE OF CONTENTS... 1 ANNUITIES SOFTWARE ASSIGNMENT... WHAT IS AN ANNUITY?... EXAMPLE 1... QUESTIONS... EXAMPLE BRANDON S

More information

Semipartial (Part) and Partial Correlation

Semipartial (Part) and Partial Correlation Semipatial (Pat) and Patial Coelation his discussion boows heavily fom Applied Multiple egession/coelation Analysis fo the Behavioal Sciences, by Jacob and Paticia Cohen (975 edition; thee is also an updated

More information

Volume 1: Distribution and Recovery of Petroleum Hydrocarbon Liquids in Porous Media

Volume 1: Distribution and Recovery of Petroleum Hydrocarbon Liquids in Porous Media LNAPL Distibutio ad Recovey Model (LDRM) Volume 1: Distibutio ad Recovey of Petoleum Hydocabo Liquids i Poous Media Regulatoy ad Scietific Affais Depatmet API PUBLICATION 4760 JANUARY 007 3 Satuatio, Relative

More information

m n Use technology to discover the rules for forms such as a a, various integer values of m and n and a fixed integer value a.

m n Use technology to discover the rules for forms such as a a, various integer values of m and n and a fixed integer value a. TIth.co Alger Expoet Rules ID: 988 Tie required 25 iutes Activity Overview This ctivity llows studets to work idepedetly to discover rules for workig with expoets, such s Multiplictio d Divisio of Like

More information

1.- L a m e j o r o p c ió n e s c l o na r e l d i s co ( s e e x p li c a r á d es p u é s ).

1.- L a m e j o r o p c ió n e s c l o na r e l d i s co ( s e e x p li c a r á d es p u é s ). PROCEDIMIENTO DE RECUPERACION Y COPIAS DE SEGURIDAD DEL CORTAFUEGOS LINUX P ar a p od e r re c u p e ra r nu e s t r o c o rt a f u e go s an t e un d es a s t r e ( r ot u r a d e l di s c o o d e l a

More information

Resistance Thermometer

Resistance Thermometer Resistnce Themmete Shethed - Minel Insulted, Type TRP Dt sheet TRP, Editin 011 Applictin Mesuing nge: 5 +60 Genel mchiney nd equipment design Mesuing tempetue f liquids, gses nd slid bdies All bnches f

More information

THERMAL ISOLATION TECHNIQUES FOR CURE MONITORING USING FBG OPTICAL SENSORS

THERMAL ISOLATION TECHNIQUES FOR CURE MONITORING USING FBG OPTICAL SENSORS THERMAL OLATION TECHNIQUES FOR CURE MONITORING USING FBG OPTICAL SENSORS E.K.G. Boateng, P.J. Schubel, N.A. Waio Polyme Composites Goup Division of Mateials, Mechanics and Stuctues Faculty of Engineeing

More information

THERMAL EXPANSION OF TUNGSTEN

THERMAL EXPANSION OF TUNGSTEN . THERMAL EXPANSION OF TUNGSTEN S515 By Peter Hidnert nd W. T. Sweeney ABSTRACT This pper gives the results of n investigtion on the therml expnsion of tungsten (99.98 per cent) over vrious temperture

More information

Multicomponent Systems

Multicomponent Systems CE 6333, Levicky 1 Multicompoet Systems MSS TRNSFER. Mass tasfe deals with situatios i which thee is moe tha oe compoet peset i a system; fo istace, situatios ivolvig chemical eactios, dissolutio, o mixig

More information

Technical risk assessment techniques and practice in mineral resource management with special reference to the junior and small-scale mining sectors

Technical risk assessment techniques and practice in mineral resource management with special reference to the junior and small-scale mining sectors Syopsis Techicl isk ssessmet techiques d pctice i miel esouce mgemet with specil efeece to the juio d smll-scle miig sectos by J.E. McGill* d H.F.J. Thet* The juio d smll-scle miig sectos i South Afic

More information

How Much Should a Firm Borrow. Effect of tax shields. Capital Structure Theory. Capital Structure & Corporate Taxes

How Much Should a Firm Borrow. Effect of tax shields. Capital Structure Theory. Capital Structure & Corporate Taxes How Much Should a Fim Boow Chapte 19 Capital Stuctue & Copoate Taxes Financial Risk - Risk to shaeholdes esulting fom the use of debt. Financial Leveage - Incease in the vaiability of shaeholde etuns that

More information

Graphs on Logarithmic and Semilogarithmic Paper

Graphs on Logarithmic and Semilogarithmic Paper 0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl

More information

Titanium: the innovators metal Historical case studies tracing titanium process and product innovation

Titanium: the innovators metal Historical case studies tracing titanium process and product innovation Titnium: the innovtos metl Histoicl cse studies tcing titnium pocess nd poduct innovtion by S.J. Oosthuizen* J o u n l Synopsis This ppe exmines innovtion in eltion to the vilbility of new mteil: the metl

More information

THE PRINCIPLE OF THE ACTIVE JMC SCATTERER. Seppo Uosukainen

THE PRINCIPLE OF THE ACTIVE JMC SCATTERER. Seppo Uosukainen THE PRINCIPLE OF THE ACTIVE JC SCATTERER Seppo Uoukaie VTT Buildig ad Tapot Ai Hadlig Techology ad Acoutic P. O. Bo 1803, FIN 02044 VTT, Filad Seppo.Uoukaie@vtt.fi ABSTRACT The piciple of fomulatig the

More information

, and the number of electrons is -19. e e 1.60 10 C. The negatively charged electrons move in the direction opposite to the conventional current flow.

, and the number of electrons is -19. e e 1.60 10 C. The negatively charged electrons move in the direction opposite to the conventional current flow. Prolem 1. f current of 80.0 ma exists in metl wire, how mny electrons flow pst given cross section of the wire in 10.0 min? Sketch the directions of the current nd the electrons motion. Solution: The chrge

More information

1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2

1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2 Chapte 5 Example The helium atom has 2 electonic enegy levels: E 3p = 23.1 ev and E 2s = 20.6 ev whee the gound state is E = 0. If an electon makes a tansition fom 3p to 2s, what is the wavelength of the

More information

The Binomial Distribution

The Binomial Distribution The Binomial Distibution A. It would be vey tedious if, evey time we had a slightly diffeent poblem, we had to detemine the pobability distibutions fom scatch. Luckily, thee ae enough similaities between

More information

INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS

INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS Vesion:.0 Date: June 0 Disclaime This document is solely intended as infomation fo cleaing membes and othes who ae inteested in

More information

Chapter 23 Electrical Potential

Chapter 23 Electrical Potential hpte Electicl Potentil onceptul Polems [SSM] A poton is moved to the left in unifom electic field tht points to the ight. Is the poton moving in the diection of incesing o decesing electic potentil? Is

More information

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts

More information

Schneps, Leila; Colmez, Coralie. Math on Trial : How Numbers Get Used and Abused in the Courtroom. New York, NY, USA: Basic Books, 2013. p i.

Schneps, Leila; Colmez, Coralie. Math on Trial : How Numbers Get Used and Abused in the Courtroom. New York, NY, USA: Basic Books, 2013. p i. New York, NY, USA: Basic Books, 2013. p i. http://site.ebrary.com/lib/mcgill/doc?id=10665296&ppg=2 New York, NY, USA: Basic Books, 2013. p ii. http://site.ebrary.com/lib/mcgill/doc?id=10665296&ppg=3 New

More information

OPTIMALLY EFFICIENT MULTI AUTHORITY SECRET BALLOT E-ELECTION SCHEME

OPTIMALLY EFFICIENT MULTI AUTHORITY SECRET BALLOT E-ELECTION SCHEME OPTIMALLY EFFICIENT MULTI AUTHORITY SECRET BALLOT E-ELECTION SCHEME G. Aja Babu, 2 D. M. Padmavathamma Lectue i Compute Sciece, S.V. Ats College fo Me, Tiupati, Idia 2 Head, Depatmet of Compute Applicatio.

More information

Your organization has a Class B IP address of 166.144.0.0 Before you implement subnetting, the Network ID and Host ID are divided as follows:

Your organization has a Class B IP address of 166.144.0.0 Before you implement subnetting, the Network ID and Host ID are divided as follows: Subettig Subettig is used to subdivide a sigle class of etwork i to multiple smaller etworks. Example: Your orgaizatio has a Class B IP address of 166.144.0.0 Before you implemet subettig, the Network

More information

Do Vibrations Make Sound?

Do Vibrations Make Sound? Do Vibations Make Sound? Gade 1: Sound Pobe Aligned with National Standads oveview Students will lean about sound and vibations. This activity will allow students to see and hea how vibations do in fact

More information

SOME IMPORTANT MATHEMATICAL FORMULAE

SOME IMPORTANT MATHEMATICAL FORMULAE SOME IMPORTANT MATHEMATICAL FORMULAE Circle : Are = π r ; Circuferece = π r Squre : Are = ; Perieter = 4 Rectgle: Are = y ; Perieter = (+y) Trigle : Are = (bse)(height) ; Perieter = +b+c Are of equilterl

More information

Implementation and Evaluation of Transparent Fault-Tolerant Web Service with Kernel-Level Support

Implementation and Evaluation of Transparent Fault-Tolerant Web Service with Kernel-Level Support Poceedings of the IEEE Intentionl Confeence on Compute Communictions nd Netwoks Mimi, Floid, pp. 63-68, Octobe 2002. Implementtion nd Evlution of Tnspent Fult-Tolent Web Sevice with Kenel-Level Suppot

More information

Gray level image enhancement using the Bernstein polynomials

Gray level image enhancement using the Bernstein polynomials Buletiul Ştiiţiic l Uiersităţii "Politehic" di Timişor Seri ELECTRONICĂ şi TELECOMUNICAŢII TRANSACTIONS o ELECTRONICS d COMMUNICATIONS Tom 47(6), Fscicol -, 00 Gry leel imge ehcemet usig the Berstei polyomils

More information

Project Request & Project Plan

Project Request & Project Plan Poject Request & Poject Pla ITS Platfoms Cofiguatio Maagemet Pla Vesio: 0.3 Last Updated: 2009/01/07 Date Submitted: 2008/11/20 Submitted by: Stephe Smooge Executive Sposo: Gil Gozales/Moia Geety Expected

More information

On the Optimality and Interconnection of Valiant Load-Balancing Networks

On the Optimality and Interconnection of Valiant Load-Balancing Networks O the Optimality ad Itecoectio of Valiat Load-Balacig Netwoks Moshe Babaioff ad Joh Chuag School of Ifomatio Uivesity of Califoia at Bekeley Bekeley, Califoia 94720 4600 {moshe,chuag}@sims.bekeley.edu

More information

Financing Terms in the EOQ Model

Financing Terms in the EOQ Model Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad

More information