The Study on Influence Factors of the Mechanical Smoke Evacuation System in Atrium Buildings
|
|
- Geraldine Watts
- 5 years ago
- Views:
Transcription
1 Availabl onlin at Prodia Enginring 52 ( 2013 ) Th Study on Influn Fator of th Mhanial Smok Evauation Sytm in Atrium Building XU Jun-bin a, ZANG Chng a, ZAO Jun-fi b, CEN Qing-quan a, WU Jia-bao a,* a Chin Popl Armd Poli For Aadmy, Langfang , China b Jinhua Fir Dtahmnt of Zhjiang Gnral Fir Brigad, Yiwu , China Abtrat Thi papr tart from th trutur fatur and fir haratriti of an atrium building, and larifi th importan of th mhanial mok xtration ytm. Th diadvantag of China od about th mok ontrol ytm dign in an atrium ar analyzd. Th influning fator of th mok rmoval ffiiny i tudid in thi papr inluding mok vauation quantity, atrium hap offiint, mok xhaut fan tart-up tim and hat rla rat.th futur rarh dirtion i put forward aording to th onluion Th Author. Publihd by Elvir Ltd. Opn a undr CC BY-NC-ND lin Th Author. Publihd by Elvir Ltd. Sltion and pr-rviw undr rponibility of Shool of Enginring of Sun Yat-n Univrity Kyword: atrium building; mok vauation quantity; hap offiint; xhaut fan tart-up tim; fir load Nomnlatur m mok prodution rat (kg/) m mhanial xhaut rat (kg/) xh z mok layr hight (m) A atrium building ro-tional ara (m 2 ) hight of atrium building (m) mok dnity (kg/m3 ) V volum flow rat of mok vauation (m 3 /) 1. Introdution Atrium building with it killful hap trutur, bright and mutual harmony of intrnal nvironmnt, build a pial form of indoor and outdoor both iolatd and fuion, and thy giv a omfortabl fling with haring th xtrnal natural nvironmnt to intrnal taff, o thy ar widly ud. owvr, bau of it omplx intrnal funtion, vratility, havy fir load, fat mok prad pd, w an't fftivly parat th fir zon and mok zon in vrtial and horizontal dirtion. Statitial data of dad popl on atrium fir how that mok i on of th main fator that auing dath. A t of xllnt dignd mhanial mok vauation ytm an xhaut mot of th mok and 80% of hat, rdu indoor mok onntration and tmpratur gratly [1]. Contrarily, mok vauation ytm will fail in fir, auing havy aualti and lo. Thr havn t bn a omplt t of tandard for digning atrium mok vauation ytm in our ountry yt. Thr i alo no lar dfinition of th atrium in th Arhittural dign pifiation for fir prottion of tall building [2] (rfrrd to a th "high gaug"). Th tandard of diffrnt hap of th atrium i too ingl. W till u th vntilation rat mthod abandond ovra to alulat of th quantity of mok, in whih th mok xhaut quantity i dtrmind * Corrponding author Th Author. Publihd by Elvir Ltd. Opn a undr CC BY-NC-ND lin. Sltion and pr-rviw undr rponibility of Shool of Enginring of Sun Yat-n Univrity doi: /j.prong
2 Xu Jun-bin t al. / Prodia Enginring 52 ( 2013 ) aording to th volum. And thr ar no rlvant proviion on atrium gomtry, fir load, and mok xhaut fan tart-up tim and othr fator influning mok vauation fft. Thrfor, it i nary to do furthr tudy of th atrium building mhanial mok xhaut ytm, put forward raonabl dign propoal and alulation mthod, improv th xiting fir thnial rgulation, and propo a t of faibl pifiation of atrium mok vauation ytm. 2. Th mathmatial modl of atrium mhanial mok xtration 2.1. Th quation of mok layr hight Undr mhanial mok xhaut ondition, th hang of total mok ar mainly rfltd in th rlationhip btwn th amount of air ntrainmnt and th amount of mok vauation. Aording to th ma onrvation quation, th uppr layr of th mok mut b: d A ( z) m m 1 xh dt m xh V 2 NFPA 92B [3] for larg pa of mok prodution uing axiymmtri plum modl: m 0.071Q z 5 / QC 3 Subtituting Eq.(2) and Eq.(3) into Eq.(1), mhanial mok xhaut mok layr hight undr th ondition of tim an b: 1/3 5/3 dz Q z Q V dt A S A A Th mok xhaut rat to maintain a rtain mok layr hight For tady tat pro, th rat of mok hould b qual to th hight of th plum ntrainmnt rat, mak dz / dt =0: 1/3 5/3 Q z Q V S 5 Th mok tmpratur, dnity an b obtaind by th formula: T T Q / m o 353 / T Undr normal ondition, T 0 =20, p =1.02 KJ/Kg, thrfor, to kp a rtain mok layr hight rquir mhanial mok xhaut rat for: V 0.059Q z 5 / QC 7 Figur 1 how th rlationhip btwn kping a rtain rat of mok layr hight and mok vauation rat ndd undr diffrnt fir load. From th hart w an know, with th inra of th hight of mok layr, mhanial mok xhaut rat inra harply, fir load i largr, th tndny alo gt gratr. But along with th inra of th fir load, th mok xhaut rat alo inra, but th inraing trnd dra. Fir load ompard with hight, hight ha dpr influn on th xhaut rat w ndd. 3. Th dtrmination of mok vauation quantity lvl Aording to "high gaug": th volum of atrium l than m 3, mok vauation lvl hould b alulatd in aordan with th volum of 6 tim/h; atrium mor than m 3, mok vauation lvl hould b alulatd in aordan with th volum of 4 tim/h, but minimum mok vauation hould not b l than m 3 /h. Thi mthod i ordinary but it i diffiult to dign th fftiv vauation ytm whn it om to th atrium with diffrnt hap and am volum. NFPA 92B formula mthod blong to th atrium building prforman-bad dign atgory, and it u axiymmtri plum modl to alulat larg pa of mok prodution, Eq. (3). Th af mok layr hight an b alulatd from Eq. (8), thrfor NFPA 92B mok ontrol ytm dign th mok vauation lvl for: z p 6
3 510 Xu Jun-bin t al. / Prodia Enginring 52 ( 2013 ) /3 V 0.059Q ( ) Q 1/3 C 9 By th quation abov, th quantity of mok xhaut i inflund by th fir load and th longitudinal hight of atrium, and with th fir load and th longitudinal hight of atrium inra, th quantity of mok xhaut will alo inra, and th rlationhip btwn thm i approximat linar. At th am tim, if th volum of two atrium qual, but th longitudinal hight diffr, th mok xhaut quantity of th two atrium diffr abolutly, whil it alulation by th high gaug qual too, whih man th hap of th atrium ha fft on th quantity of mok xhaut. 2 In ordr to tudy th influn of hap offiint ( A / ) on th quantity of mok xhaut of an atrium, fiv atrium with diffrnt volum ar dignd, and vry atrium ha ix hap, how in tabl 1. Th fir load in th ntr ground of th atrium i 5MW, and om numrial alulation i mad to mak quantitativ analyz figur 2. It i known from th pitur that th mok xhaut quantity of th atrium with am volum dra harply whn th hap offiint inra, and th gratr th volum i, th gratr th rang of th rdution. But for th atrium with th am hap offiint, th mok xhaut quantity inra whn th volum inra. mok xhaut rat( m 3 /) From top to bottom, th fir load wr : 5MW 4MW 3MW 2MW 1MW mok vauation quantity( m 3 /h) From top to bottom, th atrium volum wr: 2500m m m m m mok layr hight( m) hap offiint Fig. 1. th mok xhaut rat hangd by mok layr Fig. 2. th mok vauation quantity hangd by hap offiint Tabl 1. th gomtri of th am volum atrium with diffrnt hap Volum (m 3 ) =0.2 =0.5 =1 Lngth (m) Width (m) ight (m) Lngth (m) Width (m) ight (m) Lngth (m) Width (m) ight (m) volum =2 =4 =8 m3 Lngth (m) Width (m) ight (m) Lngth (m) Width (m) ight (m) Lngth (m) Width (m) ight (m) In ordr to ontrat th diffrn btwn th high gaug of our ountry and NFPA 92B formula mthod, w alulat th mok xhaut quantity in th atrium of mall volum (2500 m 3 ), modrat volum (17000 m 3 ) and larg volum (30000 m 3 ) with diffrnt hap offiint undr diffrnt fir load, and onvr th quantity into vntilation rat N (N = mok xhaut quantity/volum), uh a tabl 2, tabl 3 and tabl 4, and w an : (1) For atrium with th am volum but diffrnt hap offiint, th quantity of mok xhaut alulatd by th vntilation rat mthod for high gaug i th am; but th quantity alulatd by NFPA 92B will dra with th inra of hap offiint, at th am tim, inra with th inraing of fir load. Compard with th vntilation rat mthod, thi mthod an rflt th influn of quantity of mok xhaut mad by fir load and arhittural fatur. (2) In trm of th iz of vntilation rat, for mall volum atrium, th rult alulatd by vntilation rat mthod for high gaug ar far mallr than NFPA 92B. Thi will not rah th goal of mok xhaut ffiintly. For xampl, a th fir load i 3MW, with th hanging of hap offiint(0.2~8), vntilation rat will go down from 23.6 tim to 17.3 tim,
4 Xu Jun-bin t al. / Prodia Enginring 52 ( 2013 ) but far gratr than 6 tim rgulatd by high gaug ; owvr, for mdium or larg volum atrium, th rult alulatd by vntilation rat mthod for high gaug ar largr than NFPA 92B. At thi tim, it may ntrain ambint air, whih au low ffiiny of th xhaut ytm and low onomi ffiiny. Suh a an atrium of 30000m 3, with th fir our powr for 3MW, who maximum vntilation rat hang with th hap offiint i 3.4 tim, i mallr than 4 tim rgulatd by th high gaug. (3) Th omparion abov how that th rult of vntilation rat mthod hav gratr dirpany with th atual mok prodution. Although w annot mak ur that if th rult alulatd by NFPA 92B an auratly xpr th atual mok prodution of atrium fir. And th modl till rmain to b furthr diud, but th modl i bad on larg numbr of intifi rarh, and NFPA 92B ha bn ud in th atual nginring dign in Unitd Stat. It hould b mor aptabl than vntilation rat mthod in om xtnt. Tabl 2. th vntilation rat of mall volum atrium NFPA 92B formula mthod high gaug 1MW 2MW 3MW 4MW 5MW Tabl 3. th vntilation rat of modrat volum atrium NFPA 92B formula mthod high gaug 1MW 2MW 3MW 4MW 5MW Tabl 4. th vntilation rat of larg volum atrium NFPA 92B formula mthod high gaug 1MW 2MW 3MW 4MW 5MW Th dtrmination of th bt mok fan tart-up tim In th atrium fir, th diffrnt tim th mok fan tarting, th diffrnt th trnd of th mok layr hight dvlopd, in ordr to prott th afty of popl' liv and proprty, thr nd to dtrmin th mok fan tarting tim raonably. Shngping Zhao [1] propod that whn th mok fan tarting, th orrponding mok layr hight xit uppr and lowr two ritial valu, namly t 0 hould b atifid quationt 1 t0 t2, a hown in figur 3.
5 512 Xu Jun-bin t al. / Prodia Enginring 52 ( 2013 ) Th uppr ritial mok layr hight ( z 1 ) Whn th mok layr thikn l than z1, thr may lad to th ution war phnomnon hown in figur 4. At thi tim om air i dirtly inhald by mok vnt, and mak th mhanial mok xhaut ffiiny drad. inkly [4] put forward th dimnionl numbr F an b ud to drib thi phnomnon in th natural mok xtration, givn by Eq. (10). Loughd [5] think inkly modl alo appli to drib th mhanial mok xtration, but h do not giv quantitativ valu of th ritial mok layr thikn in th tudy. mok vnt mok vnt mok layr Z 1 Smok plum flow air air Z 0 Z 2 fir Fig. 3. th uppr and lowr mok layr hight Fig. 4. ution war phnomnon uv A F ( / ) 1/ 2 5/ 2 g T T0 d 10 Aording to Morgan and Gardinr rarh, whn jut happn ution war phnomnon, mok vnt whih i loatd in mok torag pool ntr poition, F tak 1.5; and loatd in dg, F tak 1.1. Thrfor, th ritial mok layr thikn i givn by: 2/ 5 V d 1/ 2 g T / T0 F 11 So, z 1 d, and whn th mok fan tarting, th orrponding mok layr hight z 0 d Th lowr ritial mok layr hight ( z 2 ) Th purpo of mhanial mok xhaut ytm dign i to mak mok layr hight tability abov a af dign hight, namly mok fan hould b tart bfor mok layr down to th afty hight, to prott th popl' lif and proprty. Thrfor lowr ritial mok layr hight hould larg than , namly th tarting xhaut mok layr hight z Th bt mok fan tart-up tim ( t 0 ) NFPA 92B givn th atrium mok layr poition at any tim a Eq. (12) whih ro tional ara do not hang with hight: tq z 1.11 ln 4/3 12 Combind with z0 d, w know that: 1/3 t0q ln d 4/ / d 4/ Thn: t0 14 1/3 Q Q So, if you want to mak mok layr maintain abov afty dign hight, th mok fan tarting tim hould mt Eq. (14), and with th pd of mok prodution.
6 Xu Jun-bin t al. / Prodia Enginring 52 ( 2013 ) Th tudy of atrium fir hat rla rat Th fir hat rla rat i th major fator to dtrmin th dlin of atrium mok layr tmpratur and mok layr hight. NFPA 92B rommndd thr typial atrium tady-tat dign fir a follow: for limiting ombutibl, th minimum fir intnity i 2MW; othrwi, th minimum fir intnity i 5MW; and th maximum fir intnity i 25MW. National Building Cod of Canada (NBC) limit th quantity of atrium ombutibl, if th atrium hight highr than 8 mtr, th atrium ombutibl hould b l than 16g/m 3. A urvy wa arrid out by Profor Chow [8] about th atrium ground fir load dnity, h found diffrnt u atrium th fir load dnity i vry diffrnt, ranging from 0~300MJ/m 2. China od do not hav rlvant rgulation about th atrium fir load, nor hav xtniv fild rarh about atrium fir load dnity. Shanghai od [7] aborption and um up th forign tudy about atrium fir load, and giv th atrium building fir hat rla rat for dignr undr th ondition of pray or not. Thrfor, th author think that our ountry hould arry out a urvy of diffrnt hap and diffrnt u of th atrium fir load dnity, inluding th fixd fir load, th movabl fir load and tmporary fir load. Finally tablih a dign fir load dnity tabl for dignr bad on prforman and onvnin. And it i nary to trngthn th managmnt of th atrium ombutibl and thir put form, a muh a poibl to rdu th ombutibl quantity, pially om ombutibl of high hat rla rat, whih i vry important for fir afty. 6. Th futur rarh dirtion Aording to th fft of th mok xhaut volum, hap offiint, fan tart-up tim and fir load to atrium mhanial mok xhaut ytm, th author think that th furthr rarh hould b tudid from th following apt in th atrium building mok ontrol dign. (1) Atrium with th am volum but diffrnt hap hould b furthr invtigatd in th rul of mok prading in tall typ, ubi typ and flat typ. And diffrnt xhaut volum alulation mthod hould b found out. (2) Th mok xhaut fan bt tart-up tim nd quantitativ rarh, ombining fir dttion alarm thnology to raliz th linkag. (3) Carry out fir load rarh on atrium building. To atrium with diffrnt u, thr hould b a diffrnt fir intnity dign mthod. Th ful quantity and laying mod in th atrium hould b rgulatd. (4) Dign a t of dign guidlin to onform to th prnt ituation in our ountry on mhanial mok xhaut ytm of atrium building. Rgulat th impat on atrium mhanial mok xhaut ytm and improv of th norm xitd. Rfrn [1] Shngping Zhao. Th Computr Simulation and Modl Tt Rarh of th Atrium mok managmnt ytm [D]. Chongqing: Chongqing Univrity, [2] GB , Cod for Fir Prottion Dign of Tall Building, China[S]. [3] NFPA 92B, Guid for Smok Managmnt Sytm in Mall, Atria and Larg Ara, USA[S]. [4] P.L.inkly. Smok and hat vnting. SFPE andbook of Fir Prottion Enginring. Soity of Fir Prottion Engirir, Boton, [5] Ph.D P.Eng. Gary D.Loughd. Ph.D.Shu Cao. Numrial Study of th Efftivn of Atrium Smok Exhaut Sytm. ASRAE Tranation:Sympoi. [6] C.F.Zhang, R.uo, L.C.Shi, Y.Z.Li. Th Study of Smok Filling Charatriti in Larg Spa Undr DiffrntTyp of Fir [J]. Fir Sin and Thnology. 2005, 24(2): 153~154. [7] DGJ , Thnial Spifiation for Building Smok Control, China[S]. [8] WK Chow, WK Wong. On th imulation of atrium fir nvironmnt in ong Kong uing zon modl [J]. Journal of Fir Sin. 1993, 11(1): 3~51.
Characteristic Equations and Boundary Conditions
Charatriti Equation and Boundary Condition Øytin Li-Svndn, Viggo H. Hantn, & Andrw MMurry Novmbr 4, Introdution On of th mot diffiult problm on i onfrontd with In numrial modlling oftn li in tting th boundary
More information(1) Then we could wave our hands over this and it would become:
MAT* K285 Spring 28 Anthony Bnoit 4/17/28 Wk 12: Laplac Tranform Rading: Kohlr & Johnon, Chaptr 5 to p. 35 HW: 5.1: 3, 7, 1*, 19 5.2: 1, 5*, 13*, 19, 45* 5.3: 1, 11*, 19 * Pla writ-up th problm natly and
More informationUtilizing exact and Monte Carlo methods to investigate properties of the Blume Capel Model applied to a nine site lattice.
Utilizing xat and Mont Carlo mthods to invstigat proprtis of th Blum Capl Modl applid to a nin sit latti Nik Franios Writing various xat and Mont Carlo omputr algorithms in C languag, I usd th Blum Capl
More information[ ] 1+ lim G( s) 1+ s + s G s s G s Kacc SYSTEM PERFORMANCE. Since. Lecture 10: Steady-state Errors. Steady-state Errors. Then
SYSTEM PERFORMANCE Lctur 0: Stady-tat Error Stady-tat Error Lctur 0: Stady-tat Error Dr.alyana Vluvolu Stady-tat rror can b found by applying th final valu thorm and i givn by lim ( t) lim E ( ) t 0 providd
More informationWhere k is either given or determined from the data and c is an arbitrary constant.
Exponntial growth and dcay applications W wish to solv an quation that has a drivativ. dy ky k > dx This quation says that th rat of chang of th function is proportional to th function. Th solution is
More informationEngineering Differential Equations Practice Final Exam Solutions Fall 2011
9.6 Enginring Diffrntial Equation Practic Final Exam Solution Fall 0 Problm. (0 pt.) Solv th following initial valu problm: x y = xy, y() = 4. Thi i a linar d.. bcau y and y appar only to th firt powr.
More informationMath 34A. Final Review
Math A Final Rviw 1) Us th graph of y10 to find approimat valus: a) 50 0. b) y (0.65) solution for part a) first writ an quation: 50 0. now tak th logarithm of both sids: log() log(50 0. ) pand th right
More informationCalculation of electromotive force induced by the slot harmonics and parameters of the linear generator
Calculation of lctromotiv forc inducd by th lot harmonic and paramtr of th linar gnrator (*)Hui-juan IU (**)Yi-huang ZHANG (*)School of Elctrical Enginring, Bijing Jiaotong Univrity, Bijing,China 8++58483,
More informationSundials and Linear Algebra
Sundials and Linar Algbra M. Scot Swan July 2, 25 Most txts on crating sundials ar dirctd towards thos who ar solly intrstd in making and using sundials and usually assums minimal mathmatical background.
More informationAn Inventory Model with Change in Demand Distribution
Autralian Journal of Baic and Applid cinc, 5(8): 478-488, IN 99-878 An Invntory Modl with Chang in Dmand Ditribution P.. hik Uduman,. rinivaan, 3 Dowlath Fathima and 4 athyamoorthy, R. Aociat Profor, H.O.D
More informationLecture 14 (Oct. 30, 2017)
Ltur 14 8.31 Quantum Thory I, Fall 017 69 Ltur 14 (Ot. 30, 017) 14.1 Magnti Monopols Last tim, w onsidrd a magnti fild with a magnti monopol onfiguration, and bgan to approah dsribing th quantum mhanis
More informationAP Calculus BC Problem Drill 16: Indeterminate Forms, L Hopital s Rule, & Improper Intergals
AP Calulus BC Problm Drill 6: Indtrminat Forms, L Hopital s Rul, & Impropr Intrgals Qustion No. of Instrutions: () Rad th problm and answr hois arfully () Work th problms on papr as ndd () Pik th answr
More information22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.
Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M
More informationCharacteristics of beam-electron cloud interaction
Charatriti of bam-ltron loud intration Tun hift and intabilit K. Ohmi KEK Int. Workhop on Two-tram Intabiliti in Partil Alrator and Storag Ring @ KEK Tukuba Japan Bam-ltron intration Bam partil ar loalid
More informationINTRODUCTION TO AUTOMATIC CONTROLS INDEX LAPLACE TRANSFORMS
adjoint...6 block diagram...4 clod loop ytm... 5, 0 E()...6 (t)...6 rror tady tat tracking...6 tracking...6...6 gloary... 0 impul function...3 input...5 invr Laplac tranform, INTRODUCTION TO AUTOMATIC
More informationConstrained Single Period Stochastic Uniform Inventory Model With Continuous Distributions of Demand and Varying Holding Cost
Journal of Matmati Statiti (): 334-338, 6 ISSN 549-3644 6 Sin Publiation Contraind Singl Priod Stoati Uniform Invntory Modl Wit Continuou Ditribution of Dm Varying Holding Cot Hala, A. Frgany M. E. El-Saadani
More informationHigher order derivatives
Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of
More informationLogarithms. Secondary Mathematics 3 Page 164 Jordan School District
Logarithms Sondary Mathmatis Pag 6 Jordan Shool Distrit Unit Clustr 6 (F.LE. and F.BF.): Logarithms Clustr 6: Logarithms.6 For ponntial modls, prss as a arithm th solution to a and d ar numrs and th as
More informationAssignment 4 Biophys 4322/5322
Assignmnt 4 Biophys 4322/5322 Tylr Shndruk Fbruary 28, 202 Problm Phillips 7.3. Part a R-onsidr dimoglobin utilizing th anonial nsmbl maning rdriv Eq. 3 from Phillips Chaptr 7. For a anonial nsmbl p E
More informationFracture simulation of fiber reinforced concrete by visco-elasto-plastic suspension element method
Fratur Mhani Conrt Conrt Strutur - High Prforman, Fibr Rinford Conrt, Spial Loading Strutural Appliation- B. H. Oh, t al. (d) 200 Kora Conrt Intitut, ISBN 978-89-5708-82-2 Fratur imulation fibr rinford
More information1. (25pts) Answer the following questions. Justify your answers. (Use the space provided below and the next page)
Phyi 6 xam#3 1. (pt) Anwr th foowing qution. Jutify your anwr. (U th pa providd bow and th nxt pag) a). Two inrtia obrvr ar in rativ motion. Whih of th foowing quantiti wi thy agr or diagr on? i) thir
More informationMA1506 Tutorial 2 Solutions. Question 1. (1a) 1 ) y x. e x. 1 exp (in general, Integrating factor is. ye dx. So ) (1b) e e. e c.
MA56 utorial Solutions Qustion a Intgrating fator is ln p p in gnral, multipl b p So b ln p p sin his kin is all a Brnoulli quation -- st Sin w fin Y, Y Y, Y Y p Qustion Dfin v / hn our quation is v μ
More information2008 AP Calculus BC Multiple Choice Exam
008 AP Multipl Choic Eam Nam 008 AP Calculus BC Multipl Choic Eam Sction No Calculator Activ AP Calculus 008 BC Multipl Choic. At tim t 0, a particl moving in th -plan is th acclration vctor of th particl
More informationUncertainty in non-linear long-term behavior and buckling of. shallow concrete-filled steel tubular arches
CCM14 8-3 th July, Cambridg, England Unrtainty in non-linar long-trm bhavior and bukling of shallow onrt-filld stl tubular arhs *X. Shi¹, W. Gao¹, Y.L. Pi¹ 1 Shool of Civil and Environmnt Enginring, Th
More informationBrief Introduction to Statistical Mechanics
Brif Introduction to Statistical Mchanics. Purpos: Ths nots ar intndd to provid a vry quick introduction to Statistical Mchanics. Th fild is of cours far mor vast than could b containd in ths fw pags.
More informationAppendix XVI Cracked Section Properties of the Pier Cap Beams of the Steel Girder Bridge using the Moment Curvature Method and ACI Equation
ppndix XV rakd Stion Proprti o th Pir ap Bam o th Stl Girdr Bridg ug th omnt urvatur thod and Equation Wt Bound Pir ap Bam Figur XV- Th atual pir ap bam ro tion [Brown, 99] Th ¾ - al i no longr orrt 5
More informationTP A.31 The physics of squirt
thnial proof TP A. Th physis of squirt supporting: Th Illustratd Prinipls of Pool and Billiards http://illiards.olostat.du y David G. Aliator, PhD, PE ("Dr. Dav") thnial proof originally postd: 8//7 last
More informationEvans, Lipson, Wallace, Greenwood
Camrig Snior Mathmatial Mthos AC/VCE Units 1& Chaptr Quaratis: Skillsht C 1 Solv ah o th ollowing or x: a (x )(x + 1) = 0 x(5x 1) = 0 x(1 x) = 0 x = 9x Solv ah o th ollowing or x: a x + x 10 = 0 x 8x +
More informationENGR 7181 LECTURE NOTES WEEK 5 Dr. Amir G. Aghdam Concordia University
ENGR 78 LETURE NOTES WEEK 5 r. mir G. dam onordia Univrity ilinar Tranformation - W will now introdu anotr mtod of tranformation from -plan to t - plan and vi vra. - Ti tranformation i bad on t trapoidal
More informationEFFECTIVENESS AND OPTIMIZATION OF FIBER BRAGG GRATING SENSOR AS EMBEDDED STRAIN SENSOR
EFFECTIVENESS AND OPTIMIZATION OF FIBE BAGG GATING SENSO AS EMBEDDED STAIN SENSO Xiaoming Tao, Liqun Tang,, Chung-Loong Choy Institut of Txtils and Clothing, Matrials sarh Cntr, Th Hong Kong Polythni Univrsity
More information4.2 Design of Sections for Flexure
4. Dsign of Sctions for Flxur This sction covrs th following topics Prliminary Dsign Final Dsign for Typ 1 Mmbrs Spcial Cas Calculation of Momnt Dmand For simply supportd prstrssd bams, th maximum momnt
More informationIntegral Calculus What is integral calculus?
Intgral Calulus What is intgral alulus? In diffrntial alulus w diffrntiat a funtion to obtain anothr funtion alld drivativ. Intgral alulus is onrnd with th opposit pross. Rvrsing th pross of diffrntiation
More informationProblem 22: Journey to the Center of the Earth
Problm : Journy to th Cntr of th Earth Imagin that on drilld a hol with smooth sids straight through th ntr of th arth If th air is rmod from this tub (and it dosn t fill up with watr, liquid rok, or iron
More informationChapter 10 Time-Domain Analysis and Design of Control Systems
ME 43 Sytm Dynamic & Control Sction 0-5: Stady Stat Error and Sytm Typ Chaptr 0 Tim-Domain Analyi and Dign of Control Sytm 0.5 STEADY STATE ERRORS AND SYSTEM TYPES A. Bazoun Stady-tat rror contitut an
More informationDifferential Equations
UNIT I Diffrntial Equations.0 INTRODUCTION W li in a world of intrrlatd changing ntitis. Th locit of a falling bod changs with distanc, th position of th arth changs with tim, th ara of a circl changs
More informationu 3 = u 3 (x 1, x 2, x 3 )
Lctur 23: Curvilinar Coordinats (RHB 8.0 It is oftn convnint to work with variabls othr than th Cartsian coordinats x i ( = x, y, z. For xampl in Lctur 5 w mt sphrical polar and cylindrical polar coordinats.
More informationu x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula
7. Intgration by Parts Each drivativ formula givs ris to a corrsponding intgral formula, as w v sn many tims. Th drivativ product rul yilds a vry usful intgration tchniqu calld intgration by parts. Starting
More informationProblem Set 6 Solutions
6.04/18.06J Mathmatics for Computr Scinc March 15, 005 Srini Dvadas and Eric Lhman Problm St 6 Solutions Du: Monday, March 8 at 9 PM in Room 3-044 Problm 1. Sammy th Shark is a financial srvic providr
More informationMultivariable Fuzzy Control of CFB Boiler Combustion System
Prodings of th World Congrss on Enginring and Computr Sin 3 Vol II WCECS 3, 3-5 Otobr, 3, San Franiso, USA Multivariabl Fuzzy Control of CFB Boilr Combustion Systm Yu-Fi Zhang, Li-Wi Xu, Pi Chn, Xiao-Chn
More informationCh. 24 Molecular Reaction Dynamics 1. Collision Theory
Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic
More informationABSTRACT 1. INTRODUCTION
Analysis of Hat Pump Cyl Using CO /DME Mixtur Rfrigrant Yoji ONAKA, Akio MIYARA *, Koutaro TSUBAKI, Shigru KOYAMA 3 Saga Univrsity, Graduat shool of nginring, Honjomahi, Saga-shi, 8-85, Japan Saga Univrsity,
More informationCOHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim.
MTH rviw part b Lucian Mitroiu Th LOG and EXP functions Th ponntial function p : R, dfind as Proprtis: lim > lim p Eponntial function Y 8 6 - -8-6 - - X Th natural logarithm function ln in US- log: function
More informationSupplementary Materials
6 Supplmntary Matrials APPENDIX A PHYSICAL INTERPRETATION OF FUEL-RATE-SPEED FUNCTION A truck running on a road with grad/slop θ positiv if moving up and ngativ if moving down facs thr rsistancs: arodynamic
More informationGEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES. Eduard N. Klenov* Rostov-on-Don, Russia
GEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES Eduard N. Klnov* Rostov-on-Don, Russia Th articl considrs phnomnal gomtry figurs bing th carrirs of valu spctra for th pairs of th rmaining additiv
More informationAnswer Homework 5 PHA5127 Fall 1999 Jeff Stark
Answr omwork 5 PA527 Fall 999 Jff Stark A patint is bing tratd with Drug X in a clinical stting. Upon admiion, an IV bolus dos of 000mg was givn which yildd an initial concntration of 5.56 µg/ml. A fw
More informationLinked-List Implementation. Linked-lists for two sets. Multiple Operations. UNION Implementation. An Application of Disjoint-Set 1/9/2014
Disjoint Sts Data Strutur (Chap. 21) A disjoint-st is a olltion ={S 1, S 2,, S k } o distint dynami sts. Eah st is idntiid by a mmbr o th st, alld rprsntativ. Disjoint st oprations: MAKE-SET(x): rat a
More informationFirst derivative analysis
Robrto s Nots on Dirntial Calculus Chaptr 8: Graphical analysis Sction First drivativ analysis What you nd to know alrady: How to us drivativs to idntiy th critical valus o a unction and its trm points
More informationOptimal environmental policies in a heterogeneous product market under research and development competition and cooperation
Optimal nvironmntal poliis in a htrognous produt markt undr rsarh and dvlopmnt omptition and oopration By Olusgun Oladunjoy Univrsity of Gulph, Ontario, Canada Sptmbr 0, 005 Introdution Pollution xtrnality
More informationph People Grade Level: basic Duration: minutes Setting: classroom or field site
ph Popl Adaptd from: Whr Ar th Frogs? in Projct WET: Curriculum & Activity Guid. Bozman: Th Watrcours and th Council for Environmntal Education, 1995. ph Grad Lvl: basic Duration: 10 15 minuts Stting:
More informationAn analytical study on the stress-strain relation of PVA-ECC under tensile fatigue
Fratur Mhani Conrt Conrt Strutur - High Prforman, Fibr Rinford Conrt, Spial Loading Strutural Appliation- B. H. Oh, t al. (d) Kora Conrt Intitut, ISBN 978-89-578-8- An analytial tudy on th tr-train rlation
More informationFr Carrir : Carrir onntrations as a funtion of tmpratur in intrinsi S/C s. o n = f(t) o p = f(t) W will find that: n = NN i v g W want to dtrmin how m
MS 0-C 40 Intrinsi Smiondutors Bill Knowlton Fr Carrir find n and p for intrinsi (undopd) S/Cs Plots: o g() o f() o n( g ) & p() Arrhnius Bhavior Fr Carrir : Carrir onntrations as a funtion of tmpratur
More informationu r du = ur+1 r + 1 du = ln u + C u sin u du = cos u + C cos u du = sin u + C sec u tan u du = sec u + C e u du = e u + C
Tchniqus of Intgration c Donald Kridr and Dwight Lahr In this sction w ar going to introduc th first approachs to valuating an indfinit intgral whos intgrand dos not hav an immdiat antidrivativ. W bgin
More informationECE 3600 Lumped-Parameter Transmission Line Models b
Lumpd-Paramtr Transmission Lin Modls b Lon-th Lins: ovr 40 (50 mils) (ovr 00 mi in som tts) Nd: Units lin th:, d stik to th sam unit th for all paramtrs mils ma also b usd Rsistan pr unit th: r Units ndutan
More informationPrinciples of Humidity Dalton s law
Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid
More informationChloride diffusion in the cracked concrete
Fratur Mhani of Conrt and Conrt Strutur - Amnt, Durability, Monitoring and Rtrofitting of Conrt Strutur- B. H. Oh, t al. (d) Kora Conrt Intitut, Soul, ISBN 97-9-57--5 Chlorid diffuion in th rakd onrt W.L.
More informationLecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields
Lctur 37 (Schrödingr Equation) Physics 6-01 Spring 018 Douglas Filds Rducd Mass OK, so th Bohr modl of th atom givs nrgy lvls: E n 1 k m n 4 But, this has on problm it was dvlopd assuming th acclration
More informationwith Dirichlet boundary conditions on the rectangle Ω = [0, 1] [0, 2]. Here,
Numrical Eampl In thi final chaptr, w tart b illutrating om known rult in th thor and thn procd to giv a fw novl ampl. All ampl conidr th quation F(u) = u f(u) = g, (-) with Dirichlt boundar condition
More informationTwo Products Manufacturer s Production Decisions with Carbon Constraint
Managmnt Scinc and Enginring Vol 7 No 3 pp 3-34 DOI:3968/jms9335X374 ISSN 93-34 [Print] ISSN 93-35X [Onlin] wwwcscanadant wwwcscanadaorg Two Products Manufacturr s Production Dcisions with Carbon Constraint
More informationModified Shrinking Core Model for Removal of Hydrogen Sulfide with T Desulfurizer
Modifid Shrinking or Modl for Rmoval of Hydrogn Sulfid with T Dsulfurizr Enguo Wang Dpartmnt of physis Lingnan normal univrsity Zhanjiang, hina -mail: 945948@qq.om Hanxian Guo Institut of oal hmial nginring
More informationAddition of angular momentum
Addition of angular momntum April, 0 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat th
More informationL 1 = L G 1 F-matrix: too many F ij s even at quadratic-only level
5.76 Lctur #6 //94 Pag of 8 pag Lctur #6: Polyatomic Vibration III: -Vctor and H O Lat tim: I got tuck on L G L mut b L L L G F-matrix: too many F ij vn at quadratic-only lvl It obviou! Intrnal coordinat:
More informationEE 119 Homework 6 Solution
EE 9 Hmwrk 6 Slutin Prr: J Bkr TA: Xi Lu Slutin: (a) Th angular magniicatin a tlcp i m / th cal lngth th bjctiv ln i m 4 45 80cm (b) Th clar aprtur th xit pupil i 35 mm Th ditanc btwn th bjctiv ln and
More informationExam 2 Thursday (7:30-9pm) It will cover material through HW 7, but no material that was on the 1 st exam.
Exam 2 Thursday (7:30-9pm) It will covr matrial through HW 7, but no matrial that was on th 1 st xam. What happns if w bash atoms with lctrons? In atomic discharg lamps, lots of lctrons ar givn kintic
More informationELEC 372 LECTURE NOTES, WEEK 11 Dr. Amir G. Aghdam Concordia University
ELEC 37 LECTURE NOTES, WEE Dr Amir Aghdam Cncrdia Univrity Part f th nt ar adaptd frm th matrial in th fllwing rfrnc: Mdrn Cntrl Sytm by Richard C Drf and Rbrt H Bihp, Prntic Hall Fdback Cntrl f Dynamic
More informationMAE 110A. Homework 4: Solutions 10/27/2017
MAE 0A Homwork 4: Solution 0/27/207 MS 4.20: Th figur blow provid tady-tat data for watr vapor flowing through a piping configuration. At ach xit, th volumtric flow rat, prur, and tmpratur ar qual. Dtrmin
More informationWhy is a E&M nature of light not sufficient to explain experiments?
1 Th wird world of photons Why is a E&M natur of light not sufficint to xplain xprimnts? Do photons xist? Som quantum proprtis of photons 2 Black body radiation Stfan s law: Enrgy/ ara/ tim = Win s displacmnt
More informationMSLC Math 151 WI09 Exam 2 Review Solutions
Eam Rviw Solutions. Comput th following rivativs using th iffrntiation ruls: a.) cot cot cot csc cot cos 5 cos 5 cos 5 cos 5 sin 5 5 b.) c.) sin( ) sin( ) y sin( ) ln( y) ln( ) ln( y) sin( ) ln( ) y y
More information( ) Differential Equations. Unit-7. Exact Differential Equations: M d x + N d y = 0. Verify the condition
Diffrntial Equations Unit-7 Eat Diffrntial Equations: M d N d 0 Vrif th ondition M N Thn intgrat M d with rspt to as if wr onstants, thn intgrat th trms in N d whih do not ontain trms in and quat sum of
More informationOn-Line PI Controller Tuning Using Closed-Loop Setpoint Responses for Stable and Integrating Processes*
On-Lin PI Controllr Tuning Using Closd-Loop Stpoint Rsponss for Stabl and Intgrating Prosss* Mohammad Shamsuzzoha a, Sigurd Skogstad a, Ivar J. Halvorsn b a Norwgian Univrsity of Sin and Thnology (NTNU),
More informationQuantitative Evaluation for Consequences of LNG Releases Based on RBI
Intrnational Journal of Sin Vol.3 o.5 016 ISS: 1813-4890 Quantitativ Evaluation for Consquns of LG Rlass Basd on RBI Xin Ma, Tonghui Shi a Shool of Mhatroni Enginring, Southwst Ptrolum Univrsity, Chngdu
More informationSearch sequence databases 3 10/25/2016
Sarch squnc databass 3 10/25/2016 Etrm valu distribution Ø Suppos X is a random variabl with probability dnsity function p(, w sampl a larg numbr S of indpndnt valus of X from this distribution for an
More informationVTU NOTES QUESTION PAPERS NEWS RESULTS FORUMS
Diffrntial Equations Unit-7 Eat Diffrntial Equations: M d N d 0 Vrif th ondition M N Thn intgrat M d with rspt to as if wr onstants, thn intgrat th trms in N d whih do not ontain trms in and quat sum of
More informationA Propagating Wave Packet Group Velocity Dispersion
Lctur 8 Phys 375 A Propagating Wav Packt Group Vlocity Disprsion Ovrviw and Motivation: In th last lctur w lookd at a localizd solution t) to th 1D fr-particl Schrödingr quation (SE) that corrsponds to
More informationThe pn junction: 2 Current vs Voltage (IV) characteristics
Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n
More informationCalculus II (MAC )
Calculus II (MAC232-2) Tst 2 (25/6/25) Nam (PRINT): Plas show your work. An answr with no work rcivs no crdit. You may us th back of a pag if you nd mor spac for a problm. You may not us any calculators.
More informationMCE503: Modeling and Simulation of Mechatronic Systems Discussion on Bond Graph Sign Conventions for Electrical Systems
MCE503: Modling and Simulation o Mchatronic Systms Discussion on Bond Graph Sign Convntions or Elctrical Systms Hanz ichtr, PhD Clvland Stat Univrsity, Dpt o Mchanical Enginring 1 Basic Assumption In a
More informationN1.1 Homework Answers
Camrig Essntials Mathmatis Cor 8 N. Homwork Answrs N. Homwork Answrs a i 6 ii i 0 ii 3 2 Any pairs of numrs whih satisfy th alulation. For xampl a 4 = 3 3 6 3 = 3 4 6 2 2 8 2 3 3 2 8 5 5 20 30 4 a 5 a
More informationThe Death of Stars - I.
Th Dath of Stars - I. Larning Objctivs! B abl to sktch th H-R diagram and includ stars by siz, sctral ty, liftim, color, mass, magnitud, tmratur and luminosity, rlativ to our Sun! Comar Rd Dwarfs to our
More information1 Isoparametric Concept
UNIVERSITY OF CALIFORNIA BERKELEY Dpartmnt of Civil Enginring Spring 06 Structural Enginring, Mchanics and Matrials Profssor: S. Govindj Nots on D isoparamtric lmnts Isoparamtric Concpt Th isoparamtric
More informationBifurcation Theory. , a stationary point, depends on the value of α. At certain values
Dnamic Macroconomic Thor Prof. Thomas Lux Bifurcation Thor Bifurcation: qualitativ chang in th natur of th solution occurs if a paramtr passs through a critical point bifurcation or branch valu. Local
More informationElements of Statistical Thermodynamics
24 Elmnts of Statistical Thrmodynamics Statistical thrmodynamics is a branch of knowldg that has its own postulats and tchniqus. W do not attmpt to giv hr vn an introduction to th fild. In this chaptr,
More informationA local bond stress-slip model for reinforcing bars in self-compacting concrete
Fratur Mhani of Conrt Conrt Strutur - Amnt, Durability, Monitoring Rtrofitting of Conrt Strutur- B. H. Oh, t al. (d) 200 Kora Conrt Intitut, Soul, ISBN 978-89-5708-8-5 A loal bond tr-lip modl for rinforing
More informationA Simple Method of Tuning PI Controllers for Interval Plant of Cold Rolling Mill
ntrnational Journal of Rnt Trns in Enginring, Vol. 1, No. 4, May 009 A Simpl Mtho of Tuning P Controllrs for ntrval Plant of Col Rolling Mill S.Umamahswari 1, V.Palanisamy, M.Chiambaram 3, 1 Dpartmnt of
More informationLecture 16: Bipolar Junction Transistors. Large Signal Models.
Whits, EE 322 Ltur 16 Pag 1 of 8 Ltur 16: Bipolar Juntion Transistors. Larg Signal Modls. Transistors prform ky funtions in most ltroni iruits. This is rtainly tru in RF iruits, inluding th NorCal 40A.
More informationPREDICTION OF THE CUTTING TEMPERATURES OF TURNING STAINLESS STEEL WITH CHAMFERED CUTTING EDGE NOSE RADIUS TOOLS
Journal of Matrial Sin and Enginring with Advand Thnology Volum, Numbr, 00, Pag 5-43 PREDICTION OF THE CUTTING TEMPERATURES OF TURNING STAINLESS STEEL WITH CHAMFERED CUTTING EDGE NOSE RADIUS TOOLS Dpartmnt
More informationINTEGRATION BY PARTS
Mathmatics Rvision Guids Intgration by Parts Pag of 7 MK HOME TUITION Mathmatics Rvision Guids Lvl: AS / A Lvl AQA : C Edcl: C OCR: C OCR MEI: C INTEGRATION BY PARTS Vrsion : Dat: --5 Eampls - 6 ar copyrightd
More informationThe Open Economy in the Short Run
Economics 442 Mnzi D. Chinn Spring 208 Social Scincs 748 Univrsity of Wisconsin-Madison Th Opn Economy in th Short Run This st of nots outlins th IS-LM modl of th opn conomy. First, it covrs an accounting
More informationAerE 344: Undergraduate Aerodynamics and Propulsion Laboratory. Lab Instructions
ArE 344: Undrgraduat Arodynamics and ropulsion Laboratory Lab Instructions Lab #08: Visualization of th Shock Wavs in a Suprsonic Jt by using Schlirn tchniqu Instructor: Dr. Hui Hu Dpartmnt of Arospac
More informationComputing and Communications -- Network Coding
89 90 98 00 Computing and Communications -- Ntwork Coding Dr. Zhiyong Chn Institut of Wirlss Communications Tchnology Shanghai Jiao Tong Univrsity China Lctur 5- Nov. 05 0 Classical Information Thory Sourc
More informationLecture 4: Parsing. Administrivia
Adminitrivia Lctur 4: Paring If you do not hav a group, pla pot a rqut on Piazzza ( th Form projct tam... itm. B ur to updat your pot if you find on. W will aign orphan to group randomly in a fw day. Programming
More informationNonlinear Saturation Controller for Suppressing Inclined Beam Vibrations. Usama H. Hegazy *, Noura A Salem
Nonlinar Saturation Controllr for Suppring Inlind Bam Vibration Uama H. Hgazy * Noura A Salm Abtrat In thi papr prnt th numrial prturbation olution of an inlind bam to xtrnal paramtri for ith to diffrnt
More informationMath-3. Lesson 5-6 Euler s Number e Logarithmic and Exponential Modeling (Newton s Law of Cooling)
Math-3 Lsson 5-6 Eulr s Numbr Logarithmic and Eponntial Modling (Nwton s Law of Cooling) f ( ) What is th numbr? is th horizontal asymptot of th function: 1 1 ~ 2.718... On my 3rd submarin (USS Springfild,
More informationDepartment of Mechanical Engineering, Imperial College, London SW7 2AZ, UK
1 ST Intrnational Confrn on Composit Matrials Xi an, 0 5 th August 017 THE MECHANICS OF INTERFACE FRACTURE IN LAYERED COMPOSITE MATERIALS: (7) ADHESION TOUHNESS OF MULTILAYER RAPHENE MEMRANES NANOSCALE
More informationMathematics. Complex Number rectangular form. Quadratic equation. Quadratic equation. Complex number Functions: sinusoids. Differentiation Integration
Mathmatics Compl numbr Functions: sinusoids Sin function, cosin function Diffrntiation Intgration Quadratic quation Quadratic quations: a b c 0 Solution: b b 4ac a Eampl: 1 0 a= b=- c=1 4 1 1or 1 1 Quadratic
More informationAddition of angular momentum
Addition of angular momntum April, 07 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat
More informationBasics about radiative transfer
aic about radiativ tranfr runo Carli Day Lctur aic about radiativ tranfr - runo Carli Tabl of Contnt Th radiativ tranfr quation. Th radiativ tranfr quation in a impl ca Analytical olution of th intgral
More informationHomotopy perturbation technique
Comput. Mthods Appl. Mch. Engrg. 178 (1999) 257±262 www.lsvir.com/locat/cma Homotopy prturbation tchniqu Ji-Huan H 1 Shanghai Univrsity, Shanghai Institut of Applid Mathmatics and Mchanics, Shanghai 272,
More informationThe van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012
Th van dr Waals intraction D. E. Sopr 2 Univrsity of Orgon 20 pril 202 Th van dr Waals intraction is discussd in Chaptr 5 of J. J. Sakurai, Modrn Quantum Mchanics. Hr I tak a look at it in a littl mor
More informationChapter 3 Lecture 14 Longitudinal stick free static stability and control 3 Topics
Chaptr 3 Lctur 14 Longitudinal stick fr static stability and control 3 Topics 3.4.4 Rquirmnt for propr stick forc variation 3.4.5 Fl of th stability lvl by th pilot Exampl 3.3 3.5 Dtrmination of stick-fr
More information1973 AP Calculus AB: Section I
97 AP Calculus AB: Sction I 9 Minuts No Calculator Not: In this amination, ln dnots th natural logarithm of (that is, logarithm to th bas ).. ( ) d= + C 6 + C + C + C + C. If f ( ) = + + + and ( ), g=
More information