{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw 5 solutions

# hw 5 solutions - Problem 2{55 pta Cunnider the dynamic...

This preview shows pages 1–7. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Problem 2 {55 pta}. Cunnider the dynamic model for sustained eeeillattene in yeast glyeehreie: % = en—eee=0te.e an 1 A _ T I = 2k1ﬁn‘1 — tip-Km +44 — fg{G,ﬁ} where G and A are the intracellular concentrations of glumue and ATP1 respectively, Vin = llEﬁ is the constant ﬂux of glucose into the yeaet cell, #1 = [3.02 is an enzyme activity, and the parameters hr, = ELI} and Km = 13.0I determine the kinetics ef ATP degradatien. 1. [LI] pts} Show that the parameter values produce a single steadywstate aulution: a 2 H115, .91 \$1.”. 2. (20 pte) Show that the linearized model at this steadynstate point in: :1:=Au: §_ —0.0354 —0.203 0ft ‘ 0.0700 0.0435 where x = [G’ 0’19". 3. [15 pte} Determine the stability of the steady state by computing the eigenvalues of the A matrix. a. «I. w; - .5 f — J 1 _. 11 .. a U)(aj_5.d.3_)_ H... .. J . dé‘ .5” x x 21:; 1956934 gird} 6+ eff/M .4! :rmsimu‘ = r (aoﬂ (D?) 6‘- (omJOmIJA‘E “0.04” gt 0,20”? .. da‘. 3 1 3 --:»-f;p;,= Mﬂ'f as“ 556+ cM' 6J’+ (mEMDJCIJ )A‘ (Knkﬁjl 2 15:,M“+ (24921 k.- ._.i I , ~. = mam (2m: ﬁfgfg )4 : 1(0. 02) (l.77)_6\+ [056191) (“3'”) F 1 | I (CH-:- 13) x -- 0211+ L71)“ ’4 3-4: 2 6.0708 6+ 0.0513514“ (5] Ax [—DﬁEI‘i Axial) ' ' . 4.! .._._ . a . _;___; . . 3 _ x x A a oH' c.0709 0.0mm X A my : Lima—m: 56-16? " " 5}! O-W ..¢-df\$f~?‘. . i” 1*mwmwwmwwwﬁru 1 ' ': pa} (aggﬁ'wﬂwﬁn 40-:mﬁﬂmﬁyu . . "= )1; '03:::3'1--)4-+"-s:n'!n \$1?"){r-fOﬁGﬁé'H—DI'HIJL . i _| .‘1 i { "#44:;51? Sgt-L"? f3” H'u‘ltll. L. :1 - tea-{rig J'fi."3;{'i.+ {*1 e ‘ 1 Problem 1 {W pts}. Consider the hatch operation of a ﬂash drum for separating a. lunar},r liquid mixture. The drum has liquid molar holdup M and liquid mole fraction of the more volatile component re. A constant rate of heat Q is applied to the drum, producing a constant vapor molar ﬂow rate V. The vapor mole fraction of the more volatile component is denoted y. A linear vapor—liquid equilibrium relation 3; = kit, where k 2} l, is assumed. Mass balances yield the following ordinaryr diﬁerential equation system: dM a! Ma: '1. (25 .pts] Solve the dose analytically to obtain: MD—Vt Milt) = Iii} .2 ¢D(Moﬂ;DVt]t—L 2. [25 pts} Linearize the 013133 about the initial conditions to generate linear UDEs for M’H’J =' M[t) — Mn and :r’rjt) = ﬁt} '— ou. atrialytioall}r solve the ﬁrst linear ODE and formulate the second linear ODE to obtain: - , Milt}. =' no as“ V V v ' ; __ IE— " = ._..__ _ ( _ ) dt + u( 1):: Maw Use 1+ Mar How would you solve the second ODE? How would you expect pour-solution to compare to the analytical solution in part 1? ' ' . ' 3. {20 pts) Generate numerical solutions to the original CIDEs givenin part 1 by applying the forward Euler method with step size h. Show that: - Mr” 2 ﬁlo — th I; \$n+l — In _ n-Lrh) 1);]:‘71 How would you expect your solutions to compare to the analytical solutions in part 1? |. ! L—I. I 1/ Ya = m y: ﬁx k7! HJX e-ﬁﬁl cl“ Hm} .____.._, Q]: n G - 2 ‘3 q JI_U NC I"? d+_-.Uy “UOJ K m _ rm T. u (l~k)("'lﬁ) [In (nu—wk fa mi) IE, (ii/go}: {#4) It» (mg?) ho _ U4. (Th-11 Hg Ho — f'ls ~15} Hui-1'): Kn - é) d C H H LU 24-”, 01de mqhm Gina—H: # iﬁuc-U x :44 (fwd XMTKD h‘msmyn.) xic+J=gc+Hrn — 1 I Lima- fﬁ: 915-1: 4— [GIG-)1 : I“ G) “*4 M1 [3: 31h“ "P1 “qu 541':le3 [mg-rm “Inn JfJ'Til-‘ﬁ ﬁduﬁ. "£0" ‘i‘wty @ dn 1% «ELK. “4/1? hi1“: {Lin—Wm ® nFm—ua “wﬁrw: mm Ha: na-nua 1;; M [th = nnﬁw I h. -1 d "F FM": {Earl—q; Mcﬂ: m. H; @6331 43 3'4; 1 q 71W“ f‘bI-AJFI 51A if Mt: xh _ A Eh“ (mm Gnarly £-+ 1H“ 51m 5.: {EL Huh-Ll] J-A‘fllw, ...
View Full Document

• Spring '10
• HENSON
• Trigraph, Numerical ordinary differential equations, ef ATP degradatien, single steadywstate aulution, ﬁrst linear ODE, constant vapor molar

{[ snackBarMessage ]}