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  1. 1. |m[. iC| Stu- I ; i S‘ *1‘ "| '| 1 . ;Iti‘ I 1 li licrc S | l1t". II1~. [|'k~~. . '__‘__ ‘L _K l. |l| L NHL A L , _. ‘i it h‘| "h1 0171.1“ - 1.tllC1C1t‘1lll. t1lUl| . 'ntc lmp. ictt. i:tur — I-'leur. | Stress ‘ . lc " L~. 3 ls; c where M — maximum bending moinent c - distzmcc from the center to the farthest fiber. In ~ moment of inertia with respect to neutral axis .1 - section modulus
  2. 2. Tlivdrwulicx — l branch of “ ‘ r . ' “ r < V‘ g xt. gnu dc llx | lll tln iiitcli. iiiic. i| pioptiiit -. of liquids, -. l ‘ulIt. l' and 1llL: ll tlppllulllon in C‘ll'_: ll1c‘L‘l'lni. ‘,. “)‘d| ‘0Sl: itic. s -— . i ll‘. illCll olpliyxics liicli tlt-. il-. lih nUl]. . ii rt--. t. Hytlrodyii-. tmics or Fluid Dyn-. tinic. s - bmncli of llit. ‘Ch. tniC, ‘hlL‘ll deals llh nllltls iii llmlliin F| ui(ls— stibstaiiccs capable of llowiiig and having particles that easily move and change their relative direction without S: p.ll'dil0ll ot inass. Liquid and gas es are classified as fluids. Density: Specific Gravity or Relative Density: . _ mats‘ m“*°'5 D°"5“Y ' voiame _ . density of a substance . specific gravity ofa substance ‘ WaF—— in symbols. P =12 v . ;fg"b°'S~ _ ps. ..: ,i. ,:. Zflm - - '5iuLlS cc '' _’_——: = Weight Density = 3%; -1:1‘: an p““° 9 @ 4 °C and 1 am, > in Synjbols‘ pmo = l g/ cc = 1000 kg/ m’ = 1.94 slugs/ fi3 ‘ = _"L 5,410 = 9si dynes/ cc = 9810 N/ m3 = 52.4 lbs/ ft’ V = 9.31 | 'N/1113 but W = mg mg Hence, 6= 7 "' Pg Hydrostatic Pressure: F l-'= X , whcreF; A . . - . « ‘ id 130 ' ; The pressure at a depth h in a liquid of density p due to the weigh‘ °m‘° flu‘ 3 V6 '5 P-pgh= Z§h _ ; ~ th fluid nlonc where P = pressure at the bottom pressure due 10 9 ’ F W _ fig =9‘/3 zfl - = h Derivation: P= 7; ’ T ‘ A ‘A A pgh 5 Note: . -. t luitl . . k , . . ‘ v ‘ ‘‘ tted unifonnl) throuvhout the l . If their is extemal pressure exerted on .1 tluid which is transmi c the total pressure at that depth IS . . : ~ ~ nthe surface of the mild p pm__M, —+ pgh , where Pm-. ..ti Pr‘-‘*“"” "
  3. 3. itr| l .1 iVi) Iii iilluj I» III . |I1n‘¢[1U; m_Lm. ‘« “ T P - Will I. Lu . I'. IL ‘pig; nu! » Ill 1 Hun 1|, I-. ,-7,. um nn .1 U‘ '1 P‘ H”) Allin: -‘ '. ~. . . . V) N m w “‘h—‘lId| :il: ‘|Ch‘fL. .lll‘| >t (| ’,. . . ) i~U“x pvt ‘ . '.n’; nl (hr: n-. n'th . .mm. .phr. -re, mg pr»; . , -_. .A_- ,1[h. _. bgflrxgn (]fth]4 V . ‘ a ll pi m. am. . l|iu. .:li1u xh. u._? . .1nd mt]: LlL . nnm_ . ,m, L,| ,, mm, phL. ,,C PR>| |Ix M xmlcvcl(.1n. 'c1.igcmluu)I~ I . ‘.lmt‘~‘, ‘il'lL'i 1l11))LicIilc(i to by w<; Lu! l_ 10113-R [-d_ 1 Jill] l0|.7‘5 l'. : “ 1 ‘ 7’ [N , ‘uxc I [Mr | ()"dym. v‘u11: -‘ 760 mm Hg: I buy 10 Pa - 7:» cm H; '—‘ 3° ‘)2! in H: 7 E0132.‘ tux “ 760 101T Fluid Pressure Variation with Depth: Common Devices for Measuring Pressure: :1. Open tube Manometcr Case 1; P —> Pm P = P: -Ll + P — Pezm = pgh P ~ P, .‘.5 P, -.. ,—. 0|’ P = Pmn ‘ Psu, ‘ [Putin P " P ~ pgh P ' Pam. 2 "pgh P _ PJ. ‘ 5 -P, -_i» > Pv. u—: umI- where P = .ibsoIulc prcssllffi thcrcturn-P Eh P 7 PM 2 g_, ugc pressure P— . ... .’ii7' p : _P 2—p-h . ‘. . saw‘ ‘T’ or P ’ ppm. ’, pgrh
  4. 4. I‘ '1“‘““. ‘ B'. u‘uxnx-tt'u . ». l wlli(‘| ;'[1L-‘I . lum-nu» l. ‘ . Rh“ ~ IL . llllln ‘V hm p“. __lm_ _ K Nu-; ‘ M’-__ . . t L dl hltlllkitlltl Lundllum [ _m“ | )u, _§uR_: 0u(. D». .. 13.0 ‘: "L‘L’ mama t, _.~. ,,J _ _ Xfitl Ibu‘ bpcclllc Ur. wtt) ol lvlcrcury (H2) ~ I31» Pm. ugh Buoyancy: Archimedes Principle ~ states that am’ bod ‘submerv d ‘ ' - ' 4 ' ‘ - ‘ of [M fluid dvbplacei . ) ,6 m mun: -used Ill 4 fluid 15 sublected to .1 bunyanl force cquul to [hc “ugh, For Lrud_x that floats. “I! X F « 0 B. l~'. T W = Wm- B-F- ‘V W : Ulufvm FED Reading of scale W; Reading 01 scale ‘ V ‘Ms W B. l~’. Ll‘. ' 0 |3_| -fl W W1 W4, whcrc. B. F. ~ But, -yam Force W Weight of object in air or the true weiglu W, : Weight of object in fluid or the appurt-nt weight B. l-, ' W Wk V_, ,m. ,. W, “ Weight ofdixpluccd fluid um, density‘ 0!" fluid [3 F V w, w, _ ~ Vm_, , V Volume ofuhjcct
  5. 5. Wefloiltl'Prhctp| .: sntesum"1n. m,mfi hm _ nemwomm f flu‘ ‘ N_‘ ‘“‘“h¢Pfesstnemcreasesastltevelocitydccreuses° ‘ "| .d'M"| ‘q‘dd°r3”‘d°““’““'5°W'°¢ll? Vented Meter: T——~ ~——. _.__. 51*‘? ho, ’ “[03 A| > A1 V2 > Vl P37’ P3 0|’ Pp_<P-, Since the amount of liquid flowin thr h th ' ' H‘ g oug ose section per umt, are all equal. therefore we can conclude that the rate of flow Q are also equal . ~ _AV_ Q ‘ At but AV = AAx hence Q = A ~ but 2‘? = V consider section l and 2 Hence, Q‘AaVx: A2V2 _ _ . Am = Azvl = constant ——~p Equation of Continuity Bernoulli’: Energy Theorem . . . - - lb l. Neglecting friction, the total head or total amount of energy per um! of Weight, 15 ‘he “me 3‘ ‘W7 P°““ “' ° pathofflow. H A V Q Total energy = velocity head + pressure head + elevation head i . —_ yglogity head 2 = elevation head P. = Q ‘E '5 pressure head Qt Q1
  6. 6. 2. With continuous steady flow the total head at an ‘ ‘ ‘ . - ypomtmastream It th head downstream pom! plus the loss ofhead between two points. ‘S “M 0 e at my H. L. = head loss . ‘’_‘I P V22 P2 23* 7; +Z. =2— +7” +2.: *H. l.. presence 3. With the jof pump from point I to point 2. V 2 P V32 P E + 3' +z. +H. A.= §-g— +35 +2, ~-H. L. H. A. = head or energy added HP ’~ gfig (output horsepower for pump) E = H. A. (energy added) 4. With the presence of turbine or motor from l to 2 H. E. = Energy given up HI’. = 99L (input horsepower for turbine) 746 Efficiency = L E = H. E. (energy given up) 5. Atthe nozzle; Qr= Q2 _‘_, v-5 2 1 -‘:2’. ;_; +*: _; , ,Z'; _12'2g +-Eu’)—-+z1+HL e. 2 HL = —‘—, -11»; -2; Qaagv HP= '7T6- 2 E = VJ‘ (velocity head at the nozzle)
  7. 7. HYDRAULICS 9_Bl: '__C_E_-any opening having a closed measuring flow of fluids. penmeten made in a Wan or pamm" used f°' Note: When the area f t k ' - - water in me tan: an lS more than 16 times the area of orifice neglect the velocity of For flow under atmospheric pressure: '1’ Y: fi 1 V22 + + Z1 = 29 to 2g V22 h : 29 v2 = ,/2gh (theoretical velocity) v = Cvvz (actual velocity) or actual velocity at vena contracta T——— coefficient of velocity A0 = Area of orifice a = area of jet at vena contracta Cc = A1 (coefficient of contraction) 3 = Aocc Q = av (actual discharge rate) Q Aocccv 3’ Q = CAo~f2’9_H c . —_ cccv (coefficient of discharge) / /// /// // f Ti it ll
  8. 8. _ A l 7‘ 7 lil - / Alrlwl/ /ill V‘: “-V‘. -.-. '
  9. 9. Thcl'mt)d'n: tmic_ A ix lllt; ‘‘| k'l‘t. ‘L' Mu it i ' ‘ k I t‘urn. :.itI= :. -. . . , ‘-llll lit: a, n- , Tu‘I'Pt rixture is the dt'_'rt--. - ul ln‘{| lL‘ . or cul. lntu U U M‘ M W! " W" an . . ion C0fl't‘rion from one scale to . |l|0llIl‘r t‘; II(: -V I am plkxxxurc, ll ' - . ,. _ . nits Cctittrrmlr. luilircrihcit Kelvin Katlinlllc P - K .1; K N l Chm Llllll1I' ~ R R B. P. of H30 , A c -mint . e—~~ — . L emp _ K 4‘ PP. of H30 ' * 273* — 4, Absolute zero ‘ 0_ ~21 9 Conversion Formulas: F ——>‘ C C i K F ——>‘R C :3 C= -3-(F-32) K= C+273 R= F+460 R= ;c F= §—c+32 c= r<—273 F= R—460 c= §-R Note: I. AT; = % ATC . also An : ATC or SC" = 917° 2. °C. °F, "K or K & °R — temperature reading 3. C°, F”. K°. & R° ~ temperature change or difference Heat — form of energy transferred from one body to another as a result of temperature difference. Sensible Heat — is the heat absorbed or given off by a substance that changes its temperature. Q = mcAT Where: Q — sensible heat :11 ~ mass c ~ specific heat AT T; ~ T, ~’ change in temperature Heat Units l. calorie (cal) 1 C01 ’ ‘H363 2. kilocalorie (kcul) IkcaI I.000 cal 3. Joule (J) I BTU — 252 cal 4. British Thcnnul Unit (BTU) ht Ii &'l‘: rl": " Hr inc“ . /C, ‘
  10. 10. »~>>>>> »”& " "‘ ‘ * ' “l ‘ W7 -l inc? one d': i’. ',TF": ‘ Sp“dr"‘ ‘H " in l‘ lllt‘ . illlLiiIlil(nl lluilrtl l (J l v N V _ HR i‘- (ii C I llll‘L' lli ~ (« - - htIl"‘ in tlic lciiilii-r. iitirv I Imp” mm M " U" l“i H70 | 'iir -lc em‘ Hill - i . C l " “ | .k. ..“ ‘ >5.-.3‘ - V ii. , (. i. -. ~.(‘. .-. i; t 0 iii 0, ii; 0)” c . i’ For ice: " ~"' ‘ "'k or _ cry‘ . . I c 0.3 0 Q . .a_ LA “TU ‘I lbii '*" “ L‘. 'C‘ 0'5 v. ' ‘ C —r__‘_. . 0 r (: f!_ C41 . L is iii. .r= A--' kc 0 5 WK. Change of Shite: Litcnl He it ~ is th - h - 1 ~. , - I w L ea that does not . ifli. ct the temperature ot the substance but changes llw state. .1. Latent be-. t off . ‘i _ '« . . - , to the liquiii smi: :i:0i'tls(: e)ixir: i: Gum 0”“ W mm mm "WNW to chmgc “ ""b"L"”°° 5°” ‘h‘ ‘°““ Lt : T3,! " °" Qr " 11114 For ice, 1.4- ‘SD SE? 7 144 —-——BlEU Note: ml 5 1., ’ ll’! —g—- '4 6 I-ll b. Latent Beat of Vaporization (I. ..) - is the amount of heat per unit mass necessary to change a substance from liquid to vapor at its boiling point. Lt-2% or Q, ,=mL. , For water, L, ‘ 540% 972 ‘B-I-lg - ga! _ :2 - BTU Also L. ,in g 9 L, ,in ‘b c. Specific Latent Heat of Sublimation of a Substance —— is the heat per unit mass necessary to convert it from the solid to the gaseous state at a given temperature. _ _ _ Sublimation — a change of state from solid to gaseous without passing the liquid state. For example, dry ice . . . ‘ t th ' rk “When work is totally converted into heat the amount of heat generated bears a constant ratio 0 ihwtgem l energy bears a constant ratio to e done. Similarly. if a certain amount of heat is transformed into mcchanica which disappeared". This is often called Joule‘s Law: 1 ’ o Flnt Law of Thermodynamics: where: produced by heat W work done to produce heat or work Q - heat energy I V mechanical equivalent of heat I -‘l. l 86 joules per caloric J -1. l 86 x I07 crgu per calorie J 778 ft-lbs per BTU
  11. 11. Thf | dL‘: l| Gglg L3“ in 30_| c'~ l--. m: . t C0|. l. nl tcmpv: r.llun: _ the mlumu ul . . . .'. mpl-c nl -' as ix nnct. »ul ptopurtttm. | 10 um “b7‘°‘u“-' WV‘-WIS‘ ~| Pl‘llt‘d to lhc gf. .t5 It ’| ‘ C0fl. l; llll. PV C Plvl V‘ PIVI 7 Puvn C b. Charle‘s Lam: At constant pressure. the volume of ii sample of gas is directly proportional to the . lb$0ll. .l1€ temperature. if P constant. V at T V = CT 3 2 C T )5 _ Y; , X1 = T. ’ T, ” T, , C c. Ga)‘-Lussac’s Law sometimes called as Amontou’s Law: At constant volume, the pressure of a sample of gas is directly proportional to the absolute temperature. it‘! -' constant P rx T P 1 CT P — — C T 2; - J11 ; Est _ C r] T1 Tn d Combmed or Perfect Gas Lave PV at T PV - CT .5/_ C T l‘. Idt‘-II (Ins llquntlon: PV mRl AhCTL R t', rtt"oll‘-lrlnl ml M, R R - M m ~. . W M RI but m nM o_r_ n ntml hcncc . PV '- nRT Where: n-“no. ofmolct. . , lb, C‘ We ft-lb pmole-°R Ol'_ cal R= 1.9858 —-—'g m°! e_K Or_ I R=8,3l4 -—-fix t't:1s45.32 Note: in chemistrzy. PV = nR T where: R = Ideal gas constant = universal gas CODSVSIDI - 1’_V_ _ _1=£11_(A31liI_¢: S_1_ R ‘ nr (1 mole)(273 K) . liter-atm R —’0.08205 —”—‘mo‘e_K
  12. 12. 3 . ‘ _ T '| ”“u M Idl‘-l| (mu : Iwtnctric Proct-ts l! ‘ l I . . ' I p (V. P.) . - V Forrnul. rs: I. Ga)‘-Lussac‘s Law: 3». 11 0, P. v or Pzvz Tl T: T; T; V| W V: 01' .5‘-_ = _T_= _ P. T. 2 w__. PdV——0 3. Q. ’ : U: ' Ur Proof: By Lgw of oConservation° of Engrgy o=4rr’n»K+Au+z; vfr+a/ J; Q 7 AU 4. Change in internal energy (AU): AU 7 lJ1"Uu: mC, (T3 T1) 5. Change in enthalpy (AB): A” 1‘ "3 4H| 7 mC‘. (T; T1) 6. ‘Change in entropy (AS): 7. T» P» AS S, —-S. mc. ln-E mc. |nF~| — Proof: By definition, /S ) AS s_. e-s. mc. ,]_I 91 lmcv| nTl r. T T» AS S, —S. me. In me. In [1 in P . _;’_. P: l an inl-. 'rn. ill rctcr I'll” « ' ~ l"“'~«' ~I| uh . l mu. lll ‘lllL, lI ti" ml“. ' — llxf lL'lll tin -, r.:1." mt For steady-Flow work (WM) -—> open system . v,. ,( ~ v (P. .— 9,; Proo f: By Law of Conservation of Energy, /9"‘. /»"‘*I¥<' Wsr S *5“/ F : + w’+Aw, +vv; , ; assuming . _«. P=sr< 2 o ~(WF2“ Wu) : ~(PzV‘PIV) 7‘ PIV ‘PZV Wsr T V (P1 — P2) 0 Another proof: AW; — Wf. -,— — W5: “ -Ww Therefore, W5, — - Awr “ (P2V - PxV) OT W5: : V(P. ~92) In C, ("I T; ‘H Ti)
  13. 13. lmbuic l't'ou-u I» an rnlrm ll‘ s I il l ‘ J . _ - L‘ . . Ik|1]| lr . . ul , . uh ltlulb. I _ ‘ ' » t "Hm ~‘-llltll tin pn. .ure l'L. 'lll. Illl U. " ,1 mi . Il l L. ‘A M 57”" s. ""“ l. Ch-nrlt-‘s Ln“: 7. For steady-Flow lnObdl'lC (W_, ,) -——p open xynlcrn it _E'. : PrVr P: V~ . . 1-_ l—: 0!’ T’ T‘ ; where P. P; W5, 0 (rl AP AK 0) W Front‘: .. *-' .1.‘ Q of» AU » Aw, «e ws, 7; Q 1 AH + WW W”. " 0 All 2. V, ‘;— l ‘ PW; * Vi) An0{hL'I' pTO0f: A“, , “'N} -‘ W5} 3. O H3’-Hg [TIC]. (T3--T1) Vi)" V1)~ W5] therefore, W5, ’ 0 Proof: . 1‘ 0 gift Mr AU i , _}¢{, . + WM 0 AU " Wm Q Llg" U. > P(V3 V, ) U, » U, + PV1 PV1 Q (U: ' pvt)‘ (Ur “' Pvl) But; H U PV . ‘ Q H; H. AH rnc, ,(Tg T. ) -8. Change in internal energy (AU): AU ll_. U, mc. ('l‘: T. ) 5. Change in enthalpy (AH): H-_i ' Hi me‘, (T) TI) 6. Change in entropy (AS): T. , AS mcpln -fl mcpln l Pl’(uf. ' Bydcl'tniliun, AS‘ S. l
  14. 14. l0lll(l'll‘I‘Il l‘roccu rt ’ ~ — . m Int 'rn. | - - . . . . . . _ l. ll) f. LV rl»l. . . . mi in run; .r. mn. , pu. ._, _ . _.. g A _, ,y. ,, _,m, _. Formulas, l. Boyle's Lu“: V. ‘V. P. Vr : P; ’; or “ . whereT, T; Tr 1: L A or P: — V‘ F: ‘I 2. vv, ,,v lPdV -c Q — c1nv]’ V VI = ct1nv; ~Inv. ):c| n}/ A l but C : P, V. = P; V3 , also PV + mRT therefore, ‘vVr. 'i ; P1V, ln¥i “ P-_oV3 In :17)‘ °r 9' P‘ w, ,. - r>, v] In —L = rev, In —L W P; P; 3. AU ‘ 0 PTOOE ‘V U: ~ U] ‘ mC. (12 * r1). Sl-“Ce Tl : T2 VT 4. O " War 0 Proof: 0 O P Q yP591(+t)kf‘ Mfr ‘WM 0 Wu: 5. AH ‘ 0 proof: 0 AH n, —H. e mc, , (T, /17') All 0 df , V: 6. il Tr)“ S1 — 3] $12 proof; Based on the graph, (3: Sniff) 0 AS (T) - Q then. -lure. ,, .10. AS g 1"R]TmV‘ mRln = mRrxn‘-'1 V: Tl 11 “m "P, 7 . Steady-Flow Isothermal (Open-System) “lg; ;“'wr W 0! Proof: o 0 Aflijfl‘ Q—-M+¢r('+Au -‘AW; +W5; Q'“Wsr but 0 : Wm: therefore, W5; = W, .; ' Q Another proof: AW; ‘: W”; -~ ‘V5; P; ”;“§t’(t"’ wsr—WNr therefore. W51: 1 WNF ‘ Q
  15. 15. lscnlroplc l‘roce~1s ~ o. ‘o11.st.1nI c11lrop_‘ prt-cc ~ . -di:1h:1tic n1c.111s no heat! ll'1lfllt. 'ffL‘Ll. P 1 1 l PV‘ .7 PdV Formulas: l. P1‘/1" = P2V: k 4 Prvlk ' C T: T1 proof: mv. ‘ = Pave‘. 2. = [: ,1f 1"‘ vi 1?‘ P2 _ P1 ’_ [XL ll‘ - Zfi [V2 1* = $3‘ prnv. .11 3"- T2‘ ' V: P1 77 ~1e%j1<%)1*" 1%? -:"l [(%1“f = [(%’,1"'l+ therefore. (I1. T2 Th—l T2 1) To | r—l (Tfl) 1>, v, ) T1 T2 V 1.s.1I‘1.'L‘tiblL' .1di.1l‘.1lIc' plum. ‘ « P 3.1 , (fi)
  16. 16. an t_'¥. "_. $‘Y; 1' v ‘ * 1w. v, - - l K —'—"]"K"” Bit KVL mRT my I l ’—f”[_"“" tlrerefore. . P ’ P V “x1 “‘ fi 1-1“ ! —‘ll*—‘k—l~LL 111c, ('l> lnCC C‘ FR? g where k c, ,‘c_ also, R cl -c, AU me, (T: — T. ) 3150. H —“lNf proof: AU ‘ mcv (T: ’ T1) " "mcv (T1 ‘ T2) ‘K’ " WN1‘ Q*0 proof: Refer to T-S diagram proof; By Law ofConservatio11,of Energy Q*43fF; ‘«§K‘: 'AU‘~)W; ‘ WNF Blll AU T‘ -WM}: Therefore Q: -)3’1er’W<r= Q=0 7. AH: mCp(r; "T| ) 8. AS=0 proof: Based on the gm? S; = S. , = 0 As= ;{— 9. Steady Flow lsentropic (open-system) WF * —AH . (ifAP: AK 0) Proof: gy Lgw of ‘Conservation of Energy. Q—AP1AK+Au«Aw, -We therefore, A“ We; —— All Another proof: /SW1 ” W141’ " Wsc but W:11 ” ~AU therefore, AW. ' AU —W ~,1 W5; ' ' WT-. .. (AU 1 AWr) WM AH
  17. 17. l‘0ltro i‘ - 1 1 V . V _ p t Procut 1‘ .111 llllkllldll) l. Ll‘xllll( 111.11, 11u, m._. “T1m. h_ l’' t‘ #5 l P1V; ‘ : P_-V3‘ " P1V1" 2. %- = lg‘ ]" " ; for derivation refer to lscntropic Process Derivation I 2 . T, A p, “; ' _ . _ . d . . .1. -T— —- [F ] . for derivation refer to lsentroprc process errvation 1 1 4. ’, ,~; 7 Pd‘! = C lvi V‘“ dV ; for complete detail of derivation refer to Isentropic Process Derivation V1 vV__ P3V3—P V1 ,7, mR§T2—T1) . r 1‘n 1v“ 5. : mCy (T2— T1) 6. The heat transferred (Q). Q = AU * W11? : mt? -11 (T2 — T1) whale: C“ fP°"{"lP. i,° specific hem Proof: Q-AP+AK+AU+Wn1= °_»__‘°v(1_, ,) °’A“*"’~* mx(r1—T11 ""°"°' Q= mc, (T, ~T1)* , _n but R‘C(l<—l) therefore _ a _ T )(k _ 1) Q= mc, (r, »r11+m°‘(T, '_, ,' Q= mc1.(T2‘ T1111 1 Q : m(T; " T| )C1, ) Q‘ mcn (T1 V
  18. 18. 3 ~ , r L _ . l 5tt. itl_-Him pl)l_lrup| c ("pm , _,‘, _., “): ’~ 0 . ,H. ii. P . K 0 1 ‘ , ~ . _ ‘ . lrt oi B_ol . i iOt L till-LI'. tliL)ll ul l: IlL‘lj_')_ . nutliL-r prim! 1 W, W, w Q " A“ ~>)', : W. , (mm. 0 AU . win Q "" ' W‘ All “M Q m. ‘.U V. 0’ XII tlit-rel'orc_ AW. 0 . ’U W. _ w(; - 0 AU AW, V, ,. Q — (AU « AW. ) but AH AU i AW. therefore. War ‘ Q — -'3“ Second Law of Thermodynamics: ln .1 heat engine running between two temperatures, higher temperature (Tu) and lower temperature (T, _), it is impossible for the input energy at higher temperature to be completely convened to work without rejecting some heat at (TL), Heat Engine: W network = W, _., . — W, Qu Input Reservoir Tii By First Law of Thermodynamics. ZQ = ZW or ZQ : ZW W W Q}; - QL ; W Qin '" Qout : out “ in W"‘Qii"Qi. Qii ‘QL: wnct Efficiency, 11 = 9fi§§tt— x I00"/ o — Q Etficiency. n 1 x 100% e 9-H—9L x 100% (1 —Q—‘ )x 100% H H “ For Carnot Cycle, g - constant " k 0_L . Qn . _ 9; e L T1, TH k or Qii TH Hence. Wlnll Camot Efiiciency. n, ,,. , Q" T . ,, X | o()q, ;, -‘(t -5g—: )x I00‘? /u -(l —1-. ::)>« I004. absolute temperature scale (“R or K) N t : I. T must ulways expressed in _ . _‘ , 0 e absorbed or rejected in fonnulus in thi. ~. topic. 2. Q must always positive either
  19. 19. Ht"I’tl‘um liifryyjy 7 -V ’ ' *— — ' P ix . i l'L‘lTl"L'| '.. lll0fl '£lL‘m tl ’ ‘. ~ l"lC-ll1l‘lL‘tli; lu}~ L 1‘, - , it i l u . . In mitt-: i and will it in Mmmc, Winter Time: input Renervoir RL‘. t. ‘|'V0lf C.0.P. -— %“— By first Law ofTl1ennodynamics SQ = EW QL “ QH ’ W W -' QH - QL therefore, cop = —91!— H — L For Ideal Heat Pump (Camot Cycle) kT.4 - kT, therefore, T C o P - Therefore for Camot cycle, 9:; _ __9H_ : .Iii. ._ C'O'P' y W Qii ‘Oi. Tn ‘Tl Typical C.0.P. range from 2 10 3
  20. 20. Summer Time: lnpiit RL''L'l'u| r COP. =9; 3)’ first Law ofThermodynamies ZQ = sw QL ~ Q“ = —W W : QH — QL therefore. TH ” TL also for Carnot refrigerator/ Ideal Refiigerator Qt. T C. O.P. =9 e———— = —J~—— W OH “ Qt. Tu " TL Note: if the problem in (Ref. And Air condition) asked for Energy effy. Ratio (BER). EER Heat extracted er hour BTU/ hr 342 C'O_P_ Power Consumption (watts) EER is expressed in unit of BTU/ watt—hour
  21. 21. I'm wnv number ex - ‘ - . . pressed in base-r s “stem wh ' - . . ) crcm the coefficients are multiplied by powers of IO: "vi -‘ n I-‘ n‘: ‘-‘ «-1- -323130-k| .|a.2iI.3-. .. ,3.m . -v , .1 _ ~‘n' ‘-MIT" ‘M: r"3*'~1.. .r"'-‘+ . ... .. +a. r‘+air'+aof° ‘ * Mr” ‘ -xzr" + . . . . . . ~ a. ... r"" I7.. tmpIL‘; '4 (for base or radix equal to 10) 3-v‘ mu «‘ “ um ~~3:3|? ‘o~ 11.3.21, . ... .. a.. ., (each digit range from 0 to 9) T '-1.. l0"+an. . I0""+an. :I0""+a. .;Io'*’+ . ... . . ..+a:1o= +.a. to' ~a. .Io" + 3.. I0" + : L; I0'2+£L3 to" + . ... ... .. + mm 10"“ 3 -. (for base or radix equal to 2) -. :,. a , ... a "42 a , ,.; . . . . ,. .n2a. ao. a . . a .2 a . , . ... .. a., . (each digit is either 0 or I) ’ ; i,, '_"‘ ~ .1 , ,., 2 "" + a ".3 2 “'3 + . ... .. + a;2z + a.2' + ao2° + a, .2" + 112" + a_,2" + , ,,, _, + a_, ,, 2"“ Table for Number of Various Bases D». -cnn. il Binary Octal Hexadecimal ttuxc I0) (base 2) (base 8) (base I6) (‘U 0000 00 00 0| OOOI 0| I 02 00 I 0 01 Z --I on I 1 03 3 ll-1 0100 04 4 H5 0101 05 5 rm 0 I I 0 06 6 (I7 01 I I 07 7 0.! 1000 I0 8 0‘? IOOI ll 9 I0 I 0 I 0 I2 A II I 0 I I I3 3 I2 I I00 I4 C I} I I 0 I I5 D II I I I0 I6 E I. ‘ I I I I I7 F Complements Two Types of Complement a. diminished radix complement or (r --I )'s complement b. radix complement or r‘s complement For diminished radix complement: (liven: _ _ N number. r base. I1 Z 110- 0‘-dig"
  22. 22. (r lI'. s complement ol‘N tr” 1) N For radix complement: Given: N number. r base. n ~ no. olidiuit r ‘s complement ol‘N r" ~ N , it‘N , « 0 rs complement ol'N 0.ifN 0 Laws for Boolean Algebra x+0'~ ‘<-l= x -~x'“l »x'= O x~x? -x= +1‘l -O=0 lnvolution (x')' = x Commutative x e y = y ‘e x ; xy = yx Associative x + (x + z) = (x + y) + z ‘. x (yz) ’ (XYIZ Distributive x(_v ~ 2) = xy + x2 ; x + y2 = (x ‘- y)(x + 2) De Morgan (x + y)’ = x’- y‘ ; (xy)' = X’ + y’ Absorption x ‘~ xy = x ; x(x + y) = x Operator Precedence For Boolean Expressions, the operator precedence IS, I . parentheses 2. NOT (') 3. AND (-) 4. OR (+) Operation Symbols AND F‘ *‘>’ OR F " X “' Y Algebraic function Truth Table xy F 00 0 01 0 l0 0 l l 1 xy F 00 0 01 I I0 I I l I
  23. 23. Inverter -Do— F _, X, x r I 0 A F lItiiTtr >— F , X X F 0 0 I I I F NAND $j}_ F '“ (X')')' xy F 00 I 0| I I0 I I I 0 )4 __ F NOR 3.” V‘ F = (x + y)’ xy _ F 00 I 0| 0 I0 0 I I 0 lixclttsive OR “ '‘‘)j )7: F = xy’ + at’): xy F l’0R) 9 = x o y oo 0 0| I I0 I I I 0 Ikclttsivc ~ NOR tXjDGE_ F = xy 4 x’: /' xy F ()r equivalence J‘ = x O y 00 I OI 0 I0 0 I I I Map lIcIhotI - also known as the “Veitch diagram“ or the “Karnaugh map“. procedure for minimizing Boolean functions. y It provides a simple straight forward Two Variable map 1h _ bl ‘ rec-varia e map
  24. 24. THANK YOU GOD BLESS YOU
  • NiaLeizylMendez

    Oct. 1, 2020
  • PatrickAngel2

    Sep. 1, 2019
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    Aug. 6, 2019
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    Jan. 14, 2019

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