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Aq!! 'rW}!! q!! !7qS!! !!! q1!! !A ! !A1A!1!!q!!q1QA1!!!A!!!ARWa!1!1q!aSqS!!!0000aR11!!0000a!!PPPPR11A!!0000q!!0000vA1!!!A!!A!W!"!aq!Q!QqSqq!Ab!Q!! 1qRA1q A !A  ! A1QAV+L TR1!! TR"! dA"1AAQq11B!SbA"a2")dAqARRAR!QS*B!RDRRAQ!1S!aBR1ᑂbHe!bR"lPYZdefine erfc(xx)=Func:Local tt,z,a:when(xx<0,abs(xx),xx,0)z:1./(1.+.5*z)tt:tt*^(z*z-1.26551223+tt*(1.00002368+tt*(.37409196+tt*(.09678418+tt*(.18628806+tt*(.27886807+tt*(1.13520398+tt*(1.48851587+tt*(.82215223+tt*.17087277)))))))))a:when(xx<0,2-a,a,0):endfuncNu0| PHx8HyHy h NO NuN?<NTJ9fNNuMEPro 1.01 09.22.00 2000 da Vinci Technology Group, Inc. Each time F5:Info is pressed, a a different dialog box is displayed. The manual is available on-line at http://www.dvtg.com/ticalcs/docs Thank you for purchasing MEPro!MEPro Frequently Asked QuestionsIs the manual available on paper? Printed copies are available for purchase from da Vinci Technologies Group. E-mail sales@dvtg.com or call 541-754-2860 in the U.S.MEPro Frequently Asked QuestionsHow do I contact the developers? MEPro is a product of da Vinci Technologies Group, Inc. in Corvallis, Oregon USA Suggestions and comments are welcome. Contact da Vinci via e-mail at: improvements@dvtg.comMEPro InformationYou can paste values with units into variables if they have compatible units associated with them. B@9J@g @g @g" @g&HzHz`HzHz`Hz}HzW`HzVHz?NPR9Nu/ 4|$R?<HzN?<Hx"jNO NN$_NuMEPro 1.01 09.22.00MEPro 1.01 09.22.00 - Navigation GuideTool Bar (top line) and Status area (bottom)provide context-dependent usage hints.ENTER often does the same thing as F6.ESC 'backs up' to the previous screen.F1:Tools/8:Clear goes back to the beginning.ANALYSIS functions solve specific problems.EQUATIONS are grouped into sets applicableto specific situations.REFERENCE has handy lookup tables.H O4|$RARCp`QJ9f`3. j0Np&>?Hy"jlN>Hy"jLNC.Hy"jNO"jdN"j if>HzN>HzN>HzN>Hz)N>HzDN>Hz_N>HzN>HzN>HzN>Hy"jLN.Hy"jN>Hy"jLNO0OLNuH 4|$RJ9gNN,pNp33p??Hy"jlNPJ9fNDv?NTRC CmLNu yoSyNN`NPNuNVH4|$RABC>N.Hn j NX>N&Hpf `B@+>/ NX(H>NJgLp ./ HnNP/Hy j N.N.Hy j NO J@gp`p`Rp ./ NX/Hy j N|.Hn j NA.N>?N#LN^NuH Y6/4|$R. jN."jN>"jXN."j N3>"jXN8 SDD33J/g"p333`D09yd 3`09H49@309B3>"j\N3."jNN# yf yg yfNXLNu/ Y4|$R. jN. j4N."jTN."jNNp#X$_NuMEPro AdvisoryError while closing windows...H8O$o`6|&S(S(T` f`F(l"fA. kPN6f. k,N"kTN`.HzN>?"kDN\OLLNuMEPro re-entered.prodata1H8Ol$o6|&Sv6 f`J9f  g g` f`  n~ mt @nFg0 @ng @gzoV @fN`N @ng @f8` @f,` @n"g@ @ ng @ f`, @f` @`ng @@f`f @gf`pAC2222222#3`J9fJ9fr`J9gdA0000000`vJ9g:``p. kNJ9f`0J9gA0000000`J9gA0000000`J9gA0000000`"kdN"k i$gJ9g`J9gJ9g2N@`^AC2222222J9g`4(k$(TCL."kPN8fTJ9g 9t 娀.?NT`&A0000000#p   ngz gfoN  fF`Z n gP f2`R `g`&$yf`,f0.N`"J9g.N` .NJ9fJ9gVJ9g"N"kdN"k ig ."k NNN"kT`l"k$"0 @g* @g`DNNvJ9fFN`6"kJg"kN>?"kDNTN>`N8>"kLN"k$"J9g ."k\NJ9g.?9"k8NTJ9g.p.?9"k8NTJ9g.?9"k8NTJ9g.?9"k8NTJ9g09g ."k4NJ9g8N"kdN"k ig."kTN."k N09g ."k4NpJ9gx."kTN."kTN"kdN"k if>?9"kPNT`2"k3|"k0) yf k"k3h >"klNJ9g0J9g(."kN.N.NJ9g>C."kPNJ@f.N"kTN."k\NOLNuDECH0Y$o6|&S6p0 nv ml @n.g @n gV @fR`B @goD @f<` @@n g< @f(`F @`go @g`N` ."kN`.Hy"kNX`6* p0 n> m4 @nVg @ n$g @ng @ f` @ f`t @ng @f`z @gto @f`f @n g @Qn g| @f`J @Tf`h @Tn g` @Qf`V @AQgPo @ATgF`"kJQg`$>N`"kJQg` >0@ ?NT.?<NT>N>N`N`40.Hy"kNX`.Hy"kNXJ@f`N`."kN`rp`bNNt`P"kdN"k i$gJ9g`.Hy"kNXJ@fXL Nu NVH<4|$RvGIK-|`tBD 4@fd@8ykTHp09lF Uf@ yf6>/. jLN.y??</."jNO RRC09BB9B@oxL<N^NuDECNV@Hx8.6|&SA|Ccp`QACEp` Q. kN6ABE(k$(T> k N>"kXN."k N<o*H.?NT$k$$R`S  gJf"k$"|JFn*"k$">NN.?<NT`J>"k N>-"k N>?NTJfN^."kN`"k$"Nx yf yg yfJgpd.?NT/Hnc"k NCc.N.Hnc"k NO J9f4>"k N.N>-"k N"k$.HncNX`Cc.N>?NT"k$"3Np0 n m @n6gl @ngd @ g^o @ f`P @n gH @fp`@ @fh`8 @Qng@ @Qn g0 @fP` @TfH` @AQn g0 @Tf8` @ATg*`.N`&N`N`N`N`NLxN^NuJ9g. yg yfAf NNNudvMEProTIHOMETIGRAPHdvMEProMechanical EngineeringMEPro 1.01 09.22.00%cInconsistent unitsGood Job! :)DECMEpro entered w/ event =error in MEpro at BrwDisp call; errCode =NVHx$n6|&S6p0 n m @ nRg @n&g @ng @f n` @f b`V @ng @f L` 6 @ f @` Z @$n$g @ng @f `: @#f ` ( @`ng @%f `  @g To @g ` . kPN3. kPN3. kPN3vIE0|pRCHm33&EI0|pRCHm&E0|pRCHmNp3########33N."kdNN` =|=|=|R=|\>HnHy"kN>Hy"kLN>Hy"kN."kTN=|=|=|=| >p???HnHyHy"kNO"."kPN3"kdN"k i$gJ9g`333P RC G&&&@0.n30.n3"k ig ]y[y2909N32909N309@ 209N3049@QBJB 33."k if0<`p@`?HnHy"kN>Hy"k8NO"k igT."k4N."k0N>Hy"kLN.Hy"kN>Hy"kLNO ` 8."k0N` ("k if yfNC."kNA#.NJfNpp3#N."kN`p`z6* 8D DQg. DTg( DXg" DRg DYg DSg D\g DVgp`pJ9g8Jf4 CA g.J9g"Np#`6<J9gACB@J1f"k1gt CdnpP."k@N8f>?<"kDN` Cf.?"kXNT/"kLNX`> Hz)?"kXNT/"kLNP>?N@T`NJg J9g@p0 n* m @Tngx @nHg0 @ngT @ go @f`z @ ng @ f` @f` @ng @go @f` @Qng @f` @Rf` @AnFg @Rng @Xg*ob @QfZ` @Xngh @TfD` @@*f8`N @ATn&g @AQng @Af` @ARf`N @Png @AXf` @`g` yf yf|C.?9NT$k$$RC.N"k$.NJf.`.p/NX"k$"`xN`nN`dN`ZN`PN`FJ9g N`4J9g*ACB@ 1fp>N`N`N`N`N`N`N`NN`NN`NN`zNN`dNN`NNtN`8J9g.ACB@J@g @g, @g:`N&p>?<NT"HN`p>N`p>N`p#J9gJg yN`J9g8 yf yg yf yfNN`JJ9g yf>N`*J9g" yfCf N`NJyo>N`"kJQg`C>N`"kdN"k i$gJ9g`J9fzJyfN*`p#>N`NJ9g09g&J9fBC9BD9BE9BF9."k N`JyfN\`NJ9f ."k N>N"kdNJ9gj"k ig\CAC.Hy"kNX`2."k4N."k4Np`N09g."k0N`NJgCBD>"kXN."k N6o(k$(T>"k NH.?*NT"k$ QJg >"k N>-"k N.?<N>?NX>N"k$"` Cg.?NTC."kPN6f>N"kT`6 CfNv>NRC Cl`.?NT>"kLNLxN^Nu/ O4|$R.Hy j\N?|` C .Hy"jNP."jNO$_Nu/ Y4|$R>?< jHN>?<""jHN>?<s"jHN\ yg yf#`p>??<"jLNp>??<"jLNp>??<"jLNp>??<"jLNp>??<"jLNp>??<"jLNp>??<"jLNp>??"jLNO X$_NuProData1MEPro 1.01 09.22.00DV01DV02MEPro AdvisoryUnable to save MEPro data. There may not be enough RAM free to create the prodata1 variable. Prodata1 "saves MEPro's place", and requires about 1000 bytes.MEPro AdvisoryUnable to save MEPro data. The prodata1 variable, which "saves MEPro's place", might be locked, open, or archived.NVH<6|&S-|J9f`\J9gN=||Yp.HziC/ "k NP-|-|=y=y=yvEI0|RCHm=yvEI-|KC-I2<2|BDt lBBJBIl nBBJBAlB@@ n0RRRRTRC Cm=y.=y0C2Ap`222222222222Q-yT=yX-yZ=y^-y`=yd-yf-yj-yn-yr-yv-yz-y~vIE0|RCHmy'=y(-y*y.y/-y0vIE40| RCHmy@yAvIEB0|4RCHm=yNvIEP0|RCHm=y=yyvIE0|lRCHm|.Hn"k NX|6"kLNJDg, Cf .Hzx` .HzNX."kTNL<N^Nu\PROdata1DV02DV02DV01MEPro 1.01 09.22.00MEPro AdvisoryThe variable prodata1 is inconsistent with this version of MEPro or with its present position in memory. prodata1 will be overwritten unless you QUIT MEPro now.NVH<4|$R|p./.Hn j NA. j ND.HzHn j NOA.NJfp`Z.?<Hn jPN\J@gp`:.?<HyHn jxNO vGJ@f69> jXNT(H,G fR./ j NXJ@f> Tf8 ,Yf0. LV/ j NXJ@fCf Ag.Hz#Np`3"3$3&vK(G0|RCHm3HvGJK-|-|-|2|rt 80h0H nIl0H n Cl  nTRRRRRC Cm33CAp`000000000000Q#3#3#3#######vKG0|RCHm3##vKG0| RCHmvKG0|6RCHm3vKG0|RCHm3t3vxvIyG0|lRCHmpp3#Np#."jTNpL<N^NuO2|"Q ofpONu>?9 i NO#pNuFolder:OPENNVH 4|$R>Hn j ?9Hz?<?<?<?<? jNOJ@g>?<Hzr?<p???? jNOJ@g.p/p??? jNO @ f>?9 j NT#. j NJc^09ngR&j$&S> j N.NC."jPN8f"j$."j N"jT` "j$">"jLN"j$">"j\N>"j\NL N^NuMEPro NEWFolder:NVH8$n6|&S:<.?<?<Hz?<p(???<? kNO8g.> ?<?<Hz?<?<?<?<? kNO8|JDgp.Hnp??? kNO :> k\N E f<(k$(TC."k(N"k$."k N"k$"p.Hn/ "k NP` EfL8N^NuProject H04|$RvG("KHz/ j NP1@D RC C mL NuN϶NNuAg&?9NT#NNNuAg&?9NT#NNNu+-*/()^=<>., oNu2/ol2/oo2/0NuH<$o6/6|&S f`PJCjBC*?/ N\*H f`0/ NX(H*m g/ k NXJg / / NP JL<NuO>N>/NzONuH Qv`".?NT.N.NRC09BB9B@op#p>NPLNuH84|$Rv&j$&S o/ j(N?< j$/ j NO (H fv0, gv j$ LNuAn error has occurred deleting this variable. (The name of the variable is in the title of this dialog box.) Use VAR-LINK to examine the current status of the variable and unlock it if necessary.H<$o6|&S(k$(T/ k(N?< k$/ k NO *H f k$ `40- @gHz/ NP"k$"`"k$/"kxNX"k$"L<NupNu#NuNVH 6.4|$RA.?NT&j$&SA.NJfx` j$. j8N j"j$$ $QB@$B 0e"j j$$ $PB@$B 1c,"j$ $Q $@f"j$"Q !+g"j$"Q !,gx`b"j$.N-n-n=nNmN?iox`&/./.?."jNO NZNd"j$" Dl4 yfx`&"y0HA (. yf yo>x`:> ? 9/N\"HA B@.@o(.0L N^NuNV> ?. 9/N hN^NuH0$o 2|"Q fA`F&j$Rpf_p // `p // Hy i NO AL NuNV"n g . )e`"Q f`?< B@. ?/ NN^Nu2/kymNu?< ? 9/NP PNuNVH 4|$RJnj`D?< ?. 9/N&Ppd// Hy j NHyNAL N^NuB@/??<NXNuB@/??<NXNuB@/??<NXNuB@/??<NXNuB@/??<NXNuB@/??<NXNuB@/??<NXNu0/ HЯ @NuH8$ovG(K`$JCf0@`0@04?NT0RCyl 0R@ @ m?/NT00 JLNu2/ A l0`7NuMEPro Error/ Q$o0| Pp./ Hy h N.HzNO$_Nu/ $o 0| P#p// Hy h NO #p#$_NuH8$o6|&S(JS/ k N/ / k NO LNuNVH 6.8. 4|$RA.?NT yf Cgp`:p`6> ? 9/N\\C""""""""Högp`pJg A.N`$&j$&S>"jN"j$.HnN"j$"L N^NuInt. err.: SafePushParseTextH8Y$o6|&S. k N6gj"J kȳe k$c . k(NX`X kȵeB"J k$b6(k$(T.N>"k N$k$$R"LR."k(N./ "k NP`./ N(PLNuNV-C?<?<?.N6H@?/NZ#fp` yB@(3A`NHyoA`/9NrX&H g"S`(IJg` g\p ./ NX/Hy"j NP#"yHB@)@gp`pH>?9NTJgJ9f~>N p ./Hn"j NC.N.Hn"j NO J9f.HnNX`C.N>?9N TN$ LLN^NuAn error has occurred Storing into this variable. (The name of the variable is in the title of this dialog box.) Use VAR-LINK to examine the current status of the variable and unlock it if necessary.H l$/ l NX/Hg0( @g./ NO`.?<?<@"l$/"lNO"l$"L<NuAngleRADIANComplex FormatRECTANGULARAngleComplex FormatH"j N"j$."j8N.HzxN.HzrNO"j$"L<NuNVH 4|$R&j$&S/. 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Nެ?<-"j N"j$//.Nh"j$"L N^NuNVtH<<.&n 0|-P> ? 9/N2\$H&* Jjg jgp`pzppƀ. n h(N-HJg> gp`DS g`R n (gbfp`p`>G -@ -@0@=@ -@C=C`*n*m$*Uv(JGg0Jg* -f. n h(NT.NJfp`p`RJg@ -fD. n h(NT$H.NߘJg(.N."n"i$.N` -f Jngx`.NJ@g(>/ NX6fJGg Jgp`p`(KJCg >NJfp`pf (n(l$(TJfCx."n"iPNJ@f$n$j$$R.N"n"i$g "n"i$"Q`"L$I."n"i HNJ@g,>N2(H f`"l(I fp`./ NX` Jnfp`p"n"iTN"n"i$"JfJgp`p."n"i(N&HJfb+ k N`8Sx` ."k(N$H0RDCl g g >+"k N`."k4NXL NuH?NϊT"oL0"kTN`2$k$$RT."k N"k$S.N./ NX"k$"`."k(N*H."k(N(H$kB@ g g gJgp` Jgp`pOdL<8NuwhenMEPro AdvisoryNo equations have been selected. Please select either a single equation to solve by itself, or several equations to solve simultaneously.MEprob MEanstypNo equations were selected.Input values: , =MEinputNo input values providedMEprob MEanstypNo input values providedMEPro AdvisoryNo input values provided. Please enter known values, or use F5:Opts/ 6:Know to designate existing values as knowns. Knowns are displayed with "" in column 1.All variables knownMEprob MEanstypAll variables known{, }Syntax error in unknowns listMEanstypMEPro ErrorSorry, internal error! Syntax error in unknowns list.MEPro AdvisoryUnable to delete one of the unknowns. It may be locked or archived. Constraint validation may be inaccurate as a result.csolve( solve(when and Syntax error in equationMEanstypSorry, internal error! Syntax error in equation.trueMEPro AdvisoryOne or more equations immediately simplifies to FALSE. In overdetermined eqn sets, roundoff error may cause the solver to conclude that the inputs are inconsistent and no solution is possible. You may want to select only eqns containing unknowns., MEPro AdvisoryIt may take a long time to find a complete solution, if one can be found at all. You may abort the calculation at any time by pressing the ON key.MEPro AdvisoryThe nsolve command will be used. The existing value for the unknown, if any, will be used as an initial guess.MEPro AdvisoryThe number of unknowns is greater than the number of equations. It may take a long time to find a partial solution. You may abort the calculation at any time by pressing the ON key.{, ==}) | and =exact()MEprobNo apparent soln for this dataMEanstypSyntax checking Solve command nowSyntax error in solve commandMEanstypSorry, internal error! Syntax error in solve command.Initial guess: =Initial guess: =noneMEguessExact/ApproxAutoAngleRadianParsing now...Solving using nSolve now...Solving now...AngleError during SOLVEToo many unknowns to finish solvingTest did not resolve to TRUE or FALSEMEPro equation set solver errorOverflowMEanstypAngleMEansMEansno solution foundMEansmatMEPro Equation SetNo apparent soln for this dataNo useable solution found.No solution found.MEPro AdvisorynSolve was unable to find a solution. It may be possible to find a solution starting from a different initial guess. To specify an initial guess, enter a value for the unknown and then use F5:Opts/7:Want to designate it as the variable to solve for.One complete useable solution found.One partial useable solution found.Multiple complete useable solns found.Multiple partial useable solns found.MEanstypNV H<:|*UvE.0|p$RCHm m$-P|=@**(&G`N fD>/9Nl$H./ m NPfRn*0H\H-RD`RE|RRCym0n*yf| 9=@kp`p@ gDn0.yoF=yJEf:.HzwN.HzN`.HzNRO N`:JngJ.f=yJEf|z>"m N"m$ R-@ .Nv-|-|` nBD"nB@1@=@ ng @`H"y.HHn"m N|#(m$(TC."m(N>"m$/"mNP-@g>."mN-HJh g,> "m N$m$$RT."m N./ Hn#N P"m$"C#."m NJf"n n`6Jf .NzC.N.NC#.NRRC09BB9B@o"n .N>-"m N"m$.HzNJX"m$"JgB.Nr.HzN~.Hz}Np"m$".HzN`J=|xEG:9B@9@`BCJ30fRnRRDEoJnf2.N.HzN.HzN"m$"` "m$ R-@$.Nǜx*IG`VBCJ30fHJf .Nz> ? 9/N6\$HA $n.NRRD09BB9B@o.N$m$$R"n$.NdJf8"m$"NE:.N.HzJN .HzEN` .$"m(N./.$"m NX"m$-Q>"m N=n(z69B@9@I-|`BD"nJ1@fSn($nS<.(` ."m(N$H0SFJ@n&m$&SCR."mPN=@Pf>/ NX<g*>NJg"m$.?NzTJg >NJf"m$">*"m NJFg.NJ@gJfp`p>NJf<|p .?NNT/Hn"m N.Hn"m NO C.N"mT`z"m$">*"m NSSC Cl>"m N"m$-QJ.gJg.HzNX>"m N"m$ R-@|J. g.`.NxD .D&I`J.f f>/9NN-H./"m NPgJ.f .N|.NJf6"m$"NE.N.HzN.H/N` l"m$-Q|"n."m(N"m$-Q . 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"m8N"m$ Q ,f"m$".` "m$".NJ.f$"m$ Q +f|.HzNX"mTN`"m$".NRCRRDnm&.NJ. g6 Cf nfJ. g .Hz`,~ nn.Hz`nl Co.HzNXJf .N|$nS&I-|`BD"nJ1@fJg|`."m(N$H.N> ? 9/N\&HA &n.NJgd *g$.N.NJf`./ NǰX`TJgN."m NJc@.N.NJf&./ NvX`RRC09BB9B@oJf .N.NJfv,EG`BEB@3P=@ nfjJg.N|` .NH"y.XHn"m NXC.N.NC.N.NRRC09BB9B@oh>-"m N"n.HzjNXJ.g&"m$"EY.N.HzlNXN̦`"n.Nb.N"n.N®Jf6"m$"NET.N.HzdNT.H/N`8"m$-QxGI`BCJ40f> ? 9/N\$HA >Nj$HJg\."m(N(m$(T>/ NX8g>NJg"m$.?NTJgn>NJgb&m$&S>"m N.NN.N.N."m N./ "m N"m$."m(N"HR.S/"m NP`"m$-QC."mPN=@f.N"mTN`"m$">"m N.NJg(."m NJc.N.N.`.N>-"m N"m$.HzNDX"LT.Nb"m$"`J"m$-QCp."mPN=@nf.N"mTN`"m$"RRD09BB9B@o"m$">"m N.N>-"m N"m$-Q>"m N.N>-"m N"m$./."m N"m$-Q.Hz`NP-HC&."mPN6fF.N"n."m(NJg.`.N"m$."m8N"mTN`"mJg"mN./."m N.Hz!NP"m$"E0 @g& @2g @gN @>g(`:E.H/NNX`?"mDNT`.H/NX>"mLN.Nݞ.HzNݮXN.N`$m$$R./."m N.HzNP"m$""m$ Q -f""m$."m(NT$H"m$.HzNX`.$m$$RT"m$."m N"m$.HzNX"m$ U".Nx"m$ Q +fz`Jg.Hz[NXJgz`JgN$m$$R>"m N>"m N."m4N>"m N>"m N./ "m(NX/"m NX`>/."m$/"mNP"m$.HzNXzN0R@>/."m$/N߬P8 DoREJDoR Dn0 @f"v>/."m$/NP8RCJDn^EnZ`0 @oPC%.Hzz? N\<6RCSC>/."m$/N6P8oSFJFo Cn>/."m$/NP EfE>`\0 f.JEoEO`NEd.NJg>.HzaNX`*0 @f DoEO`En` DoE`E.N.HzN$X"m$"N.NL"jLN"jJg"jNER./ N.HzNPN#>N>N>NOLL NuEqEquation to plotIndepIndependent variableX-UnitsHorizontal unitsX-MinMinimum horizontal valueX-MaxMaximum horizontal valueDepndDependent variableY-UnitsVertical unitsY-MinMinimum vertical valueY-MaxMaximum vertical valueAutoscaleAutoscale Vertical Range?Label GraphLabel Graph?Full Screen GraphGraph on full or split screen?xunitsyunitsxminxmax10.xmin10.xmaxyminymax10.ymin10.ymaxH@?NN>0S@?/?<?NLO :>N(H.N*j$*U>"j N fG`./ NX&H.N>-"j N Df "j$.Hz` Df"j$.HzN(X"j$"*j$*U> ? 9/N\(H Df3>HzNXJg<"j$.?NԀTJg*>Hz~NXJg"j$.?NZTJgp`pf,"j$."j$/"j(NX/"jhNX"j$."jNJg$&l g ."j NJbG.HzNX&l g ."j NJbG.Hz` Df3>HzNXJg<"j$.?NӤTJg*>HzNXJg"j$.?N~TJgp`pf,"j$."j$/"j(NX/"jhNX"j$."jNJgH&l g ."j NJbGT.HzSNX&l g ."j NJbG:.Hz8NX"j$"#3OLN~:v(`>NJfRDRCElymSC>NP8>NF:yg3vEp`RCym>/9Nf$HA.Hn?9/9/ NlOv(GI`@ f6> ? 9/Nd\0H)RDnf3nf3RRCym>?9N>?9NX`.yg>?NTyg>?NL8N^NuNVH<vEv(Gr p J"K""""""""@RCAmv(E`:>NJf,>/9NX0H%RDyf >?NTRCym"y#3vEp`RCym>/9NC.Hn?9/9/NǸOv(GI`@ f6> ? 9/N\0H)RDnf3nf3RRCym>?9NR>?9N>X> NxvGIK`*> ?/ N*\$H0* f * RDRRRCymL<N^Nu ACp`222222222222Q#3 ygNu 9f*09yf09yf 9g(#33#NuHNJf Df8RRCym DgA g3vErp`yf`RRCymACp`222222222222Q3> N#ZxvGI:K`80> ? /N\$HA :/0RDRCyl Cm3NJg"zN"y#3pO0L<8NuNVH $n6|&S.N6. k N @ m`lp ./ Hn k NA.N.Hn"k N$k$$RC."k(N>"k$/NO"k$"J@f`>NJgp`pL N^NuH84|$R(j$(T/ j(N&H?< j N?<"j N?<"j N/ / "j N?<"j NOLNuNVH<$n6|&S.NJg`.N6kĶym`>Nd(H f`g f k$-P. k(N-HB@,>/ N*H.N.N../ N.N./."k NO >"k N>'"k N>"k N.N.N>`f"k$-Q."k(N-HB@,>/ N*H.N.N.N.NNt./ N.Nx./."k NO >"k NND>("k N>"k N>"k NN"`f./ N*k$*U.NB@,>/ N~.N.N>"k N$k$$R"k$."k8N./ "k NO >"k NL<N^NuNVH<$n6|&S.NJg`.N6kym`>Nh(H f`ʹg f k$-P. k(N-H./ N.N@B@,>/ N.N.N$./."k N>"k N>'"k N>"k N./ NO.NN`$f"k$-Q."k(N*H./ N.NN"k$-Q"k$."k8N./."k N./ "k NB@,>/ N.N.N`>"k NN>>("k N>"k N./ NO.N*>"k NN`jB@,>/ Nz"k$-Q.N.N./ N.N>"k N$k$$R"k$."k8N./."k NO >"k NL<N^Nu/6930yp09n<0y?NTRy0yp09n0y?NT3&NuAn error occurred while attempting to delete scale variable which does not contain an appropriate unit expression. Default units will be used.MEPro AdvisoryNVH$n6|&S(k$(Tp ./ Hn k NA.N .Hn"k NO .N6>NJflC."kPNJ@fC.N"kTN`@"k$".NC.N.N"LR.Hz@NX"k$">?NLN^NuUndefined variablexxDECSolving for dependent variable now...MEprobMEansMEansmatUnable to define Pro(x)MEPro GrapherproPro(xmin) Pro(xmin)=>undefclrdraw:clrgraphyminprotemp1:ymaxprotemp2:min(Pro(xmin),Pro(xmax))ymin:max(Pro(xmin),Pro(xmax))ymax:when(ymin=ymax,when(ymax>0, 2*ymax, when(ymax<0, 0, 1)),ymax)ymax:DelVar protemp1, protemp2protemp1ymin:protemp2ymax:DelVar protemp1, protemp2eetemp(pro(eetemp),eetemp)Graphing now...xresTmpxres:10xresgraph pro(x)Tmpxresxres:DelVar TmpxresZoomFitgraph pro(x)Undefined variablePxlText "",26,4:PxlText "",44,4Graph completed.Unable to resolve arbitrary # in solnUndefined variableNVHNJf.p/NX>N`RRCym"y#3-n -L./. NXJg A-H `./ NXJgI.?<NT.NCv."kPN6fJ>"k N>"k N.N.N. 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(b(S`.N&(H g L`. k(N$H f`XLNu %)+/5;H0O$o46|&SAC"""""""""0@> k N>"k N>"k NRR R$m4O(L Nu_rad_deg_grad_rad_deg_gradNVH<8|(T=| l$-P. l4N&l$&S.N"*H-|-|`~."l N|p ."KT/ Hn"l NP"l$"C.N6p-@JCkL>Nz$H f> ? 9/NT\-h`$BD*>/ N>/ NP.N-H."l(N$Hc./."l NXJCkbJg\."l N cJ n _f@./"l NXJ@g,./."l NXJ@g./."l NXJ@fC.N`2"l$-Q>/.NXJg$l$$RT"l$."l N"l$"QT-I"l$."l4N n./ "l NX-H&.ؖ`./."l NXJ@g,./."l NXJ@g./."l NXJ@f&$n14<r `"l0 B1@f n.Hx"l NX-HJf|$l$$R"n."l(N./."l NX` "n."l(NC.N>"l Nd ./ "l NX./."l NX&l$&S.N*H fL<N^Nunot an equationPSrightPSleftH"kLNv"k$"Jfp`pOLL<NuwhenNVH<6|&S|>Hn?9N\J.f`Jx.>:Hn"k NX(H g&R  gC."k N8np`p`6IvE*2|r R.0Xf AI` RRCIm`R  g."k NJf`N.N>/9"kLNX yB@(BB(BS@:B@((BS@6Jg8HŋElD0jR@@4`tC.QC??/9"kNP"yB@)4 B"y)B y( @ yhJg "y)  yBB(B@(@SB3BB((@SB3*k$*U."k N6 "fx`x|$L`E>"k N0g @gD @gL @gn` Ae Zb>"k N` 0fx` _fx` hfx` 0e 9c Ae Fcv aen fcj`f 0e 9c\ Ae ZcP ae zcD e c8 g2 e c& e c e c g _gxRRFCm>"k N$MR./ "k NXgj.NJg`(k$(T.N$./ "k NX`2 f&"J! ae zb "JR./ "k NXSf"k$.N$H g`>"k N.N>-"k N>"k$/"k(N$HC.HnHn/ "k4NOp0. @09Hn"y49nJB@)@8`*"yBD)RD.Hy"k NX4.nBHBBBHB09Hn269jRCC4.0PB@ HBBBHBHn`6.PC`49jRBB0.P@B H@B@H@H°n6.PC.Hy"k NX`l49jRBBp0.H°n"49@SB6.Hy"k NX`269jRCC.Hy"k N.Hy"k NP33333#>?/9/ "k0NO p#NLL Nu approx(%s)TempChk:getType(TempChk)entry exceeds buffer length"{}[]Syntax errorMEPro Advisory: Circular definitionA variable cannot be assigned its own name as a value. To get a solution expressed symbolically in terms of this variable, where possible, simply leave the value of the variable blank. (See F5:Opts/2:Type)MEPro AdvisoryInvalid variable reference. Non-algebraic variable.MEPro AdvisoryInvalid variable reference. Conflict with system variable or reserved name.MEPro AdvisoryPlease use the Toolbar to select units instead of keying in the units on the author line. Units chosen will be used for displaying the value. Calculations always use default units. (See F5:Opts/2:Type)Invalid EntryStorage ErrorMEPro Advisory: Circular definitionA variable cannot be assigned its own name as a value. To get a solution expressed symbolically in terms of this variable, where possible, simply leave the value of the variable blank. (See F5:Opts/2:Type): storage errorAn error has occurred while storing into this variable. (The name of the variable is in the title of this dialog box.) Use VAR-LINK to examine the current status of the variable and use MEM to see how much RAM is free.NVH<>.4|$RxAZCsp`QACOpQACp`QAJ0pgp` j$"P -gp` j$. j(NT. j NT@ @o.A/Np`p."j$/"j(NXT/C/ "j NP| |C."j N6 Cnp`$> ? 9/N\"HA -n.f .pg.gz{8|}`.f.gz[8|]`z"8EH>Hn"j NX f`E|*G`*H>Hz"j NX f0RFH-RRECm2RF0 H-0RFH-.g4 .f& ."fp`p8@>"C/ "j NX&H g CSK4 `C."j N4SBLRB: E n$ Em j2LC-6B0 ft`tfA.Hns j NX0EAAs.N|`p j2FC6C00gC 0` 0FA6H"j4 FH-6(C10gC 4`4 FH-6(HBgxRFElJg&j$&S(j$(T|sCs.?9NTCs.N.Cs."j NJbp`JfFC.NJf.p/Np`C.N(j$(T"j$.NJ@g@*j$*UCs.N"j$./ "j NXJ@fx.HzwNX"j$""j$ Q fx`Jf.g .f.g .fC@."jPN6f""j$."j8N"j$."jN"jTN`0 @n"gH @vn gT @1fl`` @gZob @f\`P @ngH @*gBoJ @ufD`8 @g2o: @g*`2.HzNX`,.HzNX`>"jLN`>?"jDNTxJf`("j$S"j$."j(N(H f.S/ "j NX"j$ Q f "j$"Q !g(j$(TJ9fNJ9fJ9g>B@. >/ ?N\Jft`tJf./ "j(NX/"j NX(j$(T.?NTJft`tJg8.N g.Hz*NX"j$".?Np`6"j$"C."jPN6f&Jg$ yNf.p/NX`C."jPN6fv"j$ Q -g$. g"j$."j N`J"j$.NJ@g:>"j$/NX6f.g .gt`t` >NJg,"j$ Q fCs.N`"j$.HnsNX"jTN`4"j$"0 @(g @g`.HzNX`>"jLNv"jTN`r Cg Cg Cg>"jLNCp"j$"Cs."j NDd.HztHns"j N.HnsNO ."jNvJ9f>NJfN"j$"Jg`Cpp.HyHn"j NP yfN` yfNp.HnHy"j NL"lLNp`"l$"OPL<NuNVH4|$R?. /. jN\&g/ jNX$H0* f0* `pLN^NuH ? 9/N\C"""""""",/Jo g o gp`&xpp̀. k(N*HJg6 gp`S g`R -gbfp`p`.@0@?@` /@\ /@( /@X0/@T  /@P @/@L0@ ?@H /@D /@@ /@<0@?@80@ ?@40@?@0 /@,` k$/PdzJg.?NTJfp`p`Jo`g:J\g4 k$"P -f k$. k(NT.NJfp`p`J(gj k$"P -fB k$. k(NT(H.NJg`.N"k$.NJ@fp`p`>"k$.NJ@fp`p`".NJ@g(>/ NZX:fJo`g JXgp`p`(JJEg>NJfp`pf(k$(T fJ\fp`p`Jf."k8N"k$ Q -f$JTg"k$"QJ)f/S`~/O`v(k$(T."kN"k$."kN k"k$(QB@ 0e"k k$(PB@ 1c"k$ $Q $@f"k$"Q !+g"k$"Q !,g"k$."k HNJ@gJoHfx`(k$(T>X"k N"k$."k8NJDg "k$."kNJ@f"k$."k|NJ@g0J@g"k$."kNJ@gJY"k N"k$."k8NJfB k"k$ $QBD$@ 0@e k 0@c, k$ $P $@f k$ P +g k$ P ,fJo8fJo4f Jo0fx`J,fg k$. kNJ@ff k$. k|NJ@fVg k$. kNJ@f k$. k|NJ@g0g k$. kNJ@gg k$. kNJ@gp`pJfJ0@0fB>U k N"k$."k8N"k$."kNJ@f"k$."k|NJ@fp`p`x"k$"d."k(N$HJfbJfp`pOhL"j N&nR.NJf$"j$".HzNp#`n>N f "j$"`VN(j$(T.N"j$e"j$"p`,"j$.Np-@g"j$."j8N(j$(TT"j$."j N>_/ "j NX*H f "j$"`% (f% fS R-@&j$&SRcS.S/ "j NX` >1"j N>"j Nx.N(j$(T>N*H gJ9gJ9gJgfJg"n`"y.N>"j N&j$&SB@->/ N.N.N."j4N./ "j NP>'"j N>"j NC."jPN8f"j$."j8NN"jT`.H/NX"j$"`fCD."jPN:f."j4NNJg"n`"y.NN>"j N"j$."j8N&j$&SB@->/ N.N.NN*j$*U"j$."j8N./ "j N."j4N./ "j NO >("j N>"j N"j$."j8NNR"j$."j8NN"jT`.H/NX"j$"` gJg"n`"y.NB@->/ NX.N&H."j NJcf.N>"j N>"j NC."jPN8f"j$."j8N"jT`L DYf.H/NX"j$"`.>"jL`$.HxYNX"j$"` "j$."j8N>N&H"j$.?NTJgL"j$./ NX yg C0v yfN`N yfDN`<.N.?NT ygC0.Nv"j$"L<8N^NuCopied to clipboardNVH<4|$RNlJf`*J9g=|!A.Hy jNX`>Hn?9N\J.f`>:Hn"j NX&H fG`R`R  gv(y0|fR`RRCHm."j NJf`.NJfZ(j$(T>""j N.N"j$S*j$*U>""j N>"j NR&L` "f."MS/ "j NXSb>/ "j NX// "jNP.NL<N^NuDECH06/4|$RABDJoo:/`? jXN/ j N\:np`&j$&S?< j NH/?NP"j$ QJg ?<"j NT?<-"j NHzv?<NP yfH/??NP` yfH/??NP`v?<NT"j$"L 8NuPasted from clipboardDECNVH 4|$RNJf`ABCA.Hn jNXJ@gJb`&j$&S> j N.?.NT>"j N>-"j N.NJ9g*=|# KT-HC.Hy"jNX"j$"`XCJ10g`J.?<NT yf` yf.?.?NZX>NL N^NuH0O4|$RACp`QNJfp`Jg6&j$&S> j N>"j N>-"j N yN"j$"`.C.?9NTC.NC.NvJgFACB@ yfN` yfNOlL Nu/ O4|$RACp`QNrJf`(J9g?|%jAj.Hy jNX`N0Ox$_NuN>JfNuN6NNuToolsOpen(save as)NewCut(cut)Copy(copy)Paste(paste)Delete(delete)Clear(format)AboutToolsH O4|$RJ/ygp>Hzr jNX8f>Hzb?HzT?HzJ?Hz/`>Hz)?Hz`>Hz ?Hz`>Hz?Hz`>Hz?Hz?Hz? Hz??<?<? jN\6 Cd> j\Np(0Sk nvЀ0;Nj6&.>jFN`FN`>NP`6N`.N4`&J9f3`pN`xJ9gNNC."jPN6fCS.N"jTN` C:g>"jLN>?"jDNT`JfJ9gNNNCS."jNJf CS.NJg yfNpp3#NAOhLNuGraphHzNXNuPictJ/gNHzNXNuPictJ/g?</9N\ANuViewJ/gNВANuJgB@/?N` B@/?NTNuDECAUTORADIANSolving nowUnable to initialize variable: MEPro AdvisorySolveNVhH<8. 4|$Rgp# yf:09 @g @g`NN`N|`C>N` yft.?<N.?<N.?<N\Jg.NzxIK`BCylJ50f>NJf>N&HCn."jPN6f.N"jTN`T.Hn"j NC."j ND*./ Hn"j NC.HzNz>?"jDNORRD09BB9B@oFNJf0"yN`& yfN>NNN>N>N>N` C>Nd`A L<8N^NuSolveHzNXNuRADIANRECTANGULAR%sEditNVH4|$RACp`QACp`QABCAJ00gB@. >N\`J. g~A.?9NC.N(j$(T.?<N.?<N\Jg yNJf>HnNXJgv"j$.?NTJg\>NJgPC.?"j$/HnNO &H yf2 "f,."j N 3"f."j NR` G`G|>N>N."j N@6 CPlvPH."j@N6f>?<"jDNT`.Hz-?"jXNT/"jLNP"j$">"jXN."j NJbp`pD>?NALN^NuChooseAB@J/gA 0fNANuwhenH04|$R0/ ymp`,?/ /9N&HHz/ j NOgp`pL NuH6/8?NT`8Jf?NTJfp`pSCJCkJg?NxTJfJfp`0L8NuH8/?NTTJfp`p:`8Jf?N6TJgp`pREylJg?NTJgJfp`0L8NuMEPro AdvisoryThis "when" clause applies to all the equations in this set. The condition that it represents is necessary in order for the equations to be meaningful. This "when" clause may not be deselected.CheckH0ABEJ/!gA 0Pfp`pE yf`?N"8<?NlX> GfJf@HzHzNP`(JDk"?NTJgGE``RFGnz`C 1Pf$I`p`RF?NVTJgRElN`vE`"Jf?N4TJf gp`pRRFGoJf6Ep`RCGoC 1PfjRG6$Ip`RCym69SCE`p0SC?NTJgJCjv`RC?NTJfDmEp`RCDmN3NA,L NuMEPro AdvisoryThis "when" clause applies to all the equations in this set. The condition that it represents is necessary in order for the equations to be meaningful. This "when" clause may not be deselected.H0:/ E yf`?N8<?NX> GfJf@HzHzNP`(JDk"?NTJgGE``RFGnz`C 1Pf$I`p`RF?NTJgRElN`vE`"Jf?NTJf gp`pRRFGoJf6Ep`RCGoC 1PfjRG6$Ip`RCym69SCE`p0SC?N8TJgJCjv`RC?N"TJfDmEp`RCDmNL Nu/ABBAB@0 J@g @g @g @g&`$A?Nx`"A?NF`A?Nv` A?NTNu/ABCA 00gB@/ ?N` B@/ ?NT&Nu$ O2/A4Cp""""""""""""Q An yoA`JJf09HHHЁ$w`* yC"""""""""IHI$w JO$BNuNVXHx6. 8.4|$R Clv C$ov$ DlxCo8zA\. jPN<fv>/. jNX:f|(n`4&T|p<./ Hn j N>Hn?p??? jN\6>N"jT`>Nv>"jLN0LxN^Nu2|"QJg&/9 i NXJc/9/9NPNuNVTH4|$RABC yg2 yg( yg yg"VBB3|@`BB=|@|[A[.?.NC[.N&j$&SC[."j(N>"j$/"jN\(gz."jN(HJl gj> "j N(H fS yf2.?NTJg<>NJg0>/ Hn[NP(j$(T.N-n-n=n"j$""V#n#n3nLN^NuNVH<6.4|$R>N-Hfp`|p .?NT/Hn j NA.N.Hn"j N&j$&SC."j(N>"j$/NמO"j$"J@fp`"nB@)>/ N.N(H.?NT/N*H./ "j NO J@fp`FJg ."j NJfp`0&j$&S.N(j$(T.N"j$./ "jXrp// HzNFP/Hy`fp// HznN,P/Hy`Lp // HzYNP/Hy`2p // HzNNP/Hy`p // HzANP/Hy j NO j$ L NuAngleBaseComplex FormatExact/ApproxExponential FormatH04|$R&j$&S0/ Hk nЀ0;N 0TvJ9gHyHz|N4P`J9gHyHz\NP`dJ9g\HyHz?NP`BJ9g:HyHz,NP` J9gHyHzNP j$ L NuNVH 4|$R&j$&S.N"j$ Q #f."j$."jNNf"j$""VBB3|@`V"j$."jNA 0##3"j$"A"V#X#X3XL N^NuH8Y$o/6|&Sf`(kB@ e b0<`(kB@ e bS`(kB@ e. !b(C>S/ N~XJ@g. k(N$H`~0<`h f2 J ,g J +f" J gC>U/ N:XJ@gp`4p`0S f0<`"C>/ NXJ@g . k(N$H`0<XLNu0| P// hNXNu/ 4|$R0/ ? j N?/ "jXN"HS/ S/"j NO $_NuH8Y$o6|&S f J`(kB@ e b`(kB@ e bS`(kB@ e& !b S.N(H g L`R. k(N$H`~(kB@ "e. (b(S`.NJ(H g L`. k(N$H f`XLNuH8Y6|&S(k$(T.N$k$$R f S."k(N$H."kNp."k$/NP"k$"LNuH8$o6|&Svx(k$(T/ NXJg/ NX k"k$$QB@ 0f|p(& k$ P J@gj @g @g"`X k$ PBC( k$ $P  $@f@DC`< k$ PB@(H k$ PBB(B6f k$ $P  $@fDC`xv k$ ogp`0LNu%d useable solutions.Desired soln #? 1NVHx8.4|$Rp,@.?<2?< jNX:gH>?</. ?<p(???<? jNO6g>?<p???? jNO 6>HzRHn jLNA. j ND(.Hz1Hn j NOJCg$A.?<?< ?<?<? jNO 6JCg*p>??<Hz?<?<??<? jNO6JCgd`\.Hn j Np.Hnp??? jNO @ f2A.HnNX<J.f FmDnp`p@J.f> j\N nJ.gp`0LxN^NuH8$o6|&S?</ k N\(H g 0, @g0<` / kxNXLNu" "o4|$R`S g g jB@ 0(c0<`" jB@ "H e bp`p$ANuH 6/4|$R?NTJfp`(? jXN8? j N?"j N/"j4NO pLNu/2|"QJofp`l?/ i NTpkP nHЀ0;N:::::::>:>>>>>>>>>>>>>>:>>>>:p`p&NuH0$o6|&SJ*fP kBD0@@g> k0@g `BB re CCp`CC4? k NT`?<"k N/ N\L NuH06/4|$R&j$&S?N/ j(N?< j$/N8 j$ ?NOJg(? j N/?NPJg?NTJgp`pL NuH04|$R&j$&S o / j(N?< j$/Nˀ j$ ?NRO Jgp`pL NuH<$o&o8|(T/ l(N*H/ l(NP(H`cgp`SSbgp`pL<Nu/ 4|$R jdN"j ig"jp09Qg"j`N"jp0ygp`p$_NuH8Y$o6|&S f J`(kB@ e b`(kB@ e bS`(kB@ e& !b S.N(H g L`R. k(N$H`~(kB@ "e. (b(S`.NJ(H g L`. k(N$H f`XLNuH8$o &o$8|(Tf`v/ l N6/ l NPHðgp`Zx`L l@0g@ `H0 lB0 gB `H4Bgp`RR4RDCmpLxNu#33NpNuH ? 9/N(( p>N-Hp.?NT/Hn k NOA.NJ.g"y`.HnNX"H-I"k$-Q. "k4N*k$*U."k(N-HJg`S g`R"n )g-|-|-|-|`"k$-Q."k4N"k$-Q."k(N-H"nijg "nf.N>"k N$k$$R"nB@)>/ N.N.N."k4N./."k NP>'"k N>"k NCX."kPN8f"k$."k8NN"kT`pv.H/NX"k$"`R"nf.N>"k N.N>"k N(k$(T"nB@)>/ N.N.N.N>"k N."k4N./."k NP>("k N>"k NC."kPN8f"k$."k8NN"kT`v.H/NX"k$"`f"nfC."kPN8f."k4NNR.NND>"k N"k$."k8N(k$(T"nB@)>/ N.N.NN$k$$R"k$."k8N./ "k N."k4N./."k NO >("k N>"k N"k$."k8NNN"k$."k8N"kT`rv.H/NX"k$"`VJgP.N"nB@)>/ NX.N.N>"k N>"k N"k$."k8NJf "k$"p`R"k$."k(N$Hc./."k NXd./ "k NX./."k NX*nbdpL<8N^NuMEPro ErrorSorry, this version of MEPro only works when the calculator is using English. Use MODE/F3:Language to choose English before continuing with MEPro.J9gHz_HzNNPNuNVH 4|$R&j$&S/. NX6 Cg ? jLNT"j$//.N"j$"L N^Nu?<NTNuResolveErr: ResolveErr: NV-J4|$R.Hn j N. j NDP./. Hn j NA.p. /N$nN^NuNuSplitFull/ 4|$RJ/ g. jdN"j ifHy"j0NXN`N"jdN"j ifA`A$_NuCanclKeyCANCLNVJ. gHzB@. ?NnpAN^NuInvrsInversJ/g"Jyfp`p3pJygA`ANuruxyzRUXYZH0$o6|&S/ k NX6 Cm CnHz/ k NPJf`0 @gp @g @g`"k*@1g *@ 4`*H BtfT k*B0 g>"k*1 g, kB0 gB `H Bxg&"kB1 gB `H Byf|jj`"k*B1 g k*0 fr"k*B1 g *B `*H Btfz kB0 gB `H Bxg$"kB1 gB `H Byf2|j` k*B0 g|jRL NuH8$o6/6|&Sn`:(JS/ k NX8Co8/ / k NP"k$ QJg ?<"k NTLNu0| P h$S//NXNup33NuH009 @g @g @g`vGE`RCymAB@3`Ry?9NTJg09ym09ymN3`Ry?9NTJg,09yl`vGE`RCymL NuDECAPPROXIMATERADIANH8O y#3xvGI`N0> ? 9/N\$H JC"""""""":/ 0 Ef * 0RDRCyl Cm3JgX.?<N.?<N.?<N\"yN>N>N>NpO$L8NuH8z(NvGEIp` fRE8RRRCym"y#3 yg yfV3Nr69SCE`p0SC?NTJgJCj?NTJf Ef?NT` 3NL8NuH8O$o$6|&S.NJfpO`V(k$(T.N>"k$/NX>NJf"k$"pO`"k$."k(N./ "k NOpLNuH8O$o$6|&S.NJfpO`V(k$(T.N>("k$/NX>NJf"k$"pO`"k$."k(N./ "k NOpLNuH84|$R&j$&S//N(j$(T"KR/ N/ / "j NOLNuNVH<$n&n 6.8|(T. l N @ op`6p ./ Hn l NA.N.Hn"l NO $l$$R.NJf "l$"p`."l(NC.N*Jf "l$"p`"l$ Q -f"l$S"l$."l NJ@g"l$."lNJ@f "l$"p`>"l N>"l NC."lPN8f"l$."l8N"lT`"l$" 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numberH8$o&o8|(T g& f`6Hx/ NPJgp`"&l$&S/ lN"l$/"l HNP"l$"LNuint, >0H8Y$o&o8|(T g&p./ NXJfp`P&l$&S. l4N."l4N>O"l N>"l N"l$."l8N"l$ Q"l$" ,gp`pXLNumftincmmmftinmcmmmsmsminhrdayHzkHzMHzGHzrad/s_rs_Hz/(2)krad/s_krs_kHz/(2)Mrad/s_Mrs_MHz/(2)deg/s_degs_Hz/360Hz_Hz_Hzrpm_rpm1/_minVmVV6_VkVMV_MegaV6_VGV9_VmVV6_VVkVMV_MegaV6_VGV9_VAmAAnanoA9_ApA_picoA12_AfA15_ANkN3_Nlbfkip_kips1000_lbfdynePaMPa6_PaGPa9_Papsilbf/ft^2_lbfft2_lbf/_ft^2ksi_ksi1000_psiatmPaMPa6_PaGPa9_PapsibaratmtorrMPa6_PaPakPa3_PaatmpsitorrK_KCFRK_KR_Rt5/9_KCFK_KRm/s_ms_m/_scm/s_cms_cm/_sft/s_fts_ft/_sin/s_ins_in/_sft/min_ftmin_ft/_minkph_kphr_kphmph_mhr_mphraddeg/180._radgrad/200._radm^2_m2_m^2mm^2_mm2_mm^2in^2_in2_in^2ft^2_ft2_ft^2cm^2_cm2_cm^2^2_2_^2JkJ3_JeVcalergBtuWmW_milliW3_WkWMW_megaW6_WhpBtu/hr_Btuhr_Btu/_hrGW9_WVA_VA_WkVA_kVA13_WVAR_VAR_WkVAR_kVAR13_WkMG9_6_milli3_siemenskSiemens_kSm3_siemensMSiemens_MSm6_siemens1/K_x1degK1/_K1/C_x1degC1/_C1/F_x1degF1/_F1/R_x1degR1/_RWb/A_WbJ_Wb/_AmWb/A_mWbJ3_Wb/_Am_m__mcm_cm__cmin_in__inmm^2/m_m2m__mm^2/_mSm/m_Smm_Siemen/_mkSm/cm_kSmcm5_Siemen/_mkSm/mm_kSmmm6_Siemen/_mSm/in_Smin_Siemen/_inhenrymHHnHpH12_henryfH15_henryFmF3_FFnFpFfF15_Fm^3_m3_m^3lcm^3_cm3_cm^3mm^3_mm3_mm^3in^3_in3_in^3ft^3_ft3_ft^3m^2/s_m2s_m^2/_scm^2/s_cm2s_cm^2/_sin^2/s_in2s_in^2/_sm^2/hr_m2hr_m^2/_hrcm^2/hr_cm2hr_cm^2/_hrm^2/hr_m2hr_m^2/_hrcm^2/hr_cm2hr_cm^2/_hrft^2/hr_ft2hr_ft^2/_hrin^2/hr_in2hr_in^2/_hrWbK/W_KW_K/_WC/W_CW_C/_WF/W_FW_F/_WR/W_RW_R/_WNs/m_Nsm_N_s/_mNs/cm_Nscm_N_s/_cmlbfs/ft_Nsft_lbf_s/_ftlbfs/in_Nsin_lbf_s/_inNs/m^2_Nsm2_N_s/_m^2Ns/cm^2_Nscm2_N_s/_cm^2lbfs/ft^2_Nsft2_lbf_s/_ft^2lbfs/in^2_Nsin2_lbf_s/_in^2m/s^2_ms2_m/_s^2cm/s^2_cms2_cm/_s^2in/s^2_ins2_in/_s^2ft/s^2_fts2_ft/_s^2m^4_m4_m^4mm^4_mm4_mm^4in^4_in4_in^4cm^4_cm4_cm^4ft^4_ft4_ft^4kgtontonnekton_kton1000_tonrad/m_radm_rad/_mrad/cm_radcm_rad/_cmrad/ft_radft_rad/_ftrad/in_radin_rad/_inkg/m^3_kgm3_kg/_m^3g/cm^3_gmcm3_gm/_cm^3lb/in^3_lbin3_lb/_in^3lb/ft^3_lbft3_lb/_ft^3W/m^3_Wm3_W/_m^3mW/cm^3_mWcm33_W/_cm^3kW/m^3_kWm33_W/_m^3Btu/(hrft^3)_Btuft3_Btu/_hr/_ft^3J/kg_Jkg_J/_kgJ/g_Jgm_J/_gmcal/g_calgm_cal/_gmkJ/kg_kjkg3_J/_kgBtu/lb_Btulb_Btu/_lbBtu/slug_Btuslg_Btu/_slugkJ/kg_kjkg3_J/_kgJ/kg_Jkg_J/_kgJ/g_Jgm_J/_gmcal/g_calgm_cal/_gmBtu/lb_Btulb_Btu/_lbBtu/slug_Btuslg_Btu/_slugJ/(kgK)_JkgK_J/(_kg_K)J/(gK)_JgmK_J/(_gm_K)cal/(gK)_calgmK_cal/(_gm_K)kJ/(kgK)_kJkgK3_J/(_kg_K)Btu/(lbF)_BtulbR9_Btu/(5_lb_K)kJ/(kgK)_kJkgK3_J/(_kg_K)J/(kgK)_JkgK_J/(_kg_K)J/(gK)_JgmK_J/(_gm_K)cal/(gK)_calgmK_cal/(_gm_K)Btu/(lbF)_BtulbR9_Btu/(5_lb_K)J/(molK)_JmolK_J/(_mol_K)cal/(molK)_calmoK_cal/(_mol_K)Btu/(molF)_BtumlR9/5*_Btu/(_mol*_K)kJ/(molK)_kJmolK3_J/(_mol_K)m^3/s_m3s_m^3/_scm^3/s_cm3s_cm^3/_sl/s_ls_l/_sft^3/s_ft3s_ft^3/_sgal/min_galmin_gal/_minft^3/hr_ft3hr_ft^3/_hrft^3/s_ft3s_ft^3/_sgal/min_galmin_gal/_minft^3/hr_ft3hr_ft^3/_hrm^3/s_m3s_m^3/_scm^3/s_cm3s_cm^3/_sl/s_ls_l/_sW/(m^2K)_Wm2K_W/(_m^2_K)J/(sm^2K)_Jsm2K_J/(_s_m^2_K)kJ/(hrm^2K)_kJm2K3*_J/(_hr_m^2_K)Btu/(hrft^2F)_Btuhff_Btu/(_hr_ft^2*(9/5)_K)m^2K/W_m2KW_m^2_K/_Wsm^2K/J_sm2KJ_s_m^2_K/_Jhrm^2K/kJ_hrm2Kk_hr_m^2_K/(3*_J)hrft^2F/Btu_hrft2F_hr_ft^2*(9/5)_K/_Btum^2/s_m2s_m^2/_scm^2/s_cm2s_cm^2/_sin^2/s_in2s_in^2/_sft^2/s_ft2s_ft^2/_sft^2/min_ft2min_ft^2/_minm^2/s_m2s_m^2/_skm^2/hr_km2hr_km^2/_hrmi^2/hr_mi2hr_mi^2/_hrkm^2/s_km2s_km^2/_smi^2/s_mi2s_mi^2/_sN/m_Nm_N/_mkN/m_knm3_N/_mlbf/ft_lbfft_lbf/_ftkip/ft_kipft1000_lbf/_ftlbf/in_lbfin_lbf/_inN/cm_NLm_N/_cmkg/(sm^2)_kgsm2_kg/(_m^2*_s)kg/(hrm^2)_kghrm2_kg/(_m^2_hr)lb/(sft^2)_lbsft2_lb/(_s_ft^2)lb/(hrft^2)_lbsfhr_lb/(_hr_ft^2)kg/s_kgs_kg/_sg/s_gms_gm/_slb/s_lbs_lb/_slb/min_lbmin_lb/_minkgg_gram_gmmglbozslugtonkgm/s_kgms_kg_m/_sgcm/s_gmcms_gm_cm/_slbft/s_lbfts_lb_ft/_slbin/s_lbins_lb_in/_sN/m^2_Nmm2_N/_m^2kN/m^2_mkNm23_N/_m^2dyn/cm^2_cdnc_dyne/_cm^2lbf/in^2_inlfi_lbf/_in^2lbf/ft^2_ftlff_lbf/_ft^2kg/mol_kgmol_kg/_molg/mol_gmmol_gm/_mollb/mol_lbmol_lb/_molmolkmol_kmol3_molmmol_mmol3_molmol_mol6_molnmol_nmol9_mol#atoms_atoms1/(_na)m^3/mol_m3mol_m^3/_molcm^3/mol_cm3mol_cm^3/_moll/mol_lmol_l/_molin^3/mol_in3mol_in^3/_molft^3/mol_ft3mol_ft^3/_molNm_Nm_N_mkNm_kNm3_N_mftlbf_ftlbf_ft_lbfftkip_ftkip3_ft_lbfinlbf_inlbf_in_lbfkgm^2_kgm2_kg_m^2gcm^2_gmcm2_gm_cm^2kgcm^2_kgcm2_kg_cm^2lbin^2_lbin2_lb_in^2lbft^2_lbft2_lb_ft^21/s_invs1/_srpm_rpm1/_minPas_Pas_Pa_scP_centip2_PP_Poise_Pdynes/cm^2_dynesc_dyne*_s/_cm^2J/mol_Jmol_J/_molkJ/mol_kJmol3_J/_molcal/mol_calmol_cal/_molBtu/mol_Btumol_Btu/_molm^3/kg_m3kg_m^3/_kgcm^3/g_cm3gm_cm^3/_gmin^3/lb_in3lb_in^3/_lbft^3/lb_ft3lb_ft^3/_lbN/m^3_Nm3_N/_m^3kN/m^3_kNm33_N/_m^3lbf/ft^3_lbfft3_lbf/_ft^3tonf/ft^3_tonfm3_tonf/_ft^3W/(mK)_WmKel_W/(_K_m)W/(mF)_WmRan9/5*_W/(_K_m)Btu/(hrftF)_Bhrftf9/5*_Btu/(_K_hr*_ft)Pam^6/kg^2_Pm6kg2_Pa_m^6/_kg^2atml^2/kg^2_atl6p_atm_l^2/_kg^2atmft^6/lb^2_atft6p_atm_ft^6/_lb^2Pam^6/mol^2_Pm6mo2_Pa_m^6/_mol^2kPam^6/mol^2_Pam6km13*_Pa_m^6/_mol^2atml^2/mol^2_atl6at_atm_l^2/_mol^2Pam^6/kg^2K_Pam6kg_Pa_m^6/_kg^2*_K^.5kPam^6/kg^2K_kPam6k13_Pa_m^6/_kg^2_K^.5psift^6/lb^2F_pftlb2_psi*_ft^6/_lb^2*(5/9)^0.5_K^.5Pam^6/mol^2K_Pam6mo_Pa_m^6/_mol^2*_K^.5kPam^6/kmol^2K_kPam6m3_Pa_m^6/_mol^2*_K^.5psift^6/mol^2F_psift6(5/9)^0.5*_psi_ft^6/_mol^2*_K^.5N/m_Nmet_N/_mdyne/cm_dynec_dyne/_cmlbf/in_lbfin_lbf/_inlbf/ft_lbffet_lbf/_ftkip/ft_kipfet3_lbf/_ftmrad/s_mrads_m_rad/_scmrad/s_cmrads_cm_rad/_sinrad/s_inrads_in_rad/_sftrad/s_ftrads_ft_rad/_sNm/rad_Nmrad_N_m/_raddynecm/rad_dycmra_dyne_cm/_radlbfft/rad_lbfftr_lbf_ft/_radW/m^2_Wm2_W/_m^2kW/m^2_kWm21000*_W/_m^2Btu/(hrft^2)_Btuhf2_Btu/(_hr_ft^2)W/(m^2K)_Wm2Kel_W/(_m^2_K)kW/(m^2K)_kWm2K3_W/(_m^2_K)Btu/(hrft^2F)_Btuft29/5*_Btu/(_ft^2_hr_K)1/m_m1/_m1/cm_cm1/_cm1/ft_ft1/_ft1/in_in1/_inC/m_Cm_K/_mC/km_Ckm_K/_kmF/ft_Fft5/9*_K/_ftF/mi_Fmi5/9*_K/_mi1/m^2_m21/_m^21/cm^2_cm21/_cm^21/ft^2_ft21/_ft^21/in^2_in21/_in^2J/K_JK_J/_KkJ/K_kJK3_J/_KBtu/F_BtuR9/5*_Btu/_Krad/s^2_rads2_rad/_s^2krad/s^2_krads23_rad/_s^2deg/s^2_degs2/180._rad/_s^2kgm^2/s_kgm2s_kg_m^2/_slbft^2/s_lbft2s_lb_ft^2/_smcmftinmmkm_kmm3_mmi_mift5280_ft/ "o fA`$i g J` / NX$_NuH 2|"Qv$o 2<` iA0g  `RCJfLNuNV-J$n2|"Q J0.H//. / i N/ N$nN^Nu2/kymNu?< ? 9/NP hNuNVH$n6|&S. k N c`> / HnN`P yfZxI`:BC4@>N> /HnN.C.Hn"k NO J@f0`ZRD09BB9B@nB`v`4>N> /HnNC.Hn"k NO J@f0` RCympLN^Nu does not contain an appropriate unit expression.NVH$n 6|&S(k$(T fA`B@*>/ N.N.Hy k Np ./.Hn k NA.N.Hn"k NOC.N*Jf>/ NA`"k$ Q -f "LT."k N b ,_fp`pf"k$S"k$."kNJ@fp`pJf"LT.Hy"k NX` >/ N"k$"ALN^NuNVH<$n 6|&S fA`b./.NX*H _f R-@`-MBC*JCo2`*>/ N(H.N./ k NPJ@f-T`SCJCj nL<N^NuUnits conv. error - Will use default unitsNVH<$n&n 6.8|(TJ9g yf>N-Hf$l$$RT. l N J`d"l$-Q."l4N"l$.NJg(./ NX.N>"l N&l$&S`"nB@)>/ N.Nn.N>"l N&l$&S*K"l$."l4N./ N6P-HC."lPN8fC4fN"l$-Q"l$."l8N$l$$R.NN*l$*U"l$."l8N./ "l N./."l NP>("l N>"l N"l$."l8NN`J$l$$R.NCg CΔf./ "l NX>'`>"l N>"l N"l$."l8N"lT`f DYfZp ./ Hn"l NC.N.Hn"l NC.N>?NO"l$""l$."l8`>"lLN$l$$R"l$."l N *_f:. .R/NX"l$""l$."l8N$l$$R"l$."l N./."l N nTL<N^NuNVH $n6|&S k$. k NJ@f" k$"P #f k$. kNNfp`$ f J ,g J +f U. k N`pL N^Nu_w_w_wErr: PushValAndUnitsTokenizedNVH<$n&n 8|(TJ9g>N-Hf . l4N`*l$*U-M."l4N>*"l$/NXJ@f2"l$">*"l N./ N>X.N>"l N`:"l$.NJg"./ NX.N>"l N` "nB@)>/ N.N.N>"l N&l$&S"l$."l4N./ NP-HC."lPN6ftCЬfN"l$-Q"l$."l8N$l$$R.NN&l$&S"l$."l8N./ "l N./."l NP>("l N>"l N"l$."l8NN`Cft.N>"l N$l$$R.N.N>"l N./ "l NX>("l N>"l N.N>"l N`J$l$$R.NCg Cʌf./ "l NX>'`>"l N>"l N"l$-Q"l$."l8N"lT`("l$" CYf. ./NX`>"lLN./ "l N l$ PL<N^NuH<$o&o6/ 8|(T?NT*HJ9g g -b / lNX`?/ / NO NL<NuRECTANGULARREALREALRADIANNVH4|$R&j$&S>/. /.Nb(j$(T>&"j$/NO J@f"j$."jN>N.?<N.Hy"j N\J@g >N>N"j$."j8N(j$(T"j$."j N>N.?<N.?<NX` "j$."j N./ "j NX"j$."j(NT$H n JLN^NuNV-C0| P?<_/. h N\"H f`! (f! fSp&.N^NuH0Y$o6|&S. kNJ@gp`:S f.NJfp`". k(N.N` Qf . kN`pXL NuPopUnits errorPopUnits errorPopUnits errorH8O4|$R&j$&S j$. j(N(H j$"P g j$"P fl j$S j$"P fP j$. j(N. j NJ@g8NJg0> j N&j$&S"j$."j8N./ "j NOPp`>"j NpOL`C."jPN6f"j$S"j$ Q f&"j$"QS.NJf4.p/NX` "j$.NlJf.p/NX"j$."j N"j$."jNJ@g.p/NX"jTN`"j$" Cg >"jLN`pOL`$j$$R fOL`pOLLNuPopUnits errorPopUnits errorPopUnits errorNVH<84|$R j$-P*n. j(N(H gp`pg `S g`R ,g> j Nx`&M."j(N*H."j4N&j$&S>&/ NXJ@gNJfp`p`d"j$ Q fC."jPN6f"j$S"j$ Q f("j$"QS."jNJ@f6.p/NX`""j$."jNJ@f.p/NX"j$."j N"j$."jNJ@g.p/NX"jTN`"j$" Cg >"jLN`x` g g"K !f +&fx`n"KS."j(N."j4NNJfx`N"KW."j4NNJfx`6>&"j N>"j NB@>"j N./ "j(NX/"j NXcJgVJg"j$"p`./."j(NX/"j NXJfp`b&j$&Sz` ."j(N&HRE fx`2&j$&Sv` ."j(N&HRCDm./ "j(NX/"j NXRDEm>"j NpL<8N^Nu: storage errorAn error has occurred while initializing a constant needed by MEPro. (The name of the constant is in the title of this dialog box.) Use VAR-LINK to examine the current status of the constant and use MEM to see how much RAM is free.NVH<$n6|&SACp`Q(R$j*k$*UA. kPN6fT.N"k$."k8NNp."k$/NXJf.p/NX"k$./ NX"kT`l"k$" Cg Cg Cg CfHp ./ Hn"k NC."k ND.HzHn"k N.HnNO>"kLN"k$"L<N^NuName: Desc: any numberany numberType: Disp units: nonenoneCalc units: Example value: Default xmin: Default xmax: NVH<6.4|$R.?<P?< jNX8~JDgH>?</. ?<p???? jN:.Hn j N>N&HA. j ND(./ Hn j NOJEg$A.?<?< ?<?<? jNO :.Hn j N>N,-HA. j ND(./.Hn j NO JEg(A.?<0@ ??<?<? jNO :>N(H f -|` *l f -|`A.HxNX.Hn j NA. j ND(./.Hn j NO JEg*A.?<0@@ ??<?<? jNO :.Hn j NX fA` ./ NX-H. j NJf-|A. j ND(./.Hn j NPJEg,A.?<0@ ??<?<? jNO :.Hn j NX g$J,c,F>/ NX.N-HA. j ND(./.Hn j NPJEg*A.?<0H@ ??<?<? jNO :.Hn j N> ? 9/N&H-kA. j ND(./.Hn j NOJEg,A.?<0@ ??<?<? jNO : yf.Hn j N-kA. j ND(./.Hn j NO JEg,A.?<0@ ??<?<? jNO :.Hn j N-kA. j ND(./.Hn j NO JEg(A.p?G ??<?<? jNO :JEgp.Hxp??? jNO > j\NL?<HzX?<?<P?<(?<? jNO:vJEg0.?<0RC@ ??<?<? jNO :JEg0.?<0RC@ ??<?<? jNO :JEg0.?<0RC@ ??<?<? jNO :JEg0.?<0RC@ ??<?<? jNO :|JEgp.Hnp??? jNO > j\NL8N^NuSolveSolveJfHzNXNuJ/g yNANuNVH$n6|&S?<?. / kNP(H f` / / kxNLN^NuH8Y$o6|&S. kNJ@g J`(kB@ e b`(kB@ e bS`(kB@ e& !b S.N(H g L`R. k(N$H`x(kB@ "e. (b(S`.ND(H g L`. k(N$H f`XLNuH8Y$o6|&S g f J`(kB@ e b`(kB@ e bS`(kB@ e& !b S.N(H g L`R. k(N$H`x(kB@ "e. (b(S`.ND(H g L`. k(N$H f`XLNuProArbsMEPro Solver and GrapherArbitrary integer @%d in solution.Replace with what small integer #?0ProArbsNVH?<Hz?<p(???<? jNO:g>?<p???? jNO :C>HzHn jLNA. j ND(.HzHn j NOJEg$A.?<?< ?<?<? jNO :JEg*p>??<HzW?<?<??<? jNO:.Hn j NX<<JEgp.Hnp??? jNO <> j\N F g "j$"p`C.HnNX8J.f JDk Do "j$"p`"j$S@>"j NC>"j N>"j N>"j N>"j N"j$.HzNX` "j$"p`N"j$"Nb/./.?."j (N./ "j N.U/ "j NO"j$.N&H fZpL* j N0SCJ@n./ "j NPLNuNVH<(n 4|$Rx&L`RDR> / j NX&H f Dox.0H@??< jNX<f`>?</.?<p???<? jNO>&Lz:| `p. j N6> / j NX(H g6 K CR&LPREDmJGgp.Hxp??? jNO > j\NLN>N`"yN ygO Nuda Vinci TechnologiesNVH $n6|&SACp`Q. k NJc p.Hy`p.HnHn k NPB@*BB*BS@6B@*S@>?<?N>09S@?0S@?p??"kNP// "k@N>/ "kN>Hn"k\NO`"C."k N>Hn"k\NXX@8CoC."k NJbƖDjRCC>?<C??<?"kNP// "kN>/ "kLNC.p?TC?/ "kN>/ "kLNL N^NuHyNzXNu: H8$o6|&S/ k ND@@6A BD/ k NP: Cm& EnfA 0@fHz/ k NPUC yf(yH(tH`09 @g @gT @g @g` yg yf(yH(tH`t yf|(yH(tH`X yf(yH(tH`> yfF(yH(tH`$(y(tH`(y(tH`IH// / k NO L8Nu: H8$o6|&S/ k ND@@6ABD/ k NPJc CmHz/ k NPUC09 @g @gR @g @g` yg yf(yH(tH`r yft(yH(tH`X yf(yH(tH`> yf@(yH(tH`$(y(tH`(y(tH`I/ / k NPLNu(MEPro AdvisoryData length exceeds buffer size. The variable name will be displayed instead. The variable's value may be viewed with VAR-LINK using F6 or recalled to the author line of the HOME screen.""): data errorAn error has occurred while converting this variable's data for display. (The name of the variable is in the title of this dialog box.) There is something stored that MEPro can't make sense of. You may be able to correct the problem by deleting the variable._ERROR_Units Error : : 1 : 1 NVH<$n .6|&S|ABF yg yg yg yfp|WAW.?.NTCW.N|*k$*UC."kPN6f2CW."k(N>"k$/"kNX&g."kN(HJl g> "k N(H.?NTJg>NJg|| -f S"LJ!gH`C.?/ HnWN(H>/ "k NO g>{/ "k NX fp`p@J.g.Hn"k NX."k N/Hn"k NXD@@:."k N>J.gRGJf<> ? 9/N\"HA &. fp`p|gTGJfNGlJJ.gC."k NH<.HzNH.HnWHn"k NO `J.g0SEH.HzmHn"k NPH./ Hn"k NPC."k ND@@6J.gJCo.Hn"k NXSCJ.gJCo.Hn"k NX"kTN`h"k$" Cf"kJg"kNCW."k NDe.HzHnW"k N.HnWNN.p/NOJg(J.f" yfIJg "yJ9gC."k NJc>N(H gJ,c>_Hn"k NX g*.Hn"k NX f.A/NXJg.HnWN` .HnWNX"H(IJg&C."k ND.HzHn"k NPC."k ND./ Hn"k NP"k$"AIB@Jg gC."k NJf`x."k ND@@6."k N e Cm./ "k NXUCH.Hn/ "k N`, yf"*yCB@(m>NS@>?/ N\(P."k ND@@6 Cl`./ "k NUCH./ / "k NO J9g."k ND@@6(m ."k NJc| Cot./ "k NXJ@g^Jg&./ "k NSCH./ / "k NO `4(m."k NJc"./ "k NSCH./ / "k N` yf(y*l."k ND@@6."k N eH.Hz/ "k NPUCjvH./ / "k NPJ9g."k ND@@6*l ."k NJcp Coj./ "k NXJ@gVJg$./ "k NSCH./ / "k NO `.(l."k NJc./ "k NSCH./ / "k NLNJfv>N&HC."jPN6f.N"jT`L.Hn"j NC."j ND*./ Hn"j NC.HzNO>"jLNB@.>/. ?.N\>N>N>N>NL N^NuNV?</. ?.NN^Nu: ""NVH8$n .6|&S.?.NTCBD>N: yg yf(yH(tHSEH(tX`$ yf(y(lSEH(tX`Ij."k ND@@8."k N e4 Dm../ "k NXUDJf Do./ "k NXSDH./ / "k NP."k N fJgp`p"@`JgC`C./ "k NL8N^NuNV/. ?.NzN^NuNV-J$n / ?.N`/ ?.Nx$nN^NuNV-J$n / ?.N8B@.?/ ?.N$nN^NuNV?</. ?.NN^NuH 6/ $oJyg/ ?N / ?NO ` / ?N\LNuChooseChoose ChooseH8O$oT6|&SAB@>N8 yfH> AB@? 9/N\(HA (o(BC/&`* yfP yC"""""(o69./ k NX f&. k N^ b.Hy k NX. k N c.Hy k NX`&. k ND./ Hy k NP>Hy?/ NO 8gAB@>?NTSD yfLCJfNJg 0E@nRERC CmEC@` yfO8L8NuChooseScreen1Hy?9N\ACB@ 1gHz?9N\NuHyNXNNNu ~=H Q6/$o/#ABE00Ap0PJk( nЀ0;N0 A"zB@0P|.?N`Jg.? yN` yfC :NtЂ"@|D>/ ?NB\`D>/ ?N\`Jyg.?N.?N\X`jD>/ ?N\`XJg.? yN`@ yfC :tЂ"@|D>/ ?N\` .?N|TPL8NuNVH<. 4|$RJ9f.p/NX>?<?.NX6y=@j 09n:yJ9fygJg`09BB9B@o:09S@t4.?< Hy"j N\09C˛`JCf yo8|`@09S@HH@B@H@f,09y49BA9AS@H@H@H°l8|D>G/ ?N\\JgD."j N$09S@H@B@H@c(0 yC0 yC>:C/ "j NX&H g C0 I`p=@0y>C."j N<Hp09o< gJg>Hy"jNX0.ڐMR@Ht49mByf J9gp`p>Hy"jNXC09`"0.ڐMRCCS0.GSJgC.??<Hy"jNP0.C`$C09CSJg"yf J9gp`p>Hy"jNX0.ڐMR@Ht49l:0.CR.y>?MR@?Hy"jNP>Hy"jNXHp09l"F>?< ??Hy"j$NO 0 HgRB@9yS@6"jdN"j ig0BB9BS@6>0 H???Hy"j$NO >Hy"jN0.ALNT>?NTJ9g,09y>N,>09y?NTvGI`J9g09y@gJ9g09y@gxJ9f@J9gh09C"K tЂ"@ g0y49BA9ABo0>N4y09BA9A@n>?NTRCHp09mFp>?Hy"jlNO LNuH 4|$R jt0yfn jJPg`dp/?9 jN\6gN? jNp0/p/?9"jNp???Hy"jN6p0/p/?9"jNO LNuNV nf`N4.SBA2I"0AJ! A8p ./. /NN^Nu H8O4|$RAC:/0yjy09S@>?<?NX6/2yjy09S@>?<?NXA0P00fBC1P10f20GTITpT./ / j NPJ@f` ABD0P>?<?NXv<G`0CU@ K.?NTRCDo>?<?9NX`C.?NTTRCyo>NN3v(C1P0y`phBB@g8RDRCHmJDgL Do4vG`$0S@tj0BBBgp>??"jLNXRCDm>?<?"jLNXOLxNu NVHH<4|$RACf0.y49BA9ABo`0.y=@j 09n49SB>?<?.NXJ. gNCf>?N&Hg* g&690.y3>N*3`*."j N6ot`t n nJCoL yf 0R@3H֕"C ! gt`t n Em>/"j\NX@ nJgUDYSSQF49BBDDDjRDDHĉWD6 Cnv|2jRAA=AA=C|I=|KC-I-|C-I0.=@-|J. gH& 0.Hր"C(& 0.Hր"C"$ Ԅ8-B`AM-Hp .Hnf"n/ NP nJg>N&Hgf gb690.y3>N"H n 3p. n/Hno"j NP|{Co."j NH`("n"`p. n/Hno"j NP|Co."j N: .g E ofxp.HzHnY"j NP~Got^rp`*g gg (g )g 0DARDRRGEmp.HnYHno"j NP|{4n B n4.`t EH.HnfHno"j NPCo."j N6n(.0.H؀0| `SSCHon"D$D .Hno/"j Np ."n/ 4.FSB"n/ "j NOXnRXRF FmJ. g>NNC09Cv(GI`Jgtj"L8RDRRCymJ. gBJDg> Do(vtG`Jgp>??"jLNXRRCDm>?<?"jLNL`PHzsHy"j NP`DHzfHy"j NP`0HzXHy"j NP`HzKHy"j NP`Hy?9N\J9gpHy"j NXD@@6 CoTHy"j NX bHzHy"j `HzHy"j NPSCH/HyHy"j NO #ALNu"o0| P#/ hNXNu/ 4|$RJ9gJ9f`Nd/ jNX$_NuH Y/4|$RJ9f`J9gJ9g`|J9f 09f,Jf(J9gZJ9fJgLN`<>Hy"jLNXJ9fJ9gJJ9gBJ9g ."j0NNJ9gNp`J9f"J9fJ9fJ9gJgzJ9g689yk Hp09l>N>?NTJ9g209y>N>09y?NTJ9gJ9fJg NJ9gN*XLNuNVH6.4|$R8yjy09f`b>?<?NAB@0@=@C1@=@y=C0yS@=@>HnHy j@NLN^NuH 2/ 4|$RJ9ghJ9f`^ yB@(y69@JCo:Co2y/9 j0N?9?9/9/9"j0NONLNuJ9gJ9fNu?<NdTNuJ9gJ9fNu yB@(BB(BS@2QAJAnNu?N(TNuJ9gJ9fNu yB@(y29@JAnNu?NTNu/ 4|$RJ9gtJ9f`j yB@(yoP0/yB@(yl (3/9 j0N?9?9/9/9"j0NON$_NuJ9gJ9fNu?<N`TNuJ9gJ9fNu yB@(BB(BS@2QAJAnNu?N$TNuJ9gJ9fNu yB@(yJ@nNu?NTNuNVH4|$R09S@>?<?.NX=y09yS@=@=|B@9=@9yS@6"jdN"j ig0BB9BS@6>Hy"jN>?< ?9?Hy"j$N>?<09U@y??Hy"j$N0.D@>HnHy"jNLN^NuNVH4|$R09S@>?<?.NX=yB@9=@=|9=@9yS@6 jdN"j ig0BB9BS@60.>HnHy"jN>Hy"jN>?< 09U@y??Hy"j$N>?<?9?Hy"j$NLN^NuH O4|$RJ9g^J9f`09@ yo6vy. j0N>?9/9/9"j0NO N`p# yoJ9f`09y>NSy09yo8>N4pSyRy0yp09m@3`609y>N$09yR@>09y?NRTvJffO LNuH O4|$RJ9g`J9f`&09yyl6vy. j0N>?9/9/9"j0NO N`p#J9f`09BB9Byo09y>N8Ry09yS@H@B@H@49H°l,>NpRySyjD09y`609y>N09yS@>09y?NTvJfFO LNuQJ9gJ9f`N^J9f`p# yf`zJ9f 309yg"3>N2p`009y yl33PNuJ9fNup#09BB9ByfNuJ9f 309yS@49HH@B@H@gd09yS@309BB9Byl099B309y?N6Tp`f09y09BB9Byl099B309yR@3 yl3NuQJ9gJ9f`tNvJ9f`fp# yf`RJ9f 3p330yp09np`PNuJ9fNup#J9f 309BB9B30@p09o0y49HH@H@op`09yR@3NuDelVar NV-J4|$RACp`Q.Hn j NXA.N$nN^Nu%s%s:DelVar %sVariable "%s" does not contain useable data. A default value of %s has been set.MEPro Advisory%s,%sNVH 4|$R&j$&S> ?. 9/NC""""""""p./.Hn j NA.N>HnNOJg"j$.?.NTJfJgTC.Hn/.HzHn"jLNC.N.HnHzHn"jLNC.HzNO `&C.HnHzHn"jLNO C.N"N"j$"L N^NuH0OvEG`>> B@? /N\C""""""""Jo f B@>NRRC09BB9B@oO$L NuAnalysis ErrorH 4|$RHy?<7?< jNP6gt?<?<Hz?<p???<? jNO8g"//?<?<?<?<? jNO8JDgHxHxp??? jNO? j\NTLNuNup#Nu3NNNuType TType EType JType KType SType RType BTemperatureEMFTypeT, E, J, K, S, R, or BKnownTemperature or EMFTempTemperature300EMFElectromotive force10TempTemperature300EMFElectromotive force10MaterialMaterials usedRangeOperating Range InformationErrorError Information @@8ts?D92H ?@R8I?DV?DTp?"v`P@?6$t 8?8d$ ?()xQ?(4?H2T6@?4th0?`?yyX`@@8ts?3 ? qAdP!X40?U0u?Ee37P'ahx@?CU3y 2T&TrPU'@?%faHi?"D5P @@XiXWy?QfupPDe&4p4bpPHqhBpePDpg7PxE5RWQXR `IP!8x pyc0CgH@@XiXWy?C EF ?W"X ThP?BY"$`?#8!EbP?%V'Ip@?(xW u@?%%" r@?TWf@@P7'Sp?0BT(@fPF@?4%sP$`?A`9D@)rQw20@2d!P2!t#?hx1#u @?8P3%'%c@?270` ?7@Q7@@9GT3?'FRQVTq` 9 $Xp@$uy`XRv0Yr!%Ph!`8'7@S0c'0@8Da ?dQT5`xp#tD?"WUp5p1%?)) `Hy?"#t3`@?2uCCBIBy@?%'`4#?U5 ?r @@SW4`?Qp"Dp?(E!d"DT@?Af`)DaP@7U("?E9 @?A@H $W?'(!@@R? p$S#0?6 YPDdP`?8IvP7&AU&AP@Ftp?)"r0&`Xap@?%4 ECy?%@I5vy@$gF?Y!i0q#C?!PIu1uxr?$gC퐒H?)p@?F%PTbb?sqq"6eEMFTempMateria,Range,ErrorY> N>N @f.`&.N.NXNuNNNu"-8 to 6 C"Error"0.15 to 0.17C"Error"-270 to 400 C"Range:"Cu / Cu-Ni"MateriaDelVar Error"-9 to 6 C"Error"0.05 to 0.04 C"Error"-270 to 400 C"Range:"Ni-Cr / Cu-Ni"Materia"-210 to 1200 C"Range"-0.4 to 0.5 C"Error"-3 to 4 C"Error"-200 to 760 C"Range"Fe / Cu-Ni"Materia"-270 to 1372 C"Range"-11 to 8 C"Error"-2.4 to 1.2 C"Error"-270 to 1370 C"Range"Ni-Cr / Ni-Al"Materia"-50 to 630.74 C"Range"-11 to 3 C"Error:"-50 to 900 C"Range"Pt / 10%Rh-Pt"Materia"-50 to 1064.43 C"Range"-13 to 3 C"Error:"-50 to 900 C"Range"Pt / 13%Rh-Pt"Materia"-50 to 130 C"Error"0 to 1820 C"Range:"Pt-30%Rh / Pt-6%Rh"MateriatempEMFtempNVHx4|$Rp(>N6>N:(j$(TN Ef0>N-n-n=nNI@'1P`.>N-n-n=nN9@0HSk nЀ0;Nf8> EfN i lGJv`4Gv `,N ilGv.` GBv.N.` Ef"N i lGFv`Gv .`&N ilGv.` G8v.N.` Ef,N @vi lG2v`Gzv.`2N ilGv.` Gv.N.N.`. Ef$N i lGv `Gv x.`2N ilG\v.` Gv.N.N.` Ef,N @c@i lGnv`Gv.` Gv.N.`t Ef,N @c@i lGv`Gv.` Gv.N.`& EfG*v `G|v.N.N0 A-X-X=XUC< p `N:#HshN3SCJCj Ef&>"j NJg>?<"j N>"j N.N>?<"j N>?<"j N>z?<"j N>!"jN>"j N>?<%"j N>?<}"j N>?<"j N/./.?."j (NO>"j N`/./.?."j (NO B-|=|@/./.?."j (N>"j N"j$."j"j N"j$."jN6Nf CfF>NJfE`z>NJfE`d>NJfEz`P.`B>NJfEj`4>NJfEd` >NJfE^` .N g .NJN`NXLNu@ ,@*b0;AD(! $@@@  w` 1D`` r@AA``@@w  #@@@ @`@@0 0nd YY!!!!!!!!!!!!Input TypeCircuit Config.ZZ1_Y Impedance ()4ZZ2_Y Impedance ()5ZZ3_Y Impedance ()20ZZA_ Impedance ()50ZZB_ Impedance ()40ZZC_ Impedance ()10ZZA_ Impedance ()50ZZB_ Impedance ()40ZZC_ Impedance ()10ZZ1_Y Impedance ()4ZZ2_Y Impedance ()5ZZ3_Y Impedance ()20 ZZA_,ZZB_,ZZC_ZZ1_,ZZ2_,ZZ3_H ?< N?<NX @fHz`vE(0|\2@RDRCHoHzN؜XLNu(ZZ1_*ZZ2_+ZZ2_*ZZ3_+ZZ1_*ZZ3_)/ZZ1_ZZA_:(ZZ1_*ZZ2_+ZZ2_*ZZ3_+ZZ1_*ZZ3_)/ZZ2_ZZB_:(ZZ1_*ZZ2_+ZZ2_*ZZ3_+ZZ1_*ZZ3_)/ZZ3_ZZC_(ZZB_*ZZC_)/(ZZA_+ZZB_+ZZC_)ZZ1_:(ZZC_*ZZA_)/(ZZA_+ZZB_+ZZC_)ZZ2_:(ZZA_*ZZB_)/(ZZA_+ZZB_+ZZC_)ZZ3_Nٚ?<NT @fHz`Hz|NXNڞNuImpedance CalcsCircuit PerformanceWye  ConversionEE for ME'sDischarge coefficient00.71SoCross sectional area of orifice00.310HFluid head0425 QVolume discharge rate02100 VVelocity06100?<NTNuMEPro 1.01 Advisory>1 is not physically meaningful.MEPro 1.01 AdvisoryCaution, possible underflow.QVQ,VMEPro 1.01 ErrorSorry, overflow.NVH 4|$RB-|e=|@N?<N-n-n=n?<N-n-n=n?<N\-n-n=nN oN0oN@op`pfrN:EN9@ /./.?."jNO -n-n=nN:4N:-n-n=nN*0-n-n=nN C癙lN C癙lp`pfN @ioHzHzNPN <mN <ilHzHzNP&j$&S/./.?."j (N"j$/HzN/./.?."j (N"j$/HzNO$"j$"`NaC-n-n=nJgRHzNXNN C癙lN C癙imHzyHzcNP`NռL N^NuDischarge coefficient00.71SCross section area of tank0110SoCross sectional area of orifice, 1 is not physically meaningful.MEPro 1.01 AdvisoryCaution, possible underflow.ttMEPro 1.01 ErrorOrifice size > tank cross sectionMEPro 1.01 ErrorFluid head at t >= head at t=0MEPro 1.01 ErrorSorry, overflow.NVH 4|$RB-|e=|@NѬ?<N-n-n=n?<N-n-n=n?<N-n-n=n?<N-n-n=n?<NO -n-n=nN o@N0o6N@o,NPo"N`oN 4mN eop`pf/./.?."jNO /./.?././.?."jNO /./.?.N9@ /./.?."jNO -n-n=n-n-n=nN:0N:-n-n=nN9@ N*-_-_=_HWNI0 N:N C癙lp`pfN @ioHzHzNPN <ilHzHzNP&j$&S/./.?."j (N"j$/HzNO"j$"`NaGJg|HzNXNLN 4ilHzHzNP`JN einHzHzNP`,N C癙imHzHzNP`NL N^NuDischarge coefficient00.71SoCross sectional area of orifice00.310DlDiameter of Cone-Bottom0110H1Fluid head at t=00210H2Fluid head at t 1 is not physically meaningful.MEPro 1.01 AdvisoryCaution, possible underflow.tMEPro 1.01 ErrorSorry, overflow.MEPro 1.01 ErrorH2 must be less than H1. NV`H 4|$RB-|e=|@Ap 0-|SY-|1AY&=|@Af 0N˔>N-n-n=n>N-n-n=n>N-n-n=n>N-n-n=n>NA 0>N-n-n=nN oBN0o8N@o.NPo$N`oN ToN &fnp`pf-n-n=nNJWN)@ /./.?."jN-n-n=n/./.?."jN-n-n=nA-X-X=XN9 N:N)?PA 0B-|%=|@/./.?././.?."j NN:`N:`N)@%Az 0B-|=|@/./.?././.?."j NN9 N:`-n-n=nN3N)@Ap-X-X=XN3/./.?."jNOFN:#N:N3/Af-X-X=X _N*1A-X-X=XN zN`N:-n-n=nN C癙lp`pfN @io.HzNXN <il.HzNX&j$&S/./.?."j (N"j$.HzNO"j$"`NaCJgVNN C癙im.HzMNX`$N Eim.HzPNX`NȈL N^NuDischarge coefficient00.71VoVelocity of approach01100HFluid head0210bWidth of Weir0110 QVolume discharge rate02100?<NTNu2/3*b**(2*9.80665)*((H+Vo^2/(2*9.80665))^1.5-(Vo^2/(2*9.80665))^1.5)QMEPro 1.01 Advisory>1 is not physically meaningful.MEPro 1.01 ErrorNegative or 0 input!NV-CNB>N-n-n=n>N-n-n=n>N-n-n=n>N-n-n=nN o"N@oN0oNPop`pJf6.NN @i,o*.HzNX`.HzNXNŀ&.N^NuDischarge coefficient00.71Angle013.14HFluid head0110 QVolume discharge rate02100?<NTNu8/15**tan(/2)*(2*9.80665)*H^2.5QMEPro 1.01 Advisory>1 is not physically meaningful.MEPro 1.01 Error must be < 3.14 radiansMEPro 1.01 ErrorNegative or 0 input!NV-CN|>N-n-n=n>N-n-n=n>N-n-n=nN o,N0o"N@oN @1@lp`pJf6.NN @iNoL.HzNX`8N @1@im .Hz` .HzNXNª&.N^NufDischarge coefficient00.71HFluid head0110bWidth of Weir0.810VVelocity01100 QVolume discharge rate02100?<NTNu3.31*b*(H+f*V^2/(2*9.80665))^1.5+.007*bQMEPro 1.01 Advisory>1 is not physically meaningful.MEPro 1.01 Error 0 or Negative input!NV-CN>N-n-n=n>N-n-n=n>N-n-n=n>N-n-n=nN o"N0oN@oNPop`pJf6.NN @i,o*.HzNX`.HzNXN&.N^NuHFluid head0210bWidth of Weir0110 QVolume discharge rate02100?<NTNu3.367*b*H^1.5QMEPro 1.01 Error 0 or Negative input!NV-CNx>N-n-n=n>N-n-n=nN oN0op`pJf.N`.Hz`NXN*&.N^NufDischarge coefficient00.71H1Fluid head at t=00110H2Fluid head at t00.910bWidth of Weir0110 QVolume discharge rate02100?<NTNu2/3*f*b*(2*9.80665)*(H1^1.5-H2^1.5)QMEPro 1.01 Advisory>1 is not physically meaningful.MEPro 1.01 ErrorH2 must be less than H1. MEPro 1.01 Error 0 or Negative input!NV-CN>N-n-n=n>N-n-n=n>N-n-n=n>N-n-n=nN o,N0o"N@oNPoN 5np`pJf..NN @i8o6.Hz`"N 5im .Hz` .HzNXN&.N^NuDischarge coefficient00.71H1Fluid head at t=00110H2Fluid head at t00.910LLength of Cylinder0110DDiameter of Cylinder0110SoCross sectional area of orifice00.110KsSpace Factor0.10.5.9 QVolume discharge rate02100 tTime0601000?<NTNutQMEPro 1.01 AdvisoryKs or >1 is not physically meaningful.MEPro 1.01 ErrorH2 must be less than H1. MEPro 1.01 ErrorH1-H2 must be less than D/2. MEPro 1.01 Error 0 or Negative input!NVH 4|$RN>N-n-n=n>N-n-n=n>N-n-n=n>N-n-n=n>N-n-n=n>N-n-n=n>NA 0-n-n=nNJpA 0N oN0oxNPolNpo`N@oVN`oLN o@N o4-n-n=nN)@ N op`pJf|Na/./.?././.?."j N-n-n=n-n-n=nN9 NJ/./.?."jNN:N3/./.?."jN/./.?././.?."jNO /./.?.B-|a3=|@/./.?."jNO N:&N:N3N*d-_-_=_HWNI0 N:B-|@=|@/./.?././.?."j N/./.?.B-|%`=|@/./.?././.?."j NO-n-n=nHWN93 N9?%@&j$&S/./.?."j (N"j$.HzN/./.?."j (N"j$.HzNOX"j$"N @n*/A-X-X=X _N @ifod.Hz2`PN in .HzU`6N)@ N %in .HzU` .HzyNXNbL N^Nu Rectangular NotchTriangular WeirSuppressed WeirCipolletti WeirASME WeirsConst. Liq. LevelVarying Liq. LevelConical VesselHorizontal CylinderLarge Rect. OrificeASME WeirsEffluxNuINVALID_SOLVE_ARG1_ERRORUndefined var errorUnreal result errorDomain errorOverflow errorUnrecognized error/N0//NX6 CfN<`0 @ ng@ @gJoh @@fb` @>gJoX @g`PHz:H/N`NHzCH/N`>HzGH/N`.HzKH/N`HzHH/N`HzGH/NPN&NubBase3hHeight2 AreaArea6 yy1Displacement of axis 111.5 yy2Displacement of axis 221 I11Area moment of inertia-axis 112 I22Area moment of inertia-axis 224.5 IpPolar moment of inertia5.7 rg1Radius of gyration 10.58 rg2Radius of gyration 20.871 A! ! A qR!A!q!A!A!Aq!!A!AAA!!L@A!!AQ AA!!AQ AAA!!]BA!!1A!AAA!!"TAB@A!!A!AA!!A!AAA!!A!A!*$AA!!AQ AA"1$AA!1!{}]AQ u}"1!A!HR@A"Qq!\AA!qQA!A!A!AA!!A!A!A!!AAaQ!!Aq!!AAaQ!!A!A!A!!$$@!!A!AA!!A!AAA!!Aq!!!A!A!q!A!1 HaAQ!!QQ!!q1AQABQ!!qAA! A BBA!A QAA!!A1QqQ1!A1A! x7?<N= base.MEPro 1.01 AdvisoryInside height is >= height.NVN?<N-n-n=n?<N-n-n=n?<N-n-n=n?<NP-n-n=nN BioN Sio HztNX`= outside.NVNp?<N-n-n=n?<NXN 0il Hz0NX`HzHz~NPNZN^NudDiameter 1tThickness .05 AreaArea yy1Distance along axis 1 10 I11Area moment of inertia-axis 11 IpPolar moment of inertia rg1Radius of gyration 1 10*d*tArea:d/2yy1:*d^3*t/8I11:*d^3*t/4Ip:(I11/Area)^.5rg1:HzNXNubBase 1hHeight .5offOffset .1cTop .5 AreaArea yy1Distance along axis 1 10 yy2Distance along axis 2 10 I11Area moment of inertia-axis 11 I22Area moment of inertia-axis 22 IpPolar moment of inertia rg1Radius of gyration 1 10 rg2Radius of gyration 2 10h/2*(b+c)Area:h/3*(2*b+c)/(b+c)yy1:(2*b^2+2*b*c-off*b-2*off*c-c^2)/(3*(b+c))yy2:h^3/36*(b^2+4*b*c+c^2)/(b+c)I11:h/(36*(b+c))*(b^4+c^4+2*b*c*(b^2+c^2)-off*(b^3+3*b^2*c-3*b*c^2-c^3)+off^2*(b^2+4*b*c+c^2))I22:I11+I22Ip:(I11/Area)^.5rg1:(I22/Area)^.5rg2HzN(XNu!!Y1q!Q!!!!A!A!1"!AqA!AA!A!AAa!1!Q!!AA!A!!A!1q!!A" A! 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A ! q!  q Aj8 bWidth of top flange.5tThickness of top flange.02b1Width of bottom flange.75t1Thickness of bottom flange.03dHeight of the fin.3twThickness of the fin.02 AreaArea yy1Distance to bottom10 yy2Distance to side10 I11Area moment of inertia-axis 11 rg1Radius of gyration 110?<NTNub1*t1+b*t+tw*dArea:1/2*((tw*(d+t+t1)^2+(b1-tw)*t1^2+(b-tw)*t*(2(d+t+t1)-t))/(tw*(d+t+t1)+(b1-tw)*t1+(b-tw)*t))yy1:d+t+t1-yy1yy2:1/3*(b1*yy1^3-(b1-tw)*(yy1-t1)^3+b*yy2^3-(b-tw)*(d+t1-yy1)^3)I11:(I11/Area)^.5rg1Hz&N4XNu  `???` @(@ (@*@ @ U*@ @ @ @ @ @ @ @ @ @ @ @ ࿪*U@ @  @ @ p@ @@ *@ @  @ @  @ @  *H H  PP ??PP@H H @@ @ `@ @ P@ @@ *`@ @ @ @  W* @   @  p@   @  @ p@ *W*@D@  @*% @(p @$D ?    3 bWidth of top flange.5tThickness of top flange.02dHeight of the fin.5twThickness of the fin.02 AreaArea yy1Distance to bottom10 yy2Distance to side10 I11Area moment of inertia-axis 11 I22Area moment of inertia-axis 22 rg1Radius of gyration 110 rg2Radius of gyration 210?<NXTNu2*b*t+tw*dArea:d/2+tyy1:b/2yy2:b*(d+2*t)^3/12-(b-tw)*d^3/12I11:b^3*t/6+tw^3*d/12I22:(I11/Area)^.5rg1:(I22/Area)^.5rg2HzNPXNu bWidth of top flange.5tThickness of top flange.02dHeight of the fin.5twThickness of the fin.02 AreaArea yy1Distance to bottom10 yy2Distance to side10 I11Area moment of inertia-axis 11 I22Area moment of inertia-axis 22 rg1Radius of gyration 110 rg2Radius of gyration 210?<NTNut*b+2*tw*dArea:(b*t^2+2*tw*d*(2*t+d))/(2*(t*b+2*tw*d))yy1:b/2yy2:b/3*(d+t)^3-d^3/3*(b-2*tw)-Area*(d+t-yy1)^2I11:(d+t)*b^3/12-d*(b-2*tw)^3/12I22:(I11/Area)^.5rg1:(I22/Area)^.5rg2HzDNXNu AA!A!AAq!A!AAQQAR@@@Aq@@PPPA@@@Aq@@APPP@@@Rqm*mamaqaamqaaqaa*mRAQ!A !AAA!AQAA93 bWidth of top flange.5tThickness of top flange.02dHeight of the fin.5twThickness of the fin.02 AreaArea yy1Distance to bottom10 yy2Distance to side10 I11Area moment of inertia-axis 11 I22Area moment of inertia-axis 22 rg1Radius of gyration 110 rg2Radius of gyration 210?<NTNut*b+tw*dArea:(b*t^2+tw*d*(2*t+d))/(2*(t*b+tw*d))yy1:b/2yy2:b/3*(d+t)^3-d^3/3*(b-tw)-Area*(d+t-yy1)^2I11:t*b^3/12+d*tw^3/12I22:(I11/Area)^.5rg1:(I22/Area)^.5rg2HzVNXNu aSide length10nNumber of sides 6 AreaArea Angle0/6/2 1Radius to point10 2Radius to line10 yy1Distance along axis 1 10 yy2Distance along axis 2 10 I11Area moment of inertia-axis 11 I22Area moment of inertia-axis 22 rg1Radius of gyration 1 10 rg2Radius of gyration 2 10?< NdTNuMEPro 1.01 Error n must be > 2/n:a^2*n/(4*tan())Area:a/(2*sin())1:a/(2*tan())2:1/24*Area*(6*1^2-a^2)I11:I11I22:(I11/Area)^.5rg1:(I22/Area)^.5rg22yy1:1yy21yy1:2yy21*cos(*(n+1)/2-/2)yy1:yy1yy2NV-CN>NNZNd Cl.HzNXN`P.Nͮ0j D@@D@`@J@f.`$JCj DCCDC`CJCf.`.Nh&.N^Nu A!AQ1q 1"1 A!QqRqA!1!1 aAARqa1AqA!1A1!A!!!aqAQ!!1E`eB!OB11aA1AQ"A"92%!` d@A@@G$a1A1AEA !A1@&L!!!a(!AAqAAAAA!1A!!`A!1!!AaACAAaA1AQ!1A!Aa!Aa!qAQAa R B 2 1a! " q! q 1" !a !! 1!1B1q !1!a !1@a  !1a1a!"1BadA!!!!aAA!Q!1!AAA1qa1! !a ! 1A 1 AAA A! Aa a! !a AA !1 AA 1 a 1!a11AAa!q!1: aSide length10nNumber of sides 6tThickness10 AreaArea Angle0/6/2 1Radius to point10 2Radius to line10 yy1Distance along axis 1 10 yy2Distance along axis 2 10 I11Area moment of inertia-axis 11 I22Area moment of inertia-axis 22 rg1Radius of gyration 1 10 rg2Radius of gyration 2 10?< NJTNu/n:n*a*t*(1-t*tan()/a)Area:a/(2*sin())1:a/(2*tan())2:n*a^3*t/8*(1/3+1/(tan()^2))*(1-3*t*tan()/a+4*(t*tan()/a)^2-2*(t*tan()/a)^3)I11:I11I22:(I11/Area)^.5rg1:(I22/Area)^.5rg22yy1:1yy21yy1:2yy21*cos(*(n+1)/2-/2)yy1:yy1yy2NV-CN>NNZNd.NŘ0j D@@D@`@J@f.`$JCj DCCDC`CJCf.`.NR&.N^Nu RectangleHollow RectangleCircleCircular RingHollow CircleI Section-UnevenI Section-EvenC SectionT SectionTrapezoidPolygonHollow Polygon Section PropertiesNameProject namet0Investment (t=0)t1Cash flow (t>0) ProjectProjectkDiscount rate / period (%)PaybackPayback periodNPVNet present valueIRRInternal rate return (%)PIProfitability indexMultiple GraphsGraph multiple projects simultaneously?Full Screen GraphGraph on full or split screen?CashHzNXNuH8Q4|$R&j$&SNylp`X69SC j$S` j$. j(N"H j$ 0SCJ@n j$. j(N(Hc ./ j NX"j$ep`pPLNuDuplicate project variable name.ProjectNVH<84|$R j$"P -f j$ PJ(fp`pABCJg Cg Cf>N`H&j$&SN8:9SEfJ(j$(TT. j NJ@g^. j NvK0R@yg80 "M./ "j NXJ@f"j$".RCH/Np`RC C lH`>"j N.N"j$S090@>"j N>"j N>-"j Np .09S@C / Hn"j N|p ./ 09S@C / "j N09C "j$U"09S@C .Hy"j NOSD>?<?NX(j$(TS6` ."j(N(H0SCJ@n."j(N*H./ "j NX(j$(TJEf2>"j N09S@C .N>-"j N`./ "j(NX/"j NX./ "j N"j$.HyNP"j$"JEf$C.HyNXJf C.NpL<8N^NuDelDECDelH8Y/4|$R(j$(TN8 yoyl j$ .N`Jg&j$&SS69` . j(N&H0SC @n. j(N./ j N.?<N"j$.HyNO >NSD3`N09yn"j$"AXLNuAddDECAddH"j`"jN./ "j N"j$.HyNP>NRD>N yovGp`RCyoRy09yS@H@B@H@49H°lNp"j$"AXL<NuDECFnOffToo few cash flowsCF0FnOff(P1CF[t]/(1+x/100)^t,t,1,P1N)+P1CF0y91(x):y91(50)ymin:y91(15)ymax(P2CF[t]/(1+x/100)^t,t,1,P2N)+P2CF0y92(x):y92(50)ymin:y92(15)ymax(P3CF[t]/(1+x/100)^t,t,1,P3N)+P3CF0y93(x):y93(50)ymin:y93(15)ymax(P4CF[t]/(1+x/100)^t,t,1,P4N)+P4CF0y94(x):y94(50)ymin:y94(15)ymax(P5CF[t]/(1+x/100)^t,t,1,P5N)+P5CF0y95(x):y95(50)ymin:y95(15)ymax(P6CF[t]/(1+x/100)^t,t,1,P6N)+P6CF0y96(x):y96(50)ymin:y96(15)ymax(P7CF[t]/(1+x/100)^t,t,1,P7N)+P7CF0y97(x):y97(50)ymin:y97(15)ymax(P8CF[t]/(1+x/100)^t,t,1,P8N)+P8CF0y98(x):y98(50)ymin:y98(15)ymax(P9CF[t]/(1+x/100)^t,t,1,P9N)+P9CF0y99(x):y99(50)ymin:y99(15)ymaxFnOn 9 15xmin:50xmaxDispGPxlText "",26,4:PxlText "",44,4k(%)NPVGraphNVH4|$RJ. g.?<NT&j$&SJ9f.NNU@6> ?<?9NX Cl"j$".H/NX|P090@|.Hn"j N"j$"QS."j(N"j$""j$.HnN"j$."j(N"j$">"j N|"j$.HnN"j$"|N|>"j N>"j N>"j N"j$.HnNO"j$" 9g .N09HSk$ nЀ0;N$*06<BI`.I`(I`"IT`I`I`I` IX`IN 9gN`N.N.Hn"j NX090@C.N.NvC."jPN8f&j$&S.N.N>"jN>"jN>"j N.N.N.N>-"j N>O"j N>"j N"j$."j"jN>#"jN>"j N.N>-"j N>O"j N>"j N"j$."j?"jDNT 9fJg0"jt0yg>?9"jPNTN` "jdNN>NAZLN^NuH8Y4|$R&y69IBD#3>N3#3A09S@A .Hy j NX&j$&S.Ng j$"P gp`pJg v&j$&SS` . j(N&HRC gR` j$ > j N>"j N.N>-"j N>"j N"j$.HyNXv0XLNuData Error. Reinitializing project.Name: t%d: NVH<8.(n 4|$R*j$*UNz6yl<.H/NX"j$".N>NN>6Co`6"j$ Q f"j$S`"j$."j(N"j$"0SC @n"j$ Q -f"j$."j(NT&H`&j$&ST"j$."j N."j N6 DfDCCH.Hz/ "j NP`,UD>HzHn"jLNDCCH.Hn/ "j NO."j ND./ / "j N"j$"L<N^NuQp#####3A##>NNNPNuCashH04|$RJ/g&j$&SNS@6 j$ JCjv##p33####?<?<?NR@?NPvE0|pRCHovEG0|pRCHoNC##pAL NuNVH 6.4|$Rj"VBB3|@` j$"P g"VBB3|@` j$ PS. j(N&Hx`" f"VBB3|@`p. j(N&H0RDCm$jB@ e c( f K +g K ,g"VBB3|@`.N"V#n#n3nL N^NuPayback,NPV,IRR,PIHzNXNuclrdraw:clrgraphHzNX @NukkToo few cash flowsInvalid EntryInvalid EntryPaybackNo PaybackPaybackNPVPINA since CF0>=0PIsolving for IRR nowCF0CFnIRRnSolve((CF[t]/(1+IRR/100)^t,t,1,n)=CF0,IRR=k)IRRMEProbmeansmeanstypmeinputsIRRNA since CF0>=0NVhH<84|$R j$-P.NJf< j$ BB=|@/./.?. j (N"j$.HzNO"j$.N-n-n=nNU@6 Cl"j$".H/NX"j$"QS."j(N*H#3.?<NTJf6.?<N#3p#"j$"`xI-|G`J."j(N*H.?<NTJf..?<N n 6p#"j$"`Z0RDCo#3>N8-n-n=n-n-n=n-n-n=nx*N9?N@NaN*EB-|=|@`HRD>N-n-n=nN i l RENBN:VN:dNCCm&j$&SN il.HzNX`nNb>N4Ng>N$N*NJ$N@ilBB=|@/./.?."j (N"j$.HzdNO/./.?."j (N"j$.HzFNONpim.Hz*NX`>NJsNzqN*/./.?."j (N"j$.HzNO"j$"#"j$"QS."j(N"j$""j$.HzN"j$."j(N"j$">"j N"j$.HzN"j$">"j N>"j N>"j N"j$.Hz|N.N>"j NGb>"j N.N>-"j N"j$.HzpNO.N.N.N.NNpil"j$."jN8 @g @g`K#IG`KEIR>N6 Cf0<`0< Nb>N-n-n=n&j$&SBB=|@N0i@n>.N0 @g @g `.`.N"KR./ N`0 @g @g`N 2ioNa/./.?././.?."j N/./.?.Na/./.?././.?."j NOHWNI0 /./.?."jNO-n-n=nNJ-n-n=nN: N9@1AY&SYN3N*-n-n=n`Na@`N 2inolNa/./.?././.?."j NO-n-n=nN9@ -n-n=nN*`Na@-n-n=nNPio/./.?."j (NO `>*"j N.HzNX"j$./ NX"j$"NL<N^Nu@@ ?  @@   @ @D@A@@@ @@@ @ @@ @(P@ @@C ?@d@(P @ (P @JZkJJP`ps9/?<N6?<NXp@fN\&NuMEPro 1.01 AdvisoryPs > 22.08 or < .006113 MpaNV-J/A-X-X=X _4|$RN ?amN @"io.HzzNXNN @3i:l8B-|Bgv=|@B-|8p=|B-|T=|`6B-|8u=|B-|Xu=|B-|%x =|/./.?."jNNPN*NC"V#n#n3n$nN^NuTempTemperature1004001000PsSaturated pressure.01.120 TsSaturate temperature1004001000 VsSpecific Volume01100 HEnthalpy100011000 SEntropy100001010000?<NTNuMEPro 1.01 AdvisoryTs > TTsVsHSNVDH 4|$R&j$&SN>N-n-n=n>N-n-n=n/./.?.NO -n-n=nN $il.HzLNXN/./.?."j (N"j$.Hz>N"j$"B-|F1=|?A$ 0B-|Ry=|?A` 0B-|5y(=|?AB 0B-|"=|?A 0B-|7A7=|B-|G=|B-|44=|?A 0B-|@=|@Na/./.?././.?."j NN:'NuN9 N/./.?."jN-n-n=nNy!BN:A/./.?."jN-n-n=n-n-n=nNJAN*a/./.?."jN-n-n=n-n-n=nN9!$N*1N9%`NJQ/./.?.-n-n=nN3 NaN*/A-X-X=X _NJqN:N:eHWN5 /./.?."j (N"j$.HzN"j$"B-| A!=|@B-|@@=|Az 0B-|H P=|Ap 0B-|i0=|@B-|Tr=|?A 0B-|uSp=|?A 0B-|3p=|?Af 0B-|us`=|A 0B-|(t =|A 0B-|=|@A 0B-|A=|A 0B-|btb=|?A 0B-|(BY=|A 0B-|dV=|?A 0B-|E=|@-n-n=nN9 zN-n-n=nN9 pN:0N-n-n=nN9 N-n-n=nN9 N:0N-n-n=nN9 N f-n-n=nN9!N:1NA 0Na/./.?././.?."j N/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO-n-n=nN9!N!N9 N-_-_=_N9 N-_-_=_N9 NAt 0-n-n=nNJ@N*`/./.?."jN/./.?.Na/./.?././.?."j NON:GNuN9 N-_-_=_N9 tNJ/./.?."j (N"j$.HzN"j$"B-|F)a=|@B-|9=|?B-|sP=|A~ 0B-|T4=|?Aj 0B-|pFP=|A 0B-|FP0`=|AV 0B-|=|?A8 0B-|w@=|@AL 0B-|F=|A. 0B-|hTE=|?A\ 0B-|B@=|AR 0B-|B =|?AH 0B-|=|@-n-n=nNJ@N*`/./.?."jN/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.N3 N#8/./.?."jNO /./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NON:GNuN9 ~N-_-_=_N9 jN-_-_=_N9 N-_-_=_N9 VNN9".N"L-_-_=_N9 \N-_-_=_N9 RN-_-_=_N9 HNHWN92 NJ%/./.?."j (N"j$.HzzNO"j$"NL N^NuTemperaturePressureKnownTemperature or PressureTsSaturated Temperature1004001000PsSaturated Pressure.01.120 TsSaturated Temperature1005001000 PsSaturated Pressure.01.120 VfSpecific Volume -liquid01100 VgSpecific Volume -vapor 01100 HfEnthalpy -liquid100011000 Hfglatent heat of vaporization100011000 HgEnthalpy -vapor100011000 SfEntropy -liquid100001010000 SfgSg-Sf100001010000 SgEntropy -vapor100001010000 UfInternal Energy -liquid100001010000 UgInternal Energy -vapor100001010000TsMEPro 1.01 AdvisoryTs < 273.16 or > 647.3 KPsVfVgHfUfHfgHgUgSgSfSfgNVH 4|$RB-|ds=|@Nf &j$&SN>N @fd>NA> 0/.D/.@?.>N|A 0/./.?."j (N"j$.HzNO`>NA 0A-X-X=XN @'1`m*/A-X-X=X _N @dsio.HzNXNB-|E=|@A 0B-|@H=|B-|Au =|B-|6=|?B-| =|B-|S=|?B-|6h=|?Ap 0B-|=|A 0B-|w=|?A 0B-|=|?A 0B-|9h=|A 0B-|9W5=|@Na /./.?././.?."j N/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NON9"N"N:N2HWN94 NBHWN96 NbHWN95 NR-_-_=_N9 pN-_-_=_N9 N-_-_=_N9 N-_-_=_N9 NA-X-X=XNJp/A-X-X=X _N*N/./.?."jNA> 0/.D/.@?.>"j (N"j$.HzmNO,"j$"Ng" NI"N'" B-|=|@A 0B-|8=|A 0B-|Q=|@A 0B-|xF@%=|AL 0B-|8a@=|B-| X"8=|@B-| =|B-|=|?B-|GTB=|?B-|1U=|?A 0Na/./.?././.?."j N/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.B-|P=|?/./.?././.?."j NO/./.?.-|3333-|333=|?/./.?././.?."j NO/./.?.-|3333-|3333=|?/./.?././.?."j NON9 N -_-_=_N9!N-_-_=_N9!LNN:#N0HWN94 N@HWN95 NPHWN97 NpHWN96 N`N9 A 0/./.?."j (N"j$.HzN"j$"B-|=|@A~ 0B-|5W=|@A 0B-|RXE=|@A 0-|0-|DiFV=|AB 0B-|u=|B-|CU0=|B-|v=|B-|6vS=|@B-|F$7=|B-|1U=|?A 0B-|"=|@A 0Na/./.?././.?."j N/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.B-|P=|?/./.?././.?."j NO/./.?.-|3333-|333=|?/./.?././.?."j NO/./.?.-|3333-|3333=|?/./.?././.?."j NON9 N ~-_-_=_N9!N-_-_=_N9!BNN:#N0HWN94 N@HWN95 NPHWN97 NpHWN96 N`N9 N9 N) >A 0/./.?."j (N"j$.HzNOD"j$"B-| 0=|@A 0A-X-X=XN,il-|p-|bF=|@-|-|#C6=|-|-|=|-|-|qb=|@-|-|55"=|-|0-|e1 =|@Af 0-|P-|dxTX=|A 0Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NON:#N:NCHWN95 NSHWN97 NsHWN96 Nc-_-_=_N9 fN-_-_=_N9 N`A-X-X=XNXil-|-|9#=|?At 0B-|&q)5=|-|P-|b&@=|@-|0-|W=|-|`-|"C=|-|0-|hy7e=|@-|`-|H=|A\ 0-|@-|r5@=|@A 0Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NON:#N#tN:NCHWN95 NSHWN97 NsHWN96 Nc-_-_=_N9 \N-_-_=_N9 N`Na-|P-|DW=|-|p-|U"UQ=|A 0-|p-|d9=|@-|P-|Exy=|-|0-|t=|Na/./.?././.?."j NO/./.?.B-|P=|?/./.?././.?."j NO/./.?.-|3333-|333=|?/./.?././.?."j NO/./.?.-|3333-|3333=|?/./.?././.?."j NON:Nu-_-_=_N9!NHWN96 NeN:#N5HWN94 NE-n-n=nN9#/./.?."j (N"j$.HzNA>-X-X=XN9 NJ/./.?."j (N"j$.HzN"j$"B-|w!=|?A 0B-|F&h=|@A 0B-|y1=|A8 0B-|8tF=|B-|)ES=|@B-|c=|B-|V3=|@B-|`(=|B-|%=|@A 0Na/./.?././.?."j N/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.B-|P=|?/./.?././.?."j NO/./.?.-|3333-|333=|?/./.?././.?."j NO/./.?.-|3333-|3333=|?/./.?././.?."j NON9 -_-_=_N9!N-_-_=_N9!8NN:#N0HWN95 NPHWN94 N@HWN97 NpHWN96 N`N9 /./.?."j (N"j$.Hz>N"j$"B-|=|@Aj 0-| -|Ext4=|?A 0-|-|PA(=|@A 0-|@-|$=|A. 0-|@-|HQ=|-| -|&y=|@-| -|sdT=|-|-|Iah=|@-|`-|Th@=|B-| 0=|@A* 0Na/./.?././.?."j N/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.B-|P=|?/./.?././.?."j NO/./.?.-|3333-|333=|?/./.?././.?."j NO/./.?.-|3333-|3333=|?/./.?././.?."j NON9 N j-_-_=_N9!N-_-_=_N9!.NN:#N0HWN94 N@HWN95 NPHWN97 NpHWN96 N`-n-n=nN9#*/./.?."j (N"j$.HzNA>-X-X=XN9 NJ/./.?."j (N"j$.HzAN"j$"B-|=|@A` 0B-|7s=|?A 0B-|'h=|A 0B-|i15=|@A$ 0B-|CH9=|B-|Fr=|@B-|Rb=|@B-|b"=|B-|=|@Na/./.?././.?."j N/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.B-|P=|?/./.?././.?."j NO/./.?.-|3333-|333=|?/./.?././.?."j NO/./.?.-|3333-|3333=|?/./.?././.?."j NON9 N `-_-_=_N9!N-_-_=_N9!$NN:#N0HWN94 N@HWN96 N`HWN97 NpHWN95 NPN9@D(A4 0/.:/.6?.4"j (N"j$.HzNO"j$"A-X-X=XN,il-|`-|6=|-| -|pf5=|@-|`-|Cf=|-|0-|H`fs=|@-|`-|yu =|@-|p-|X39=|AR 0-|-|3q=|@A 0Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NON:#-n-n=nN:NBHWN95 NRHWN97 NrHWN96 Nb-_-_=_N9 RN-_-_=_N9 N`A-X-X=XNXilB-|'b=|?AV 0-|`-|W=|-|P-|T =|@-|-|X"4=|@-|`-|c3Tx=|-|`-|vT=|@-|-|%#DS=|AH 0-|-|XS=|@Az 0Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NON:#N#VN:NCHWN95 NSHWN97 NsHWN96 Nc-_-_=_N9 HN-_-_=_N9 zN-n-n=n`B-|=|@B-|2He=|-| -|)Ug=|A 0B-|24=|@-|-|gg=|-|@-|6=|Na/./.?././.?."j NO/./.?.B-|P=|?/./.?././.?."j NO/./.?.-|3333-|333=|?/./.?././.?."j NO/./.?.-|3333-|3333=|?/./.?././.?."j NON:Nu-_-_=_N9!NHWN96 NeN:#N5HWN94 NE-n-n=nN9@D(/./.?."j (N"j$.Hz׹N"j$"/A4-X-X=X _NJ /./.?."j (N"j$.HzxNO"j$"NL N^Nu?<N     ?<NX @f` NuNuTTemperature2003001000 CPSp. heat at const. pressure CVSp. heat at const. volume HEnthalpy UInternal energy EEntropy function IPRIsentropic pressure func. IVRIsentropic volume function GSpecific heat ratio ASpeed of sound275?< NTNuNV-C/A-X-X=X _N C癙lN 癙op`p&.N^NuCPCVHUEIPRIVRGACP,CV,H,U,E,IPR,IVR,G,AMEPro 1.01 ErrorSorry, overflow.MEPro 1.01Error T <= 250 or >2000 KNVTH 4|$RB-|(pt=|?Al 0xN>N-n-n=nN @%oN @ np`pfNa/./.?././.?."j N/./.?.Na/./.?././.?."j NO/./.?.Na/./.?././.?."j NO-n-n=nN9(HN9?xN-_-_=_N9Ipx`N-_-_=_N9?w@NN@4 -n-n=nNI$lNa/./.?././.?."j N/./.?.Na/./.?././.?."j NO-n-n=nN9?EN9?YN-_-_=_N9V5hNN@@-n-n=nN9 l-n-n=nNJ/./.?."jN-n-n=nN9?I0N9?NN@-n-n=nN) lA 0-n-n=nN9!l/./.?."jNNI A 0Al-X-X=XN*1NzNNaN*Av 0Av-X-X=XN9!lN:!N9@/./.?."jN-n-n=n/./.?.NOPJf/./.?.NO Jf/./.?.NO Jf/./.?.NxO Jf~/./.?.N^O Jfd/./.?.NFO JfL/./.?.N.O Jf4/.|/.x?.vNO Jf/./.?.NO Jfp`pJfJfp`pfL&j$&S/./.?."j (N"j$.Hz N/./.?."j (N"j$.HzN/./.?."j (N"j$.HzN/./.?."j (N"j$.HzN/./.?."j (N"j$.HzN/./.?."j (N"j$.HzlN/./.?."j (N"j$.HzNN/.|/.x?.v"j (N"j$.Hz0N/./.?."j (N"j$.HzNO~"j$"JgF.N NJg.HzNX`.HzNX`NL N^Nu Saturated SteamSuperheated SteamAir PropertiesSteamTablesSteam TablesThermocouplesCapital BudgetingEE For ME'sEffluxSection PropertiesHardness NumberAnalysisRatio011000Deflection0101000bDeflection at free end0101000cDeflection at midpoint of beam0101000maxMax. deflection0101000aAngle at left end of beam/20/2bAngle at right end of beam/20/2crCritical stress01000110maxMaximum stress01000110rReduced stress01000110tTangential stress01000110aDist. of load from fixed end0101000aoDeflection w/o load011000AreaArea01010000bDistance from free end0101000cDist.centroid to column edge0101000EYoung's modulus01000110ecrEccentricity ratio01100ErReduced modulus of elasticity01000110EtTangent modulus of elasticity01000110IArea moment of inertia011000KeEffective length factor01100kStiffness0110000LLength011000MmaxMax. bending moment0100110MOMMoment applied to the beam0100110PPoint load01000110p0Load at right end of beam010000110p1Load/unit length01000110PcrCritical load01000110PtTangential load01000110rRadius of gyration011000SSection modulus0110000srslenderness ratio011000vBeam deflection011000v1Slope of deflection curve01100xDist. from left end011000xeeccentricity offset011000xlLocation of pt of max deflection011000! !aA!q!A! !! ! A a! !A1A! A @ 4  @ ! !&RT* ! A1Ep B@ !1!!QQ!A"AA!!!!qA!A!AR  !!A!A1A !! ! !!   q q !z(tan(a)=p1*a^2/(24L*E*I)*(2L-a)^2tan(b)=p1*a^2/(24L*E*I)*(2L^2-a^2)when(0xa,under the load v=p1*x/(24L*E*I)*(a^4-4a^3*L+4a^2*L^2+2a^2*x^2-4a*L*x^2+L*x^3) v1=p1/(24*L*E*I)*(a^4-4a^3*L+4a^2*L^2+6a^2*x^2-12a*L*x^2+4L*x^3)when(axL,outboard of the load v=p1*a^2/(24L*E*I)*(a^2*L+4L^2*x+a^2*x-6L*x^2+2x^3) v1=p1*a^2/(24L*E*I)*(4L^2+a^2-12L*x+6x^2)when(xL,applies to all eqns '! aAa1qAqaA A1! !1  Qa!1 A A!  !a!!! A1QA  B !1!! QQ! A"AA AA!!!AA!!AAqABAQ!A!AR !A!!!AA !! !A! q!!!AA!1a 1Q!1a!"a!Q!AA!! AA AqA  !z0tan(a)=P*a*b*(L+b)/(6L*E*I)tan(b)=P*a*b*(L+a)/(6L*E*I)L=a+bwhen(0xa,inboard of load v=P*b*x/(6L*E*I)*(L^2-b^2-x^2) v1=P*b/(6L*E*I)*(L^2-b^2-3x^2)when(ab,outboard of load c=P*b*(3L^2-4b^2)/(48E*I) xl=((L^2-b^2)/3) max=P*b*(L^2-b^2)^1.5/(243^.5L*E*I)when(xL,applies to all eqns 'A A!A!!A1!Q1qa1A1!Q1a!A!q!A A AA! !A Ba -mA !R1!! !QAQAA Ba q! AAQ A A1A11q A 1QA A 1A A !A ! B! "A!A AA!1AA! !A! A1A qA!!A1 A! A! ! !A1 ! a!A1 a!!A{(tan(a)=MOM/(6*L*E*I)*(6*a*L-3*a^2-2*L^2)tan(b)=MOM/(6*L*E*I)*(3*a^2-L^2)when(0xa,inboard of load v=MOM*x/(6*L*E*I)*(6*a*L-3*a^2-2*L^2-x^2) v1=MOM/(6*L*E*I)*(6*a*L-3*a^2-2*L^2-3*x^2)when(xL,applies to all eqns'! !aA!q!A! !! !A! !1A!@ B1@ !RT* !p8q @ A!!1A!!1a!a!1A! a A!1 a A! a2A!Q aQ!1! 11Q "A!1!!q!1p@! Ȣ2  #  AAq q  q!!!u*b=p1*a^3/(24*E*I)*(4*L-a)tan(b)=p1*a^3/(6*E*I)when(0xa,inboard of load v=p1*x^2/(24*E*I)*(6*a^2-4*a*x+x^2) v1=p1*x/(6*E*I)*(3*a^2-3*a*x+x^2) when(axL,outboard of load v=p1*a^3/(24*E*I)*(4*x-a) v1=p1*a^3/(6*E*I)when(xL,applies to all eqns '! !aA!1qAqAA!1! ! !! ! !A! ! !A! !A !! q! !!A!!!A!a!1a!1! a AA! a A!1 a2!Q aQA!! 11!1Q "!1!Aq!11p! ,@  #  q q  q!!!u*b=P*a^2*(3*L-a)/(6*E*I)tan(b)=P*a^2/(2*E*I)when(0xa,inboard of load v=P*x^2/(6*E*I)*(3*a-x) v1=P*x/(2*E*I)*(2*a-x)when(axL,outboard of load v=P*a^2/(6*E*I)*(3*x-a) v1=P*a^2/(2*E*I)when(xL,applies to all eqns ' AA1!AAaQ1qA1AaA!Qq!  AAAAB  aA*R  B!QAAB qA  A!  AqAa B!1 A1A QA 2 B! 1 B 1AA1A!!A QA!!1 BQa!a1A Aa! ) X$&q1a 1 X8`BQt(b=MOM*a/(2*E*I)*(2*L-a)tan(b)=MOM*a/(E*I)when(0xa,inboard of load v=MOM*x^2/(2*E*I) v1=MOM*x/(E*I)when(axL,outboard of load v=MOM*a/(2*E*I)*(2*x-a) v1=MOM*a/(E*I)when(xL,applies to all eqns ' a  a ! T1QR!1BRqRAa1!1!a TqaAQ!AJQ!!R!!aR!!A$1 !BQ!![ !5 !!!!!!!!!!!!!!!!!!!!!a!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"A!Q!Bqq!A!Q!qRAq"AA1;4Pcr=^2*E*Area/(Ke*L/r)^2Pcr=^2*E*I/(Ke*L)^2cr=Pcr/Arear=(I/Area)'AQaB AQ!P y<r~| AQP A1QA!B!A !RB ;1B! BQB !QC@ 5Q! q!RB !*1qqAQ([A!@! 5A!!!B @!H %)Aa *!A!a *!AAQ*pAa1!!q!AQa1!"` 8*qA"0!! &!qq! )AƁB!!!a!!!AS!!AR1!!BR!!B"1!!Aa!1!AA!AA!B1a!Q!! !1Q !A q!QA! !A!1A 1aQS!"11A AB q!QB! !1B h9c=P*xe*L^2/(8*E*I)Mmax=P*xe/cos(k*L/2)'r=(I/Area)max=P/Area+Mmax/Smax=P/Area*(1+(xe*c/r^2)*1/cos(L/(2*r)*(P/(E*Area))))ecr=xe*c/r^2sr=L/r' FB !QB a!1B "C RBQR1rAQA!!QA!q!Q1A!aQBa1Ba!B!RA!11A!1a!aT!AQA!$AQq4E!Q1Aaq!QA A14E!A!A!!QA aA1Q!!AA1Q! A1QA!!!$(E! !E!!B>$EA !1!AAAA AA!AAA!AA1A!!AaACBAQbJC|qqR!RqAB!AQ!RAW!q!L BQ!aAAqBᡁAQ!A1A!A!V1A!!AR*@P!R!H@PH!A!1R*@PA"!BB+@! l!A!!AAS!A!AR1A!!AABR!A!AB!A!A!A!SAA1"qA!A!1q!AQA!!!AAq 9=P/Pcr=P*L^2/(^2*E*I)Mmax=P*ao/(1-)max=ao/(1-)max=P/Area+Mmax*c/Imax=P/Area*(1+ao*c/(r^2*(1-)))max=P/Area*(1+(ao*c/r^2)/(1-((P/(^2*E*Area))*(L/r)^2)))' 1Q1 AQ1QR!!1BqRAa!1!a!qaAQa!AJ !!Ra"!a!!A !"!!!!!!A!!A!!A!!A!A!!!!!!!!!!!!!!!!!!!!!!!!A!!A!!A!!A!!A!!!!!!!"!Q!qq!!Q!AqRA1q"AA1>5Pt=^2*Et*I/L^2t=^2*Et/(L/r)^2Er=4*E*Et/(E^.5+Et^.5)^2r=^2*Er/(L/r)^2'!  A ! A1 ! !  Aa!!!!A " !  a1  !!!󑁑1!0Temperature coeff.0.0011AArea01614GConductance01814ICurrent-1001100lenLength0110PPower0101000Resistivity19151RResistance010019RR1Resistance at T1010019RR2Resistance at T2034Conductivity0.11T1Temperature 1200300400T2Temperature 2200300400VVoltage1501150R=*len/AResistanceG=*A/lenConductanceG=1/RConductance=1/ConductivityV=I*ROhm's LawP=V*IP=I^2*RP=V^2/RP=V^2*GR=1/GRR2=RR1*(1+*(T2-T1))Phase delay/20/2EaAvg. emf induced in armt.150100300EmaPhase voltage150100300IaArmature current1000100IIfField current1000100ILLoad current01001000IrRotor current/phase0101000IsbBackward stator current10010100IsfForward stator current010100KeMachine constant0125KefField coefficient0125KeMInduction motor constant0125Flux0110p# poles0216PPower010010000PaMech. power available010010000PmaPower in rotor/phase01001000PmeMech. power01001000PrRotor power/phase01001000RR1Rotor resistance/phase00.1100RaArmature resistance00.1100RdAdjustable resistance00.1100ReExt. shunt resistance0101000RfField coil resistance010010000RlLoad resistance0101000RrEquiv. rotor resistance0110RsSeries field resistance01100RstStator resistance010100sSlip0.51sfSlip for forward flux0.51smMaximum slip0.51TInternal torque010010000TbBackward torque010010000TfForward torque010010000TgmaxBreakdown torque010010000TLLoad torque010010000TlossTorque loss0101000TTmaxPullout torque010010000TmmaxMax. positive torque010010000TsShaft torque010010000VaApplied voltage0100400VfsField voltage0100400VtTerminal voltage0100400mMech. radian frequency0500015000rElec. rotor speed0100010000sElec. stator speed0100010000XLInductive reactance0101000Vt=Ke**m+(Ra+Rs+Rd)*ILTL=Ke**IL-TlossEa=Ke*m*T=Ke**ILm=Vt/(Ke*)-(Ra+Rs+Rd)*T/(Ke*)^2T=Tloss+TLKe*=Kef*ILT=Kef*IL^2/Vt=(Re+Rf)*IIfVt=Ke**m+Ra*IaTL=Ke**Ia-TlossEa=Ke*m*m=Vt/(Ke*)-(Ra+Rd)*T/(Ke*)^2T=Tloss+TLT=Ke**Ia/Ia=IIfVt=Ea-(Ra+Rs)*IL/Ea=Ke*m*Vt=(Re+Rf)*IIfVt=IL*RlVt=Ea-Ra*IaIa=IL+IIfEa=Ra*Ia+(Re+Rf)*IIf/r=s-p/2*ms=1-p/2*(m/s)Pr/Pma=sr=s*sPma=3*Ir*EmaPme=3*(p/2)*(m/s)*PmaPme=T*mT=3*(p/2)*(Pma/s)Pma=Rr*Ir^2+(1-s)/s*Rr*Ir^2Pa=(1-s)/s*Rr*Ir^2Rr=RR1/KeM^2 /Pma=Rr/s*Ir^2T=3/2*(p*Pma/s)T=3/2*(p/s)*(Rr/s)*(Va^2/((Rst+Rr/s)^2+XL^2))Tmmax=3/4*(p/s)*(Va^2/((Rst^2+XL^2)+Rst))sm=Rr/(Rs^2+XL^2)Tgmax=(3/4)*(p/s)*(Va^2/((Rs^2+XL^2)-Rst))Rr=RR1/KeM^2/sf=1-p/2*(m/s)Tf=p/2*(1/s)*(Isf^2*Rr/(2*sf))Tb=(p/2)*(1/s)*(Isb^2*Rr/(2*(2-sf)))/Polytropic coefficient,n102100vVelocity range016110arkmRK coeff.-molar016110arksRK coeff.-mass0500050000avwmvan der Waals coeff, molar0.110avwsvan der Waals coeff, mass0.001.1bvwmvan der Waals coeff, molar01100bvwsvan der Waals coeff, mass00.001.1brkmRK Coeff.-molar010001000000brksRK Coeff.-mass01000100000cnSp. Heat:Polytropic Process011000cpSp. Heat @ const. press.011000cvSp. Heat @ const. volume011000fDistribution function.01.51hs21Enthalpy Change-Mass:12100001001000000hm21Enthalpy Change-Molar:12100001001000000kSp. Heat Ratio,k101.510mMass01100000MWTMolar Mass0101000NNo. moles011000pPressure01000110p1Init. Pressure01000110p2Final Pressure01000110pcrCrit. Pressure01000110Q12Heat xfer:12100001010000RmUNIVERSAL Gas Constant8.314510sm21Entropy Change-molar:12100001010000ss21Entropy Change-mass:12100001010000S21Total Entropy Change:1210010100TTemperature200300500T1Initial Temp.200300500T2Final Temp.200300500TcrCritical Temp.200300500um21Int. energy change-Molar:1210010100us21Int. energy change-Mass:1210010100VVolume01100V1Init. Volume01100V2Final Volume01100velVelocity01001000vmMolar Volume01100vrmsRMS velocity01001000vsSp. Volume011000vs1Initial Sp. Vol.011000vs2Final Sp. Vol.011000W12Work Performed:12011000vm=V/Nvs=V/mp*vs=Rm/MWT*Tp*V=N*Rm*Tp*vm=Rm*TIdeal gas lawMWT=m/N-V2/V1=T2/T1Charles LawW12=p*(V2-V1)W12=N*Rm*(T2-T1)S21=m*cp*ln(T2/T1)Total Entropyss21=cp*ln(T2/T1)Entropy per Mass of substancesm21=MWT*ss21Entropy per moleQ12=m*cp*(T2-T1)Q12=k*W12/(k-1)k=cp/cvcp=cv+Rm/MWTMWT=m/N -p2/p1=T2/T1Q12=m*cv*(T2-T1)Q12=V*(p2-p1)/(k-1)S21=m*cv*ln(T2/T1)ss21=cv*ln(T2/T1)Entropy per Mass of substancesm21=MWT*ss21Entropy per molecp=cv+Rm/MWTk=cp/cvMWT=m/N -p2/p1=V1/V2W12=N*Rm*T*ln(V2/V1)W12=p1*V1*ln(V2/V1)Q12=W12S21=Q12/Tss21=Rm*T*ln(V2/V1)ss21=S21/msm21=MWT*ss21MWT=m/N -us21=cv*(T2-T1)us21=(p2*vs2-p1*vs1)/(k-1)hs21=cp*(T2-T1)hs21=k*(p2*vs2-p1*vs1)/(k-1)ss21=(cv*ln(T2/T1)+(Rm/MWT)*ln(vs2/vs1))ss21=(cp*ln(T2/T1)-(Rm/MWT)*ln(p2/p1))ss21=(cp*ln(vs2/vs1)+cv*ln(p2/p1))hm21=MWT*hs21um21=MWT*us21sm21=MWT*ss21cp=cv+Rm/MWTk=cp/cvp1*vs1=Rm/MWT*T1p2*vs2=Rm/MWT*T2-vrms=((3*Rm*T)/MWT)f=4**(MWT/(2**Rm*T))^(3/2)*vel^2*^((MWT*vel^2)/(2*Rm*T))*v-(p+avws/vs^2)*(vs-bvws)=Rm/MWT*Tvan der Waalsavws=27/64*(Rm/MWT)^2*(Tcr^2/pcr)bvws=1/8*(Rm/MWT)*(Tcr/pcr)MWT=m/N-(p+avwm/vm^2)*(vm-bvwm)=Rm*Tvan der Waals, avwm=27/64*Rm^2*(Tcr^2/pcr)bvwm=1/8*Rm*(Tcr/pcr)-p=Rm/MWT*T/(vs-brks)-arks/(T^.5*vs*(vs+brks))arks=.4275*(Rm^2/MWT^2)*(Tcr^2.5/pcr)brks=.0867*(Rm/MWT)*(Tcr/pcr)MWT=m/N-p=Rm*T/(vm-brkm)-arkm/(T^.5*vm*(vm+brkm))arkm=0.4275*Rm^2*(Tcr^2.5/pcr)brkm=0.0867*Rm*(Tcr/pcr)-p1/p2=(V2/V1)^kIsentropicT2/T1=(V1/V2)^(k-1)T2/T1=(p2/p1)^((k-1)/k)W12=m*cv*(T2-T1)W12=(p2*V2-p1*V1)/(k-1)W12=p1*V1*((p2/p1)^((k-1)/k)-1)/(k-1)vs2=vs1*(T1/T2)^(1/(k-1))us21=cv*(T2-T1)us21=(p2*vs2-p1*vs1)/(k-1)hs21=k*(p2*vs2-p1*vs1)/(k-1)k=cp/cvMWT=m/Nvs1=V1/mvs2=V2/mp1*vs1=Rm/MWT*T1Ideal Gasp2*vs2=Rm/MWT*T2Ideal Gascp=cv+Rm/MWTIdeal Gas-p1/p2=(V2/V1)^cn=cv*(-k)/(-1)T2/T1=(V1/V2)^(-1)T2/T1=(p2/p1)^((-1)/)W12=(p2*V2-p1*V1)/(-1)W12=p1*V1*((p2/p1)^((-1)/)-1)/(-1)Q12=m*cn*(T2-T1)cp=cv+Rm/MWTIdeal Gask=cp/cv -dThermal Diffusivity0.0011sAbsorptivity of Surface0.510Emissivity0.5101Emissivity of 10.012Emissivity of 20.01sEmissivity of shield0.01Wavelength0610maxPeak wavelength0610Density01100eElectrical resistivity011000e1Electrical resistivity011000oElectrical resistivity at T=0011000sReflectivity of Surface01100Stefan-Boltzmann Constant5.670518Thermal time constant01100Angle010100AArea01100A1Area01100A2Area01100AsTotal Surface area01100brc11st Radiation Constant, W*m^23.741832016brc22nd Radiation Constant, m*K.01438786brc3Wein's displacement constant, m*K.002897756EEmissive power0101000EbBlack body emissive power10011000EbMonochromatic emissive power01001000E1Emissive power 101100E2Emissive power 201100EsEmissive power011000Fs2rRadiation shape factor0110GsIrradiation03002000hConvection coefficient01100h1Convection coefficient0110h2Convection coefficient0110JsRadiosity011000kThermal conductivity01100k1Thermal conductivity0110k2Thermal conductivity0110k3Thermal conductivity0110k4Thermal conductivity0110kiThermal conduct. insulator0110LLength01100L1Length0110L2Length0110L3Length0110mmass0110NfNo. of finish01100NsNo. of shields01100periPerimeter01100qHeat xfer rate-conduction100011000qHeat flux100011000qcHeat xfer rate01100qc1Heat xfer rate0110qc2Heat xfer rate0110qcxHeat xfer rate0110qcyHeat xfer rate0110q12cHeat Flux0101000qfHeat Flux0101000QrateHeat xfer rate-radiation01100qsHeat transfer rate011000qTTotal heat xfer rate011000rRadius0110raInner radius01100rbOuter radius01100roOuter Radius0110rcritCritical radius0110Rc1Thermal resistance-Convect.01100Rc2Thermal resistance-Convect.01100Rc3Thermal resistance-Convect.0110RcvThermal resistance-Convect.01100ReqEquivalent thermal resist.0110RkThermal Resistance-Conduct01100Rk1Thermal resistance-Conduct01100Rk2Thermal resistance-Conduct01100Rk3Thermal resistance-Conduct01100Rk4Thermal resistance-Conduct01100RkiThermal resistance-Insulator01100RsThermal resistance, 2nd kind01100R1sjThermal resist sj:type 101100R2sjThermal resist sj:type 201100SShape factor0110TTemp at x or x,t03002000T1Temp 103002000T2Temp 203001000T3Temp 303001000TfTemp of fluid03002000Tf1Temp of fluid 103001000Tf2Temp of fluid 203001000TiTemp (x,time=0 or ,time=t)03002000ToTemp (0,time=t)03002000TsSurface temp. of emitter1003002000timeTime011000xDist. from the left/side len03002000`u$$XU< $!~u$ ÇP? VPcP5?vPPFDPE$FPE ~$F 4P?$? P??p@?P ?) ? `?0p?`?p@4P ? P?p@4?@ PD?0@  p@??@PT?CpB? DPA Sp~ @   Te?ɿT* *P?Ѐp?0d D ? 9q=k*A*(T1-T2)/Lq=k*S*(T1-T2)q=q/AS=A/LShape Factor:Rect.PlateS=2**L/ln(rb/ra)Shape Factor:Hollow CylinderS=4**ra*rb/(rb-ra)Shape Factor:Hollow Sphere]_Y  AAA!A  ! !A A A ! A!q !!! " !Q !! A1q!!! A!AAA"q!A !!!!!AQAQ H!A  !1 qq@@@@@@@@@@@@@@@1PPPPPPPPQq@@@@@@@ۑ@@@@@@@@!k+qc=h*As*(Ts-Tf)Newton's Law of cooling]Rqq1RqQRqR1qS!gVAVVVVVVV1qVq1VVVVQRV=qBAAVqUqq TqSqq1 q a 11 A q!1 I5Eb=*Ts^4Stefan-Boltzmann LawE1=1**T1^4E2=2**T2^4Qrate=A1*Fs2r*(E1-E2)]T=T1+(T2-T1)/L*xq=k*A/L*(T1-T2)Rk=L/(k*A)]|y aQrA!!qA! TQ1!aA!~u$ Ç RaQ_QR1!vqARqAaA!ARA!AAa1Qq!ARAAQQ!aAQRAAQaa1!!RA1aR!A a!A!RaEa !aE(|REQ`aA!QAQA!RA@A |A!!aAa1A1RA!QB!aaB!!R!: HQ!BqkARH  aQA11RA!aAaR! a !Rda_Q!A1R a !Q1q1!! q 1 A !!A? !!AA9(T-T2)/(Tf-T2)=(L-x)/(L+k/h)Rk=L/(k*A)Rcv=1/(h*A)T1=(Tf/Rcv+T2/Rk)/(1/Rcv+1/Rk)T1=(Tf*h+T2*k/L)/(h+k/L)qc=(Tf-T1)/Rcvq=(T1-T2)/Rkq=qcq=(Tf-T2)/(Rcv+Rk) ]WUUUX0F}C 0AmC `@`w3@ @}w@' @m{w& @ @}w! @m  @~w#  @#!!@m{p# @ !@ @ !C} @"Dmۍ@#!B @"A "Gm{ '@? @}  @m3 b @~wK @K @m{wK" @3#W @}wCU2 @mQ @~wb @ @m{w# @#` @}w#  @m  @~w! @ `m{w&*' }7 0 m a~c  ݀ m; (?_6Qrate=*Fs2r*As**(Ts^4-T1^4)Qrate=k/L*(T1-T2)T1=(T2+Fs2r*(*L/k)*Ts^4)/(1+Fs2r*((*L)/k)*T1^3)]A!A 1!8!!1A AA! !A!A!AA A!!!A!AA A !d d !!BB!qB!Ba!!A !aA!$ "IRAAB"Q!!Aq AA!a!AAA!A8AAA!!AB1A AAd8!!A!B!AA1A!! !!!a11!aB!ABaq !AA!AQ!BgC>B1`Q!!Q !!!!1!! A!1! ! A !1!! !A!A !"!!   "qa!!A!!A!Q! 1 q A! A"Q1!!11AH!AA AA" q! ! A! ! A!!  A1!1!1!!9Rc1=1/(h1*A)Rc2=1/(h2*A)Rk=L/(k*A)q=(Tf1-Tf2)/(Rc1+Rc2+Rk)T1=Tf1-Rc1*qT2=Tf2+Rc2*q] @@ @@   @ @  >8@@d@@ @((DP  BV ? 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D! |$D#E!8&N+%X`E1JU@(>`(0 N|``N MJHąqBTR%@UUDLc\ĄPT@ @TUDUw@=@T8Rk1=L1/(k1*A)Rk2=L2/(k2*A)q=(T1-T3)/(Rk1+Rk2)q=(T1-T2)/(Rk1)q=(T2-T3)/(Rk2)when(x<0 and x mv6pom `( H VEZ@x>H(REP\7q=(2**L*k)/ln(rb/ra)*(T1-T2)Rk=ln(rb/ra)/(2**L*k)when(r>=ra and rrb, (T-T1)/(T2-T1)=ln(r/ra)/ln(rb/ra)when (ra=ra and rrb, (T-T1)/(T2-T1)=(r-ra)/(rb-ra)*(rb/r)when (raD((E1`O1( (ED׻EO|QP]1 D E$ 1X7 1 $F$ pP1~17D$rS@?5184@*D$8S%1(W?~,D$0(@?1`MWU, *%!MUUU1E0*@_ \UUUE& *E)\U$D$* 1T" A $_ / QX E$'TD1QP_E$?PĠ1~:@WD$ }PUDA1>jUՠ$^DUUUDj𱪪 *TUUG$TUUD @0`UU@ VU}d@&>A)?VD@D$?0)ߟD<NDD&Uއz( U!CiDDDDD$U 1qSDDDDDDD$9q=(T1-Tf)/Reqq=(T1-T2)/Rk1T2=T1+(T1-Tf)/Req*Rk1T3=Tf+(T1-Tf)/Req*Rc3Rk1=ln(rb/ra)/(2**L*k1)Rki=ln(ro/ra)/(2**L*ki)Rc3=1/(h*2**ro*L)Req=Rk1+Rki+Rc3when (ra 0;@@^gUUU I8+@@Y Ϫ KI3xVOUUU pH+@@aϪ@H+@@ LUUU@?@`_˪? ^HUU@ ҟ ˪:~ @hU~@z  BcU  $0'Y= x.t  +0p R?0R_@ N?dR xBR@v@ !@@@@@ 85q=(T1-Tf)/(Rk+Rcv)Rk=ln(rb/ra)/(2**L*k)Rcv=1/(h*2**L*rb)rcrit=k/hwhen (raҒV!!q!ZV1!1!!!!qS1!V1!!a!1qS!1!A1!Q.!1Q1H(A1YAH"1!A!!AAIA!1! 1 AqA!!!1@&A!1Qq@ HJ% @&AQ!1A!q!1"!! q AQAQ a AQAQ !AR@e ! AR@% aA!!q!A a!Q!A!A A1!A1a aA!A! A!1 !:QH-QL=WnetQH=m*Rm/MWT*TH*ln(V2/V1)QL=m*Rm/MWT*TL*ln(V4/V3)TL/TH=(V2/V3)^(k-1)TL/TH=(V1/V4)^(k-1)=1-TL/TH=Wnet/QHk=cp/cvTH/TL=(p2/p3)^((k-1)/k)TH/TL=(p1/p4)^((k-1)/k)p*V=m*Rm/MWT*T 1 1AZ1! A aQ! Aaq1a Aqq ()qQ!A!!Ab1 R`*QQ2a!LZa!Q AAQq1A AAqa!A AqA2 Aqq Aqq AAqq AqA 1Aq A!qA AqAqqA1!!!ѡq1!!qAq!!BqqQqA Aaq1 A!qQA AqQ1 AqA1Aa1AQQ1AQ1AAqqAbLqAk(AAc Aa1AaA!q aAaaAq1AaHZa1!AHBqa~HZaB(1aaA!1!QQ!qAB< 1QqB!AA!AA!AA !AQ 1q!AQ A !1AQ!!1aQAAQ!Q1!A!AQ!"11AqA!#Bqq!1a!A7Qin=mr*cp*(T3-T2)Isobaric HeatingQout=mr*cv*(T4-T1)Isochoric CoolingWr=Qin-QoutNet PowerWr=mr*cp*T1*cr^(k-1)*(cor-1)-mr*cv*T1*(cor^k-1)Net Power=1-Qout/QinEfficiency=1-T1/(k*T2)*((T4/T1-1)/(T3/T2-1))Efficiency=1-(1/cr^(k-1)*(cor^k-1)/(k*(cor-1)))Efficiencyk=cp/cvRw=(k*(cor-1)*cr^(k-1)-(cor^k-1))/(k*(cor-1)*cr^(k-1)-(cor^k-cr^(k-1)))Work Ratiomep=Wr/(V1*(1-1/cr))*timeMean Effective Pressurecor=V3/V2Cutoff Ratiocor=T3/T2Isobaric Heatingcr=V1/V2Compression RatioT2=T1*cr^(k-1)Isentropic Compressionp2=p1*cr^(k-1)Isentropic Compressionp2=p3Isobaric HeatingT4=T3*(cor/cr)^(k-1)Isentropic ExpansionT4=T3*(V3/V4)^(k-1)Isentropic Expansionp4=p1*(T4/T1)Isochoric CoolingV1=V4Isochoric Coolingp*V=m/MWT*Rm*TIdeal Gas Lawtime=m/mrCycle duration11AA Qq A! 1A !R1Q A!QAQ!a!AA!q AQB!A1R1Q q1!aA1A!AA1q1! Aa! Aq1! !Q1 A11 !Q1 Aq Aq 1A AA1%¡Qq$$!Q2AQ!AAqB!q!Qa1q AqQAq11AQQ!!A11RQ2uq1]J%`qTơq!1"A!aA A2AqA! QQ!>!a Q!A!AA1%=AB!Q1!!a&BXB A1A Q!Aq1Q!AAQaa!A1!1a!Q!A!A1A!!A!AA1a1!!q1!A!"!!!a!Qaqq7Qin=mr*cv*(T3-T2)+mr*cp*(T4-T3)Heat Intake RateQout=mr*cv*(T5-T1)Heat Exhaust RateWr=*QinNet Power for Work=1-(T5-T1)/(T3-T2+k*(T4-T3))Efficiency=1-Qout/QinEfficiency=1-1/cr^(k-1)*(rp*cor^k-1)/(k*rp*(cor-1)+rp-1)Efficiencycp/cv=krp=p3/p2Pressure Ratiocr=V1/V2Compression Ratiocor=V4/V3Cutoff RatioT2=T1*cr^(k-1)Adiabatic CompressionT2=T1*(p2/p1)^((k-1)/k)Adiabatic CompressionT3=T2*rpIsochoric HeatingV2=V3Isochoric HeatingT4=T3*corIsobaric Heatingp3=p4Isobaric HeatingT5=T4*(V4/V5)^(k-1)Adiabatic ExpansionT5=T4*(p5/p4)^((k-1)/k)Adiabatic ExpansionT5=T1*p5/p1Isochoric CoolingV1=V5Isochoric Coolingp*V=m/MWT*Rm*TIdeal Gas Lawtime=m/mrCycle duration1\R Q a! 1 a! q!1 Q qA1 q"1 A qAq b1 QA a QA1 qa1 qq q A!q AqA!q%qA!A!aqAQ!1!qqQ!q!1q!qq!Q!q!Rq!Qqqq!qqqQAqQqQAAqqAqQ1A1QqQQ_!AqA1P!q!QQRѢa1!1Qj_AAqas"qAAqqqq1AAq q1AAqAq aQAqaaAAa1AqAAaQ 1qA1QqAA!RAUqA1 A AA!A A!qq1AqA!AaAA1!!aAQ!AQ!A!A1!BA1!1B!A!Q!#!q!9Qin=mr*cv*(T3-T2)Heat intake rateQout=mr*cv*(T4-T1)Heat exhaust rateWr=mr*cv*T3*(1-T1/T3*cr^(k-1))*(1-1/(cr^(k-1)))Net Power for WorkWr=*QinNet Power for Work=1-(T1/T2)*((T4/T1-1)/(T3/T2-1))Efficiency=1-Qout/QinEfficiency=1-(1/cr^(k-1))Efficiencymep=Wr/(V1*(1-1/cr))*timeMean Effective PressureRw=1-T1/T3*cr^(k-1)Work Ratiok=cp/cvcr=V1/V2Compression Ratiocopt=(T3/T1)^(1/(2*(k-1)))Optimum Compression RatioT2/T1=cr^(k-1)Isentropic CompressionV3=V2Isochoric HeatingT3/T4=(V4/V3)^(k-1)Isentropic ExpansionV1=V4Isochoric Coolingp*V=m/MWT*Rm*TIdeal Gas Lawtime=m/mrCycle duration1!  Qa1!Z12A! 1BaA!111!!AAA1A1Q"A1q1A!AA212Q!0!-P!8|1qq1 Q!1!a %21q 11q 1q 1! !1!11A1!HK1!AHH1!1AAaa00Q1qqA!11!q!1!1R1A11"1!1q!qq1! q1!!1!!!qA1!!AQ!!1AQ1!qAqqBR!q1A1!qqA"q!a1q1!AQAR?`<a!AA A!!1AAA!$!1"1aA1L* J$qQ!q!A!aB!q !Q!11!Q!AA (%(1Ё!5AA!A!!"A!1!AA"qq111!8Qin=mr*cp*(T3-T2)Heat Intake RateQout=mr*cp*(T4-T1)Heat Exhaust RateWr=*QinEfficiency=1-(T1/T2)*(T4/T1-1)/(T3/T2-1)Efficiency=1-Qout/QinEfficiency=1-rp^((1-k)/k)Efficiency=1-(p1/p2)^((k-1)/k)EfficiencyRw=1-T1/T3*rp^((k-1)/k)Work Ratioropt=(T3/T1)^(2*(k/(k-1)))Optimum Pressure Ratiok=cp/cvrp=p2/p1Pressure Ratiorp=(T1/T2)^(k/(k-1))Isentropic Compressionp2=p3Isobaric Heatingp3/p4=(T3/T4)^(k/(k-1))Isentropic Expansionp1=p4Isobaric Hoolingp*V=m/MWT*Rm*TIdeal Gas Lawtime=m/mrCycle Durationln(p2/p1)=MWT*hs/Rm*(1/T1-1/T2)Half thread/cone angle01090ball:3, roller bearings:3.3301090Specific weight010100HRate of heat loss0101000TFTemperature rise010200Total radial change0.110iChange in inner radius0.110oChange in outer radius0.110pSag w/o load 01100yDeflection01100Eccentricity0.11Poisson's ratio01101Poisson's ratio of 10.112Poisson's ratio of 20110iPoisson's ratio-Inner Ring0.11oPoisson's ratio-Outer Ring01101Min angle0101802Max angle010180aAng. from hinge pin, loc. pa010180Density01001000Stress01000100000bStress0100001000000cCompressive stress01000100000itTangential stress inner rim0100010000000otTangential stress outer rim0100010000000rRadial stress1100010000000sSafe stress0100010000seShear endurance limit01000010000000sypShear yield point010000100000000tTangential stress1100010000000xxStress along x axis0100016yyStress along y axis0100016zzStress along z axis0100016Torque01000100000aTorque amplitude0100010000mMean torque0100010000Angular velocity01010000Absolute Viscosity0.110fCoefficient of friction0.110AArea010100acRadius of contact area0110bWidth0110CConstant: Max when C=10.11CaApplication factor0110CfSurface condition factor0110CHSpecific heat0110clrClearance0.11CmLoad distribution factor0110cofCoefficient of friction0.11conAConstant A010100conBConstant B010100CPElastic coefficient01000001000000000CSSize factor0110CvDynamic factor0110dDiameter0110d1Diameter 1 or outer diameter0110d2Diameter 2 or inner diameter0110dcMean Collar Diameter0110dmMean diameter0110dpPitch diameter0110dsShaft diameter01100dwDiameter0110dxX-section dimension0110dyY-section dimension0110EYoung's modulus016110E1Young's modulus - 1016110E2Young's modulus - 2010000010000000eccEccentricity0.110effEfficiency0.51.0EiYoung's modulus inner mat'l016110EoYoung's modulus outer mat'l016110FForce01316FDRadial design load01000100000flLoad factor0.11FRRadial rating load01000100000fwFace width0110FxForce along x01316FyForce along y01316GModulus of Rigidity0110gfGeometry factor0110gravGravitation const, m/s^29.80665hHeight/Depth0110IArea moment01100JMech equivalent heat0101000KaApplication factor0110KldLoad distribution factor0110KsSize factor0110kspGeometry factor0110KvDynamic factor0110kwGeometry ratio0110LLength0110LDRequired Design Life0110LfLewis form factor010100LRCatalog Rated Life0110MaMoment amplitude01010000mmMetric module011MnMoment mean01010000MOMMoment of Inertia0100010000NSignificant speed01001000NDRequired design: no. revs01000100000ND1Required Design speed01001000nfNo. coils/leaves010100NRRated # revs0100100000NR1Rated speed01001000nsFactor of saftey010100pPressure0100010000000paMaximum Pressure at a0100016PbLoad per bearing area0100010000000pdDiametrical Pitch0110piPressure inside1100010000000PldLoad0100010000pmaxMaximum Pressure0100016poPressure outside1100010000000psSupply pressure0100010000QsSideflow010100rRadius0110riInside radius0110rjJournal radius0110rnRadius of neutral axis0110roOutside Radius0110RaxReaction x-axis(anti-clock)0100010000RayReaction y axis (anti-clock)0100010000RcxReaction x axis (clockwise)0100010000RcyReaction y axis (clockwise)0100010000SfldSommerfeld #01100UResilience0101000umaxMax. velocity01001000VVolume of Spring0110WtLoad01000100000xDistance from center axis0110yDistance0110zz-axis dist.from contact pt0110!AqA!!A1QAqqqQa2qqSQaqᱤUqq!W1qrѱRqQW *R!RAQ1Ს1QQ1a1RQaAaq!qQ1aQq!!!Aq!W*V UqAqQ"V!!!"Aq!qqQ1!aQqA!aq!RQa!a1!QQ1Ს1RAQ! W *RAQa 1!ѱRqQ!aqrq!!AW1 !Aqq! !U! ᱤ qqSQaqq a2!QAqqqQAT1 A11 !A !q  A!y8t=(pi*ri^2-po*ro^2-ri^2*ro^2*(po-pi)/r^2)/(ro^2-ri^2)r=(pi*ri^2-po*ro^2+ri^2*ro^2*(po-pi)/r^2)/(ro^2-ri^2)when (rri,applies to all eqnst=*^2*((3+)/8)*(ri^2+ro^2+ri^2*ro^2/r^2-(1+3*)/(3+)*r^2)r=*^2*((3+)/8)*(ri^2+ro^2-ri^2*ro^2/r^2-r^2)when (rri,applies to all eqnsA?#!) ?*)w~HSu` @ }|@7@!^$@A{T@S@{pa @@}| @_@ @? @7 @@ @a @ @@@h@@A@ @_U@ A D@ Ap$@@$@ @a @  @ @7 @? @_@@}A|@h@{qAAB!{T^X 7\}|@` + B p w p?!pA ?P8it=p*(r^2+ri^2)/(r^2-ri^2)ot=p*(ro^2+r^2)/(ro^2-r^2)o=(p*r)/Eo*((ro^2+r^2)/(ro^2-r^2)+o)i=(p*r)/Ei*((r^2+ri^2)/(r^2-ri^2)-i)=abs(i)-abs(o)when (rri,applies to all eqnsABABAA ABA  AAA!  ABAAQA AA1AB!A!B! AA!AA AAA!HRIAAQ!B1q!1B!AAQ!Q!HIB AA1AA!ASA aA!AA1AA, A!AA AAAA!Q!BA: t!!R *R!?AH$R(! CL@@@@!a1R", QAA $ !@RAA !AAB!QAAA!AAA! AaA!S1qA1q!AAQAA)cb!AaA`!AA!Aq spBAAA! A1! ! AA! aAA!A!A!A! AA11Aёq A!AAAA!!AA A!AA!!AA AA!  A 8A=b*hrn=h/ln(ro/ri)=F/A+MOM*y/(A**(rn-y))ro=ri+hrn=x+ywhen (riri,applies to all eqnsac=((3*F)/8*((1-1^2)/E1+(1-2^2)/E2)/(1/d1+1/d2))^(1/3)pmax=(3*F)/(2**ac^2)xx=pmax*((1-z/ac*tan(ac/z))*(1+f)-1/(2*(1+z^2/ac^2)))zz=pmax/(1+z^2/ac^2)p @A @`*p @ p D@0@H@@P8@P@T ' %  $@@7 @DD$?` p H e$I/wU` HH! e? pDD WU@; @T*p$ 8^UUU". 0 a$ UUU  d(0@ H($XUUU0$H$8.ΝcT`UUU $ B{y UUU #pɝ,UUU0hH0$ȠVU"(.Ș.VUU* *H IVUH T} *VU $ @$ Uup@T  `@Pr \I!T?zH!`pг.TT 88@TRQ8UѪ9!Q@T}%Q(H"W88 H T*`  8ac=((2*F)/(*L)*((1-1^2)/E1+(1-2^2)/E2)/(1/d1+1/d2))pmax=(2*F)/(*ac*L)xx=2**pmax*((1+z^2/ac^2)-z/ac)yy=pmax*((2-1/(1+z^2/ac^2))*(1+z^2/ac^2)-2*z/ac)zz=pmax/(1+z^2/ac^2)ND=LD*ND1NR=LR*NR1ND/NR=(FR/FD)^FR=FD*((LD*ND1)/(LR*NR1))^(1/)@@@ O@A@ GX ` pG@a@@-@\8@M@T*@Y@J@Z@-@\@M@*@Y@J@Z@-@\@M@8*@Y@J@Z@-@\@M@*@Y@TJ@Z8@-@QEP@`O 0?  $H((j?(((*$H)99=(4*^2*rj^3*L**N)/clrcof=(2*^2**N)/Pb*(rj/clr)cof*rj/clr=2*^2*SfldSfld=(rj/clr)^2*(*N/Pb)Qs=(*ps*r*clr^3)/(3**L)*(1+1.5*ecc^2)umax=ps*clr^2/(8**L)H=2**cof*Pld*r*NTF=(2*H*grav)/(*CH*Qs) ""A(: Q!AAAQ!!A1!A1!!1!(@Aq!SA!SAS HSAA!SA! q AA!!a1!q!Aa1!Aq A ! A :%=(6*Wt*L)/(dx*dy^2)=Wt*pd/(dx**Lf)Lewis Formulab=(Wt*Ka/Kv)*(1/(fw*dp))*(Ks*Kld/gf)c=((CP*Wt*Ca*CS*Cm*Cf)/(Cv*fw*dp*gf))ds=(32*ns/*((a/se+m/syp)^2+(Ma/se+Mn/syp)^2)^(0.5))^(1/3)Rcx=pa*b*r/sin(a)*(conA-f*conB)-FxRcy=pa*b*r/sin(a)*(conB+f*conA)-FyRax=pa*b*r/sin(a)*(conA+f*conB)-FxRay=pa*b*r/sin(a)*(conB-f*conA)-FyconA=(sin(2)^2-sin(1)^2)/2conB=(2-1)/2-(sin(2*2)-sin(2*1))/4F=*pmax*d1/2*(d2-d1)=*f*pmax*d1/(8*sin())*(d2^2-d1^2)F=*pmax*(d2^2-d1^2)/4=(F*f/(3*sin()))*(d2^3-d1^3)/(d2^2-d1^2)A ! !Aa ! a!1!a ! aAB !!A A!A 1000000aQA1!1A1 B1A R1! qAqB !AQAB q1!AqA!A1AAQq!AA>H@ <1! >>Q_^ AAA!!aa!11Aq!qAaq!a!1A !A AA!1!q! A1 A!!q!1A1!AA AAq!A A!11 A!1AA AA1q! A!1A1Aq!!1 q A1Aq1 W!*d!!RѡQR(*2]k7@kaA!SAQR!(*!!S!q!qR8Pld=b*h^2*s/(6*L)I=b*h^3/12U=Pld*y/2y=Pld*L^3/(3*E*I)Pld=b*h^2*s/(6*L)I=b*h^3/12U=Pld*y/2y=Pld*L^3/(2*E*I) q" " q!1 qA! 8B!1 1B1 qq! !BT|q$s"1!Aq" Aaq, r2lq A!J!Q q!1* A _U*a q1!AaQQ!1!1A1qRqdRAq!Q1QC1S!qQAATq!AqA!!CA!!A!1 CA!A!!1AAA 1A AAA`AQ A!! AQ1q AA!! AAAqQ A A1A A  1A A QA A!qQA`A!`AAAAp!A!pQA"aAp!A!pA`A!`AAqQ! w6Pld=nf*b*h^2*(s/(6*(L+p*tan())))y=(6*L^2/(nf*b*h^3))*Pld*((L+p*tan())/E)1U!!!UA!!1a1!U!!a1UB z<<'1d1Ua px8!AU!!qU$$HEU$$U!A!U!11AqSA!@۞1R 1xI0xRA!QA!BQW}}}}}R$ QW}}}}}R !aW}}}}}U !!!U!x!!!OOO!U!!ߟ!!!1qUA!AA1qA!AAq!UA!AAA!AUA!!Ua! q1a"AA U" !a!1!AA !U!"!Q !"1!A !U A!a QQU a A5Pld=*d^3*s/(32*r*ksp)I=*d^4/64U=s^2*V/(8*E*ksp^2)y=2*r*L*s/(d*E*ksp)kw=2*r/dksp=(4*kw-1)/(4*kw-4)y=r* qQ11Aa! `0d`AAB B! EA A 0 !1e AQAQ )08@!QQ@b!@I a`A1Q!!!!AAAQ 1>`AQA!aAB!!!AAA"Ad1qAq1A Q!!!A 1Aa!<?1q ]+Pld=b*h^2*s/(6*r*ksp)I=b*h^3/12U=s^2*V/(8*E*ksp^2)kw=2*r/hksp=(3*kw-1)/(3*kw-3)Pld=*d^3*s/(16*r)U=s^2*V/(4*G)y=2*r*L*s/(d*G)y=r*UAUAA!AQUA1qUAA"UAQaUB!$}U$RU!A"TUAAQAAAUA@`AQUAH@RABUHJAHVQ$ aHB!QHb!aH!QHAAAQAUHCAAQHGUAAAAUA AAAU A!UBABEU$dJA!CVBCaAaUAAUAA!AR!R!A1!Q$1!q1!qR!R!UP7aW a aW a a  aW !Q a R aW !a a AaW a1a aW q!a a!aW !` a  A_ aW  A.aHHaWHaHPIaW$P1a$!aW$a$paW!" a1!R1q`A!Ra1q0`S 1!q1 1A!Aq !a!Q!A!aW !a!"A!aWA! !aA!!A!aW$A!aA!AQ!aW$Aa!aHq!aWH1!aHQaW A1a!a AQAaW !!Q!a !!aW q!A!a !AaW A !aA aSAR!A !QAAA aS! !AAA aSARq! !a aW a aW;Pld=2*b^2*h*s/(9*r)U=4*s^2*V*(C^2+1)/(45*G)C=b/hy=4/5*r*L*s*(b^2+h^2)/(b*h^2*G)y=r*!B"QAAaq!AQ"Aa" " !a !1AqAqA1aq1A1q!q!qqlѡRq!1 1!q1A<01q!1* q _1qQqGqAQ1AqRAA11@11O1<qA1!q@QW11qSqA1AAqAA111Bq1BqQq1A1FaqARAS!1!QqTRB!a"QAA!AaA1U"AQQ!"Aa!A!Q QqA !A!A AA Q9Pld=*d^3*s/(16*r*ksp)U=s^2*V/(8*G*ksp^2)ksp=(4*kw-1)/(4*kw-4)+.615/kwkw=2*r/dy=*nf*r^2*s/(d*G*ksp)A !!1A!Q!AAAQ!q11qA1!!1A! Aq!11q1><0xH||||1QA$!1Q$  >A p#|R _Gq!S}}}}A1AqS}}}}1qR1S}}}}1 !?!? Aq  !=== >Aq$!|@>@BOOO!_GqH|||tAH||||qAAq!A1q >1p#A1q A!q!!? A1 q>xAA|@!!_Gqq!!!AAA!1qRq11!Q 1q"1 !"1Aq!1 !YA!1 QaAAA 4Pld=2*b^2*h*s/(9*r*ksp)C=b/hU=4*s^2*V*(C^2+1)/(45*G*ksp^2)when C=1ksp=(4*kw-1)/(4*kw-4)+.615/kwy=7.2**nf*r^3*Pld*(b^2+h^2)/(b^3*h^3*G)kw=2*r/b  B1 AQA AaBQ1BaAQAQ!aQ!A!1"A!11a!AQ!1RB1!1> !TqAqSBq!q%P`AAQ1<1A1AQ1QBQqpQaR1qR lg5W<~!AQ1TqA1BQxAQ!AA11A2 O?? R"q11!!!AA  a aA 1 q 1AAA!qB ၡRB! Aa1Ba AAQB! $ǕY5Tp=2**(Ip/k)=k*=2*/TpB@#A!!RRA ! uL !!RQB @SQA qQ A!Qg@*AQ!d@*BQA QA qA BQ!@!QA!QѡAaB!A!!A !!A A 0a!A A!1 !!q A! B0aAa!q1Aaȑ!!A A!aAq!!d&1A!!AdjbJ!!A!!A!!A(&aQ!RA AQa aQS !!AQA [.x=xm*sin(n*t+)v=xm*n*cos(n*t+)xo=xm*sin()vo=xm*n*cos()xm=(xo^2+(vo/n)^2)vm=xm*n=tan(xo*n/vo)n=(k/m)Tn=2*/n BaсB1q1 AQ!Tm% RHR2Q! "HRAQ! !QMEq R !q!Q A!A"AQQg@*n%TAQ!5&d@*AaQ!R BA"VV]A !QQA gqA !!B!A!@!!AqA!!a!Aa!Q!!B!Aa!A! !A!AA0aA!! !q1 A!! B Aa0aA1A!ga!!A A!aq!!  1  !!!!AaQ!RAAQaaQS!!AQAx.x=A1*^(1*t)+A2*^(2*t)A1=xm*2/(2-1)Soln. for x=xm & dx/dt=0 @ t=0A2=xm*1/(2-1)Soln. for x=xm & dx/dt=0 @ t=0=c/(2*m*n)1=n*(+(^2-1))2=n*(-(^2-1))n=(k/m)Tn=2*/nBx=(A1+A2c*t)*^(n*t)v=n*(A1+A2c*t)*^(n*t)+A2c*^(n*t)A1=xmSoln. for x=xm & dx/dt=0 @ t=0A2c=A1*nSoln. for x=xm & dx/dt=0 @ t=0n=(k/m)Tn=2*/nBx=xm*^(*n*t)*sin(d*t+)v=*n*xm*^(*n*t)*sin(d*t+)+xm*^(*n*t)*d*cos(d*t+)xo=xm*sin()vo=*n*xm*sin()+d*xm*cos()d=n*(1-^2)n=(k/m)xm=(xo^2+(vo/n)^2)=tan(xo*n/vo)=/((4*^2+^2))=c/(2*m*n)Td=2*/dTn=2*/n Bxp=xm*cos(f*t)xm=xf/(1-(f/n)^2)Mag=1/(1-(f/n)^2)n=(k/m)Fo=k*xfBxp=xm*cos(f*t-)xm=xf/((1-(f/n)^2)^2+(2**(f/n))^2)^.5=tan((2**(f/n))/(1-(f/n)^2))Mag=1/((1-(f/n)^2)^2+(2**(f/n))^2)^.5=c/(2*m*n)n=(k/m)Fo=xm*(k^2+c^2*f^2)Tn=2*/nTf=2*/f B1!aQA!1XQ !X !2p@, ,B8BG >A€aA!11!AbXqq aA01#'81 A!pA"q 111q AX  Q  AAA QQ A!!1Q!!1!A!Aq!!q!!q!A!A1!q!ql$f1=1/(2*)*(4*Ten/(m*L))Ten=W/(2*sin())W=m*gravtan()=2*st/LBaA1'#7T$ 1!ASQAR"JJQBQ!Q"SSTBqAѡVBqSQARAQ!BR!B%!%7H#qA"QAS"A AQA J J!E>J1!JqAAむA[1A!!!Q"AZ1!!a1!! q"A! !"! !!" !Q!a1!!! !"!"L! !AR!!! !! Eq! B!! A!! Aa!7'A!JQB!a!!A3EA!qJEAA!!!AuA!!! B1!! HVASA!!!AAR1@!ARABRA! R!ATB!B!AH!*!AAAA!!APPPPa1Q!0000a!!@@@@!A!APPPPa1 !A11`pp`pA`p`p!AQ`p!9n=(grav/st)st=W/keff=1-1/((f/n)^2-1)W=m*gravBAQbdAAbaAQ"A1 G"AA! AQ! 1!A1 !!&EB#WaB&E!R!Q!!&ESrdu!BR!Q!&GA!1"QaHR!!AQ!qaA!"! !!Rq1q1rAaB1B Q1  L2Q4QaqBQQ!Q !qBQq1!QrAR1 A! QqQAQ !A! \8AqTI!aRBQA"!A!”AAABQA"QpAQ.BCARCq *f1=6.93/(2*)*(E*I*grav/(W*L^3))Center Load/Beam Wt Negl.fn=Kn/(2*)*(E*I*grav/(w1*L^4))Unif. Load, w/Beam wtf2=6.93/(2*)*(E*I*grav/(W*L^3+.486*w1*L^4))Unif. Load & Center LoadBf1=13.86/(2*)*(E*I*grav/(W*L^3))Center Load/Negl. Beam Wtfn=Kn/(2*)*(E*I*grav/(w1*L^4))Uniform Load & Beam Wt/lenf2=13.86/(2*)*(E*I*grav/(W*L^3+.383*w1*L^4))Unif. & Center Load/f1 & fnBf1=1.732/(2*)*(E*I*grav/(W*L^3))Center Load/Negl. Beam Wtfn=Kn/(2*)*(E*I*grav/(w1*L^4))Uniform Load & Beam Wt/lenf2=1.732/(2*)*((E*I*grav)/(W*L^3+.236*w1*L^4))Unif. & Center Load/f1 & fnBfn=Kn/(2*)*((E*I*grav)/(w1*L^4))Uniform Load & Beam Wt/lenBAA!AQ1AR! a!1 ! *dqqq(*qkaq1q(*{1q1ؿJq1/B A'@, AaRT "L EnA  )! .Q1! a aAq1 qa1A!1q!!!Q!Q " @!1aQ1 Aqa11#!!!!A1A ,qqqqq`"11!qAQ "q "aHHRa!!UAQ 0!a!BQa!!UAQaH!QR a  >  Q ! Q  a  q 3fn=Kn/(2*)*(D*grav/(wa*r^4))D=E*tr^3/(12*(1-^2))wa=W/(*r^2)r=(ra+rb)/2Bfn=Kn/(2*)*(D*grav/(wa*ar^4))D=E*tr^3/(12*(1-^2))wa=W/(ar*br)Kn=^2*(na^2+(ar/br)^2*nb^2)ONLY if all edges supportedBTTemperature change1000100Density of incoming air110100Humidity ratio0.51Degree of saturation0.51AArea0101000akThermal coefficient for air01100BInfiltration Coefficient01100BFBypass Factor0.110COPCoeff. of performance0110COPhPeformance Coeff.-heat pump0110COPrPeformance Coeff.-refrig.0110cpSp. heat at const. press.CsCoefficient in shading0110EEffective space emiss.0.11e1Emissivity0.11effvVolumetric Efficiency0.11e2Emissivity0.11FHeat Loss coeff.01100FsgSolar heat gain factor0110h1Enthalpy0101000h2Enthalpy0101000hiEnthalpy-Inside Air01100hinFilm coefficient01100hoEnthalpy-Outside Air01100houtFilm coefficient01100kAdiabatic expansion coeff.0110k1Thermal conductivity:10.510k2Thermal conductivity:20.510k3Thermal conductivity:30.510LLength011000maAir Mass01100mwWater vapor mass01100nPolytropic exponent0110naMoles of air0.110ntTotal moles0.110nwMoles of water vapor0.110p1Pressure110001000000p2Pressure110001000000p3Pressure110001000000p4Pressure110001000000paPressure-air0100010000periPerimeter010100phiPressure-High110001000000ploPressure-Low110001000000prPressure ratio01100ptPressure-total0100010000pwPressure-water vapor0100010000pwsPressure-sat'd water vapor0100010000qaRate heat xfer-dry air01100QrateRate of Heat Loss01100QinHeat flow0101000QoutHeat flow0101000qremHeat removed011000qtRate heat xfer-incoming air01100qwRate heat xfer-moisture01100RhThermal resistance-Convect.01100RkThermal Resistance-Conduct.01100RmUNIVERSAL Gas Constant8.314510TTemperature0300400T1Temperature0300500T2Temperature0300500T3Temperature0300500T4Temperature0300500TclTemperature of coil0300500ThiTemperature-High0300500TiInside Temperature0300400TloTemperature-Low0300600ToOutside Temperature0300600UOverall heat transf coeff.0101000V1Volume011000V2Volume011000V3Volume011000V4Volume011000VfAir Vol. Flow rate11001000VtTotal volume011000W23Work of Compression per Stroke011000WinWork0101000xd1Thickness Material 10.110xd2Thickness Material 20.110xd3Thickness Material 30.110xaMole fraction of air0.110xwMole fract of water vapor0.110U=1/((1/hin)+(1/hout)+Rk+Rh)Rh=1/akRk=xd1/k1+xd2/k2+xd3/k31/E=1/e1+1/e2-1Qrate=U*A*(Ti-To)Qrate=peri*F*(Ti-To)qw=**Vf*cp*(Ti-To)qt=*Vf*(hi-ho)qt=qa+qwVf=B*L RCOPr=Qin/(Qout-Qin)COPh=(Qin+Win)/(Qout-Qin)COPh=COPr+1Win=Qout-QinRCOPr=Tlo/(Thi-Tlo)COPh=Thi/(Thi-Tlo)COPh=COPr+1RCOP=(T3-T2)/((T4-T1)-(T3-T2))COP=1/(pr^((k-1)/k)-1)pr=phi/ploRrA!a! !aqA1 Q2 Q! q1 qa q1q q q    a 11Qq1q!!!A 1 q  1q1qq1q1q Aq !Q!q!Q !Q! AqQQQQ! N6pr=p4/p1pr=p3/p2effv=(V2-V1)/(V2-V4)effv=1-(pr^(1/n)-1)*V4/(V2-V4)V1/V4=pr^(1/n)V2/V3=pr^(1/n)W23=(n*p2*V2)/(1-n)*(pr^((n-1)/n)-1)RCoeff. thermal expansion0.000011Shear strain0.011xyShear strain along xy axis10110TTemperature difference0501000Equivalent elongation011000maxMax. elongation011000rDisplacement from R0110stStatic Elongation01100tElongation0.11Strain10110maxMaximum strain10010tThermal strain10110xxStrain-x axis10110yyStrain along y axis10110zzStrain along z axis10110Poisson's ratio0.11Inclined plane angle01090lAngle of twist/unit length10110pPrincipal angle90190p1Principal angle 190190sPrincipal angle-max shear90190s1Principal angle-max shear 104590Stress11000110Normal stress01000181Stress in 1110001102Stress in 201000110avAvg Stress0100019maxMax stress0100019stStatic Stress0100019x1Stress-principal axis 11000001319xxStress along x axis151000019yyStress along y axis151000019Shear stress11000110Shear stress0100018acMax Shear-angle of twist AC01000110avShear stress11000110cbMax Shear-angle of twist CB01000110maxMax. shear stress01000110x1y1Shear stress-principal axis0100019xyShear stress0100019Angle of twist010360bAngle of rotation at B010360cAngle of rotation at C010360Radian frequency01417AArea0110000bBase011000dDiameter01100daDiameter at end A01100dbDiameter at end B01100EYoung's modulus010000110evVolume dilation0.0011freqFrequency0100018GShear modulus01000110gravgravitational constant, m/s^29.80665hHeight011000IpPolar moment of inertia010000110IpaPolar mom. of inertia of A010000110IpbPolar mom. of inertia of B010000110kStiffness0100016LLength011000LaShaft length-diameter da011000LbShaft length-diameter db011000LmLength01100MMass of Load110100NNormal force16100016PLoad01110PwrPower011000RThermal strain force01110radRadius01100RbReaction force-bottom0115RpMohr's circle radius0100019rpmRev. per minute010010000rsShaft radius0110TTorque010010000TaReactive torque at A100001010000TbReactive torque at B10000100016ToLoad torque100010001000000UElastic strain energy0100016VShear force16100016velMax. Velocity10001010000VfFinal volume011000ViInitial volume0110000wWidth01100WtForce0116 !!!!! !1 !q !!  ! ! A1 ! qa! A Aѱ AѱA AAAAA(AAAѱ!AQ A!!AQ AA!AA1A!! A!! A!!qS !11A!QB! !A!B""QqQ"A!G!!"!B'!!!!!!AA!!Qq!1!A!w7=P/A=/L=*ETVi=b*h*wVf=Vi*(1+)*(1-*)*(1-*)ev=(1+)*(1-*)^2-1 !A A!AAq! ! A!1!! A QA qq 1 1 _R!Aa11RB!ABBA B1AqAqTB!!AAQ11B2AqA!B `Y11AH}^0Aa'1!AAqQAQ!BQ!AѱQBQ!AѱQ!BQ!AѱQBqQAѲQAQAQAAѱqQAQQAQAѱQAaAQABѱQAAQABѱQAAQABѱQQAQBѱQUqRa!S!Bѱqa1!A!QBѱqa11A!!B1a1A1A!B@Wq1Q1 !AAA1X1qZ aQA7Tav=P/Aav=G*Hooke's Shear LawG=E/(2*(1+))T=P*L/(E*A)k=E*A/LTA 1! !Q !AA!A1a !A!ARAA!AQa qAA!!A` "qp "!A `BRAQ!!!!!!BQq1! A!Q!Ѣ!B  H AA!!aA!!AAAA!!A !!!  !! ]4VL5!!Cq1\q!! A !!11! !!>  !! 1 !&A!!!)AA!$FN" HJx/GJ!B` 1ѢRAQq !Q `` !!Q1QAQ1 !A ` !aAp `A!A !FBqAA1 AQqAC1Q ! 1 !AQ Q !A Qz9t=*Tt=t*LR=A*E**TT ! A! A ! !1 !AQ ! ! !B !a !AQ !AQ !B !B ! !qB@"B@"B@1B A!R"AAQB!B!Aq ! ! !! !q ! ! ! ! !"AA!"A!"!"A!""A!AA!1qH@ !    *T 8!!qa1T !"a!!Q!IA!a&!"1U6!b*G "qq !E@Wt*(h+max)=E*A*max^2/(2*L)max=Wt*L/(E*A)+((Wt*L/(E*A))^2+(2*Wt*L*h/(E*A)))^.5st=Wt*L/(E*A)max=st+(st^2+2*h*st)^.5max=Wt/A+((Wt/A)^2+(2*Wt*h*E/(A*L)))^.5max=st+(st^2+2*h*E/L*st)^.5max=(Wt*vel^2E/(A*L*grav))^.5M=Wt/gravT1! !1 Aa1 a"! A!A ! AAA !!" AqAa A1! !AAQ !"!aABa!a!qaBAA1A"2 !CY@A!Aa!AAA!AA"1PAA1AA!!B!!QA!BABAA!!AAAA!A AA !!A AA A AA "A As%N=P*cos()V=P*sin()=P/A*(cos())^2=P/A*sin()*cos()TqA AAA1R R"A!A "!!A ! A !A(A A!R"A1 R!A" A!Q#!aAA1AA!!A!qAAQA!1AaARq"QAAAA!!AR AA1 AARQGJqA!A&NK8!ABF*0AB( BABAABAAA! !B!A A1BRAA AAA!!Aa!B!AAAA!!QSAA AAQA1R AAAA!"AQAA1R!!1BB!1Aq@AB!!AA!!QA A1!! ARA A1 AqA !! QQ AA с A1 QAAAB! A"! HA AA AA Aa !!1R(AA! !R A#A! " A" q" !Q! A 8x1=2*xy*cos()*sin()x1y1=xy*((cos())^2-(sin())^2)Ttan(2*p)=2*xy/(xx-yy)Rp=(((xx-yy)/2)^2+xy^2)1=(xx+yy)/2+(((xx-yy)/2)^2+xy^2)2=(xx+yy)/2-(((xx-yy)/2)^2+xy^2)1+2=xx+yycos(2*p)=(xx-yy)/(2*Rp)sin(2*p)=xy/Rpq!Aq1 A!1A!AA!!AaAA!1AL0AAA!AQA11A!"AO1A!QA!AQ\11B! XBPh11B!AQJ21JP! AAQA1!!A!"A HA!A1B!A!!!AAA1AA!AAAAq!q!!Q!A!x@aQ!AB!!!AAA!A"1R !A"Q!RTtan(2*s)=(xx-yy)/(2*xy)tan(2*s)=1/(tan(2*p))s1=p-/4max=(((xx-yy)/2)^2+xy^2)max=(1-2)/2T qA aAAQ1R aAaA RAA"AaAaA"A A!AaaA!A A!aaAA!R AR!AaZqAAR*!A !!AA!AA!1A!FRq!!>y1AAAh!ׁAAR!!1!q!AA9B!qAAAAR#1AG`A!AAB!a!AB!!qaABAl?rABAAA!nvAB!zA1B?ARA$a}NAA$!}B!A!~AAAA!q~ASA $(@AQA1RhuaRAAA!"hQaA1R1qa1B!!!ёB!Qa1AA!!!A1`a1!TѢ!!A1!1 "A1!A !!! 11!R !1"!Q"q $EP! AA!Q!AA1! B! ! AQ BQ1A AQ9xx=1/E*(xx-*yy)yy=1/E*(yy-*xx)zz=/E*(xx+yy)xy=xy/Gxx=E/(1-^2)*(xx+*yy)yy=E/(1-^2)*(yy+*xx)T<@ P8I0L0@P@@C8 c@ _UUWUUV@ S@ !8P  |@P@@@@\ @@DRUPZ*@iAP!H@/3BTP@@B5T@V@D4@@<@@PP@A@F d|I 3 8׷U_^[DI 5 (xF @(ST($@@QAQA4a 1!AQ!! i!%B!^_ATK9SAA !l$ATѢ!ARSL\ ۇARIASnSAQ!06ѣASq@QT!!PmhARP%hS@&BnKr1068@*XERP-h@aS!Rb!!aa!2Q@X`@"HERa1A!T @tJnKr!AQP ȰT1%Qa!!AQUAR!!UA1R!q!Av@!ѤAQS!QAARmTATA1#QB!PA"AQ@1RaTE1ARaU"Br"qa [`!RA!AT@1UR#Ab1qѦ"B!R AUaU"B'%aAWqU1¥AXAUa!q1"]:BQRAZqUa!2q14!ARQA!A_QWr%7CM=I00/VdGM=I00/Vd-CGVd=I00*tan()/xo 1 !1A1!A1!1A! 1A a1 1Aq1 q  !! 1A 1! Q! Qq! A1qAq1b@AA!!Aaqa bA8qAaA qBQAXAqAaAqB!AqAqQ1qAATё A!q!AAqAA  1t5=/gravp1=*grav*h1p2=*grav*h2pavg=1/2**grav*(h1+h2)hR=2/3*(h1+h2-(h1*h2)/(h1+h2))L=(h2-h1)/sin()dR=(hR-h1)/sin()p1/+v1^2/(2*grav)+h1=p2/+v2^2/(2*grav)+h2ht=p2/+v2^2/(2*grav)+h2pt=*htht=hs+h1hs=hp+hvhp=p1/hv=v1^2/(2*grav)Et=m*grav*ht=/grav Nre=de*v*/Reynolds numberNre=de*v/kNre=de*Qf/Nre=4*Qm/(**de)Nre=4*Qv*/(**de)k=/de=do-diFull flow - annulusde=bxFull flow - squarede=2*bx*by/(bx+by)Full flow - rectanglede=dHalf-filled - circlede=4*bx*by/(bx+2*by)Partial flow - rectanglede=4*byShallow streamde=2*by*(btop+bbot)/(bbot+2*bside)Partial flow - trapezoid1A!A!AQ!A!A!A!!A!1Aaa!!qA!!A``!!AP !!!"A1AAA!qq1AQ11qqTASA!"QQ1AUq1!a1RqR1AV!!ᱤqX1AX!AQ!X1BX!!!!AA1!X1AXA!!!A!X1AX!AX1AX!X1AX!X1AX!X1AX!X1AX`)!V*X1+1.!(8 1AAQ1 Q qQa A! !ё qQA!Q Qq 3tan()=ax/(ay+grav)ph=*grav*h*(1+ay/grav)tan()=^2*r/gravh=(*r)^2/(2*grav)v=*rA A A Q Q qq Q Q A A A A A A A A Q Q qQaqQaQQQQAQAQAAaAaAAA AAA1 QAQqqAq QQ AA AAA APA PP A 0aQA Q aq!A!AQ!aaA1!!A!1!!A1a!0Aa! > A QaW!q1R Qa1 q1Q!A!A I>$BA AA1QAAC A!a A aA A! A1 A1 AA qAAqA1 1 A! 6/x*(Re)=5o=*uo*(Re)/(3*x)Fs=.664*b**uo*(Re)Re=uo*x/ku/uo=.332y(Re)/xcf=2*o/(*uo^2)Cof=1.33/(uo*Lp/k)^.5=k*=*kcf=.058/Re^(1/5)Re<17Cof=.074/(uo*Lp/k)^(1/5)Re<17o=cf**uo^2/2Fs=b**uo^2*uf=(o/)Re=uo*x/kRf=uf*y/k=.37*x/Re^.2Boundary layer depthv=5*k/ufViscous layer depthwhen(yv, u=o*y/Viscous Profile,Re<17when(v0Roughened Surface u/uf=1/vk*(ln((y-hd)/kf)+)Rough surface =4.7*y/LmHydrodynamic Stabilityuavg=(*d^2)/(3**sin())uavg=grav*d^2/(3*k)*sin()So=tan()u=grav*So/(2*k)*y*(2*d-y)umax=grav*So/(2*k)*d^2y=dNre=uavg*d/ko=*sin()*(d-y)=k*=*grav PPPPPPPa0000000a@@@@@@@Aq1!qq!A q1Aq!A A11!A!A1A!A!A!A1A!A1A!A !AA1!Aaq aAaA1Q !AAQ d!qQ1A!11AQ AA"1A `@ AApqA!Aq1A!!AR1,A!!AN !BS8A !QAqqB!QGqR1AaQ!X|1AARqQ!BSABR!!AA!AqRA!A2AA1QA@A2A ,@@1AqA1!Aq!AAR,@!ARAA(xAAQ!aA)&AA1AAAA1AA!AA1!A qAqq q!A11A qAA!@@@@@@@A PPPPPPPa0000000a@@@@@@@ AA !AQASAa aARAAQASAa aA҂A ! q ;p1/+h1=p2/+h2+hfu=(d*y-y^2)/(4*)*(hf*/L)o=d/(4*L)*hf*hf=32*(*L*uavg)/(*d^2)Darcy-Weisbach equationNre=abs(uavg)*d/kLaminar if Nre<2000Q=uavg*/4*d^2fr=64/Nre=*grav=k* p1/+h1=p2/+h2+hfEnergy Equationabs(hf)=fr*L*uavg^2/(2*grav*d)Darcy-Weisbach equation1/(fr)=2*log(Nre*(fr))-0.8Nre>3000uf=uavg*(fr/8)Rf=abs(uf)*y/kNre=abs(uavg)*d/kTurbulent if Nre>3000abs(o)=uf^2*Q=uavg*/4*d^2=*grav=k*when(03000Nre=d^(3/2)/((fr)*k)*((2*grav*abs(hf))/L)u/uf=5.75*log(y/kf)+Kcabs(hf)=fr*L*uavg^2/(2*grav*d)uf=uavg*(fr/8)abs(o)=uf^2*=*grav=k*when(43&0RS!!AU\2hfa=hfbva=(2*da*grav/(fa*La)*hfa)vb=(2*db*grav/(fb*Lb)*hfb)Qt=Qa+QbQa=va**da^2/4Qb=vb**db^2/4A! q  A 1A!A! Qq q! q< Aq1qA qA_pA1!qPA qa1aAQ!QqA AQ1Aa11q QrqA1qAx1 q!qBq$E1 QaAQ>A2! BA~!q!AqA! ~|xAA}"!!AQ"A!AAQA1!B9%a"CA!"BQ!a!"Bq !1"Cq ""q !"qq q"q !!1 !1 A a1 _8p1/(*grav)+v1^2/(2*grav)=p2/(*grav)+v2^2/(2*grav)+hfv2=Fva*(2*(p1-p2)/)Qv=fc*A2*(2*(p1-p2)/)Fva=1/(1-cc^2*(A2/A1)^2)dc=vc*cccc=Ac/A2fc=Fva*dcNre=v1*d1/kv1=Qv/A1hp1=p1/(*grav)hp2=p2/(*grav)ht1=hp1+v1^2/(2*grav)ht2=hp2+v2^2/(2*grav)when =m, Fluid= manometer fluid h=(p1-p2)/(*grav)when m, Fluid manometer fluid h=*(Qv/(fc*A2))^2/(2*grav*(m-))v1^2/2+k*Rm*T1/(k-1)=v2^2/2+k*Rm*T2/(k-1)v1=f2*A2*v2/(f1*A1)v2=(2*k/(k-1)*((p1/f1)-(p2/f2))/(1-(f2*A2/(f1*A1))^2))^(1/2)p1/p2=(f1/f2)^kQm=dc*f2*A2*v2f1=p1/(Rm/MWT*T1)f2=p2/(Rm/MWT*T2)hp1=p1/(f1*grav)hp2=p2/(f2*grav)ht1=hp1+v1^2/(2*grav)ht2=hp2+v2^2/(2*grav)h=(p1-p2)/(m*grav)Nre=v1*d1/kQm=Yc*Ao*fc(2*f1*(p1-p2))square orificeYc=1-1/k*(1-p2/p1)*(.41+.35*(Ao/A1)^2)square orifice!B! A"A !  11  A! qq! A!A!q !11 qQ1 qѡ Aq; !QA!;Aq !A1AA!A!!QAA !Aa10 A&p!Aa1!!R!q!Bq!1a!q!!!!! a!! 1!!qa!! 1!!1!A!!1!!1aqaQ)SAёC1!QJ"AQA"A!aAсQQBAQQx$AqaQAAA1A 11 A!qAA!1A! ?!QA B " I m:A!!R!!B! 4Qm1=1*VF1Qmf=f*VfQm2=Qm1+QmfFx=(Qm2*v2x-Qm1*v1x)Fy=(Qm2*v2y-Qm1*v1y)!!A  1qAA TAA A@!  Aa@ AaAA A!A !AqqAA1AA11!AA!A!!AAQ!qQA1BAaAARASAAR!Aa!"a!!8p1B!qq A!11qa1"q$PA(ORQ1pAq!A!Q>@!Q!!QBAQ!SASAA!Q1B!A !Aa  0 IA  Bd*!A@@A A  TH2AusA8HRQ-QQ!SWTAQ2!QQASAQ!QQ!SA!Q 1A!qQw4Fx=Qm*vxForce on plateQm=*VflVfl=vx*AA=*d^2/4vy=(vo^2-2*grav*h)Velocity at plate heightFy=Qm*vyForce on plateQm=*VflVfl=vo*AA=*d^2/4A!1QB!R!q1AAATaRѡ1aAAaq1!ATa!HJAR!!BSABqAAR!B"Q!qAA AB A!C0!sAQAR"RAqA1qQ1A!AQARAQR!!Q!A1qQ1q!! 1AQAqq A"1"! ! q ! A !1a Aa aA !1aB  1 qA1! A1 "!q1!q1  0q!!10qa0>AA10>a"AA!qBAQA AQA !! AA !A!! (@R (AR ($L A! !A!Q !!A"  1!a"Q#!.vx=v2*cos()-v1vy=v2*sin()Fx=Qm*vxFy=Qm*vyQm=*VflVfl=v1*AA=*d^2/4v1=v2No Frictionvx=(v-vbl)*(cos()-1)vy=(v-vbl)*sin()Fx=Qm*vxFy=Qm*vyQm=*VflVfl=v1*AA=*d^2/4v=v1-vblNo FrictionAngular acceleration01100hChange in height01100rOutreach beyond perimeter01100Eccentricity0110pAngle0Displacement angle01Collison angle 102Collision angle 201iInitial collison angle 102iInitial collision angle 201fFinal collison angle 102fFinal collision angle 20oInitial displacement angle0tProjectile Angle at time=t0Stress010001000000lLoad per distance010001000000oLoad per cable length010001000000Torque01100Precession rate01100Angular velocity01100oInitial angular velocity01100sAngular Velocity01100Coefficient of friction0.1101Coefficient of friction0.1102Coefficient of friction0.110aAcceleration01100agGravitational acceleration01100anNormal acceleration01100apoApogee-Max. distance to c/m010010000AreaArea010010000atTangential acceleration01100axAcceleration along x axis01100clCable Length0.510crCoefficient of restitution0.510CsConstant0.00000001.0011FForce01100FaHorizontal force010010000FFrictional force01100FnNormal force01100FtTangential force01100GUniversal grav. const, Nm6.6725911gravgravitational const, m/s^29.80665haHt. low point to left supp.0101000hbHt. low point to right supp.010100hcCharacteristic length0101000hcmDist. rotation axis to c/m01100hsConstant011000IMoment of inertia01100IcmMoment of inertia - c/m01100IpMoment of inertia01100KEKinetic Energy01100KErKinetic Energy:Rolling01100LDistance between A & B010100LaDist. low point to left supp.0101000LbDist. low point to right supp.010100LmAngular momentum01100mMass01100m1Mass 101100m2Mass 201100mcmMass of Icm01100MeaMass of the earth15.97624145mrMass of rolling object01100pLinear Momentum01100PEPotential Energy01100perPerigee-Min. dist to c/m010010000PwrPower01100rRadius01100raRadius-semimaj. ellipse axis01100rbRadius-minor ellipse axis01100rdDist. betw. c/m of m1 and m201010000000rinInner Radius01100roInit ht/dist planet center01010000000routOuter Radius01100rmRadius of m to rot.center01100rwRadius01100sFinal position01100saArc length01100sarcCable len. from lowest point010100sdDisplacement01100soInitial position01100sxox position at t=001100sxtx position at time t01100syoy position at t=001100syty position at time t01100tTime01100TaTension at left anchor010001000000TbTension at right anchor010001000000TxTension at a location x0101000TETotal energy01100ToTension at lowest point010001000000TpPeriod of one cycle01100vVelocity01100v1fFinal velocity of 101100v1fxFinal velocity 1:x-axis01100v1fyFinal velocity 1:y-axis01100v1iInitial velocity of 101100v1ixInit velocity of 1:x-axis01100v1iyInit velocity of 1:y-axis01100v2fFinal velocity of 201100v2fxFinal velocity of 2:x-axis01100v2fyFinal velocity of 2:y-axis01100v2iInitial velocity of 201100v2ixInitial velocity of 2:x-axis01100v2iyInitial velocity of 2:y-axis01100vcCritical velocity0100100000vcmLinear Vel. of c/m01100vescEscape velocity01100vgrVelocity due to gravitation01100voInitial Velocity01100vpTangential velocity:perigee01100vtopVel. top of rolling object01100vtVelocity at time=t01100vxoInit velocity: x axis, t=001100vxtVelocity: time=t, x axis01100vyoInit velocity: y axis, t=001100vytVelocity: time=t, y axis01100WWeight010010000xDist from origin: x axis01100yDisplacement0101000yoInitial vertical position01100F=m*aNewton's Second Lawp=m*vKE=1/2*m*v^2PE=m*grav*hTE=PE+KEPwr=F*vxv=vo+a*ts=so+vo*t+1/2*a*t^2v^2=vo^2+2*a*(s-so)s=so+(v+vo)/2*ts=so+v*t-1/2*a*t^2xy-yo=vo*t-1/2*grav*t^2v^2=vo^2-2*grav*(y-yo)y-yo=1/2*(vo+v)*ty-yo=v*t+1/2*grav*t^2v=vo-grav*tx=o+*t-o=o*t+1/2**t^2^2=o^2+2**(-o)-o=1/2*(+o)*t-o=*t-1/2**t^2xsa=rw*(-o)vcm=*rwKE=1/2*Ip*^2Lm=Ip*Ip=Icm+m*rm^2vtop=2*vcmKEr=KE+1/2*mr*vcm^2mr=mcm+mPwr=* xFt=m*at=Ft*r=m**r^2=I*Pwr=*x=(m*grav*r)/(I*s)Lm=I*sx a1a !1 q! AA !! ! !! !!!A (!! 1! ! (!A AAA!! !A_QqaB1!B)@QA!!!!!Q A1H !p1G !AA !! 00A 11!`Q (!"a!( RHQ @0!Б QaA!!A"!A!!A!q!!AQ!!Aaq!A !"!AQq!!qQ"!A#"!!q! !!!A! A! !!Q!QAAAp6vxt=vxo+ax*tsxt=sxo+vxo*t+1/2*ax*t^2vxt^2=vxo^2+2*ax*(sxt-sxo)vyt=vyo-1/2*grav*tsyt=syo+vyo*t-1/2*grav*t^2vyt^2=vyo^2-2*grav*(syt-syo)vxo=vo*cos(o)vyo=vo*sin(o)vxt=vt*cos(t)vyt=vt*sin(t)vo=(vxo^2+vyo^2)vt=(vxt^2+vyt^2) x1  a A ! !! !! A! !AA !!AqTAA !!A! !!! !! A !  a 1a1 !Q ! Q ! Q!   11 AA!!A!AQ Q!AQ Q(@ QQ!Q AQA!1 $II HБ! B!AW ^@!j"m1*v1i+m2*v2i=m1*v1f+m2*v2fm1*v1i^2+m2*v2i^2=m1*v1f^2+m2*v2f^2v1f=(m1-m2)/(m1+m2)*v1i+(2*m2)/(m1+m2)*v2iv2f=(2*m1)/(m1+m2)*v1i+(m2-m1)/(m1+m2)*v2ixQ Q AQ !A A! !  a ! a1Z! a!A !!! 1!! !A! !AA !qA"AA !qA! !!! 1!!! AA X  h!14 1! !a1 aq! AQ!! T! B1 A !!1A!A A A AAA AQ AaQA A!qQAQQ Q"!1Q 1 ! qk5m1*v1i=m1*v1f*cos(1)+m2*v2f*cos(2)m1*v1f*sin(1)=m2*v2f*sin(2)m1*v1i^2=m1*v1f^2+m2*v2f^2xm1*v1i+m2*v2i=m1*v1f+m2*v2fv1f-v2f=cr*(v1i-v2i)v1f=((m1-cr*m2)*v1i+m2*(1+cr)*v2i)/(m1+m2)v2f=((m1*(1+cr))*v1i+(m2-cr*m1)*v2i)/(m1+m2)x %L2@ !H DPpq^QH) %(@@<p@ `   % IB-S>k@D MB % IB@ @! !    0 {}׵U0 B B iD@iD$Qi@ 4]@!$)! `A+!AA`@ Ќ R@`qD^ D  $ 0 J!d HRP@9`@pd5v1ix=v1i*cos(1i)v1iy=v1i*sin(1i)v2ix=v2i*cos(2i)v2iy=v2i*sin(2i)v1fx=v1f*cos(1f)v1fy=v1f*sin(1f)v2fx=v2f*cos(2f)v2fy=v2f*sin(2f)v1i*sin(1i)=v1f*sin(1f)v2i*sin(2i)=v2f*sin(2f)v1f*cos(1f)=((m1-cr*m2)*cos(1i)*v1i+m2*(1+cr)*v2i*cos(2i))/(m1+m2)v2f*cos(2f)=(m1*v1i*cos(1i)*(1+cr)+(v2i*cos(2i)*(m2-cr*m1)))/(m1+m2) xF=G*m1*m2/rd^2ag=G*m1/rd^2Acceleration due to gravity of m1vesc=((2*G*m1)/rd)ag=v^2/rdCircular OrbitF=m2*agCircular OrbitTp^2=4*^2/(G*m1)*rd^3Circular Orbitv=*rdag=^2*rdCircular OrbitLm=m2*rd^2*Ang. Mom. m2 orbiting m1PE=G*m1*m2/rdKE=G*m1*m2/(2*rd)TE=KE+PE xc@@` UUp#@@ @@`@ @@@8 AH@UH@8 U N ׏  @_  @_` |   ` ` p  (P, #%TE4!A@`<0Area=/2*(per+apo)*(apo*per)Area=hs*Tp/21/rd=1/per*(1-G*m/(per*vp^2))*cos()+(G*m)/(per^2*vp^2)Tp=/hs*(apo+per)*(apo*per)hs=vp*perv=hs/rdapo=per/(((2*G*m)/(per*vp^2))-1)Apogeera=(per+apo)/2Semi-major Axisrb=(per*apo)Minor Axis=1/per*(1-(G*m)/(per*vp^2))*hs^2/(G*m) x1/r=1/ro*(1-G*Mea/(ro*vo^2))*cos()+(G*Mea)/(ro^2*vo^2)=Cs*hs^2/(G*Mea)hs=vo*roCs=1/ro*(1-(G*Mea)/(ro*vo^2))vesc=((2*G*Mea)/(ro))vc=((G*Mea)/(ro))per=roPerigeeapo=ro/(((2*G*Mea)/(ro*vo^2))-1)ApogeeTp=/hs*(apo+per)*(apo*per)ra=(per+apo)/2Semi-major Axisrb=(per*apo)Minor Axisv=hs/r x   !! a! !QAaX a  a  a!!aABAalTa!AQABaABa!!aa!aA!1Q!Aa!V@!A!RArqb!A!QQ!Q&@* a!5)F=*FnFn=W*cos(p)*W*cos(p)=W*sin(p)=tan(p)W=m*gravxA!AB! AH!QA!QQA !! ! !1 ! !A!    IJ1)Qa!!A!Q1!A(p qA Aq H !q q!q!AqU!1!1a1!!!!AA!a! !  ! ! A`p`p`p`p`p`p\2Fa=1*W+W*(2*cos()+sin())/(cos()-2*sin())Fa=W*(1+(2+tan())/(1-2*tan()))W=m*gravxq AA!AaA!QA!AA!A!A!AAqA!AqAA!AA!A!q!Aa!AAQAApA!!AA!AA!A A!A A!A!RQLaղR?1PRaP!Q Q!QA qA!AAA`pp`A`!p`F/Area=*(rout^2-rin^2)=Fn/(*(rout^2-rin^2))=(2**Fn*(rout^3-rin^3))/(3*(rout^2-rin^2))x! q A !a! Aa !1! AQ!Q Aa !1a! !  h* A!RA1A !1!A aAQAq1 A! A!L$!A !J1 !B! A1A!B1 !!B! !q!qC!B A!)C1))CaB>BQ!C J!A1DaBA! DpB )1EaBQ"AB!E 1 E!E1 11!!E1 AQ 1!!!1 11 ! ! ! !!"!! A!A 1!A1 !A! !"!A!!! Q! 9y=l*x^2/(2*To)L=La+LbTo=l*La^2/(2*ha)To=l*Lb^2/(2*hb)Ta=l*La*(1+La^2/(4*ha^2))Tb=l*Lb*(1+Lb^2/(4*hb^2))x!"! A!A q!A !A!q!!!!A!q!! Q!!!1a!A  !Q!AaA !1AQA! h*Aa1 A!R ! !1!2! a!AQAA!  A  1&B  Aa!qA2!!!!сAq!qAQaQa!!!QAA\QqQ11))Ƀa!AQ1a!H(!1!HA,!1a!aBAq1!!Q !1 a!11P!!21!B"<AA"a!AQ1!!!!1 1 1a!!a1 1 AA!1aq AA!!A q 1a1Q!! Qa! A! ! !! !1 1! !__V__V9y=hc*cosh(x/hc)L=La+Lbhc=To/osarc=hc*sinh(x/hc)ha=hc*(cosh(La/hc)-1)hb=hc*(cosh(Lb/hc)-1)Tx=o*hc*cosh(x/hc)Ta=o*hc*cosh(La/hc)Tb=o*hc*cosh(Lb/hc)cl=hc*(sinh(La/hc)+sinh(Lb/hc)) xLinear Harm. Osc.Ang. Harmonic Osc.Simple HarmonicSimple PendulumPhysical PendulumTorsional PendulumPendulumsFree VibrationOverdamped Case >1Crit. Damping =1Underdamped <1Natural VibrationsUndamped ForcedDamped Forced Vib.Forced VibrationSimply SupportedBoth Ends Fixed1 Fixed/1 Free EndBoth Ends FreeUniform BeamsCircular Flat PlateRectangular PlateFlat PlatesStretched StringVibration IsolationUniform BeamsFlat PlatesNatural FrequenciesNatural VibrationsForced VibrationsNatural FreqNat. & Forced Vib.Simple Harm. MotPendulumsNat. & Forced VibWaves & OscillationGeneral CycleReverse CarnotReverse BraytonCompression CycleRefrigerationHeating LoadRefrigerationRefrigerationNorm Stress,StrainVolume DilationShear Stress/Mod.Stress/Strain-BasicAxial LoadTemperature EffectDynamic LoadLoad ProblemsStress on Incl.SectPure ShearPrincipal StressesMax Shear StressPlane Stress-HookeStress AnalysisPure TorsionPure ShearCircular ShaftsTorsional MemberTorsionStress/Strain-Bas. Load ProblemsStress AnalysisMohr's Circ-StressTorsionStrength MaterialsElasticity:IdealCapillary RiseFluid PropertiesUniform FluidCompressible FluidTroposphereStratospherePressure VariationPressure VariationFloating BodiesIncl. Plane/SurfaceFluid StaticsLinear Accel.Rotational Accel.Fluid Mass Accel.Bernoulli EquationReynolds NumberEquivalent DiameterFluid Mass AccelFluid DynamicsLaminar Flow:PlateTurblnt.Flow:PlateLam.Flow:Incl.PlaneSurface ResistanceIncompressible FlowCompressible FlowVenturi MeterSmooth Pipe:LaminarSmooth Pipe:TurblntRough Pipe:TurblntFlow: Pipe InletSeries Pipe Sys.Parallel Pipe Sys.Venturi MeterConduit FlowVertical PlateHorizontal PlateStationary BladeMoving BladeOpen JetJet PropulsionOpen JetImpulse/MomentumFluid PropertiesFluid StaticsFluid DynamicsSurface ResistanceFlow in ConduitsImpulse/MomentumFluid MechanicsLinear MotionFree FallCircular MotionConst. AccelerationRotation/RollingForces In Ang. Mot.Gyroscope MotionAngular Motion1D Collisions2D CollisionsElastic Collision1D CollisionsOblique CollisionsInelastic CollisionElastic CollisionInelast. CollisionCollisionsLaw of GravitationKepler's LawsSatellite OrbitGravitation EffectsFrictional ForceWedgeRotating CylindersFrictionParabolic CableCatenary CableStaticsLaws of MotionConstant AccelerAngular MotionProjectile MotionCollisionsGravitation EffectFrictionStaticsDynamics & Statics3.14159265358979323846264338327950288419716939937511circle ratio12.718281828459045Napier constant10.577215664901533Euler constant11.618033988749895golden ratio1.00729735308fine structure1c299792458speed of light in vacuumm/s_m/_s08.854187817620412permittivity of vacuumF/m_F/_mF9.64853094Faraday constantC/mol_coul/_molG (_Gc)6.6725911Newtonian constant of gravitationNm^2/kg^2_N*_m^2/_kg^2grav (_g)9.80665acceleration of gravitym/s^2_m/_s^2h6.626075534Planck constantJs_J*_shb1.0545726634Dirac constantJs_J*_sk1.38065823Boltzmann constantJ/K_J/_K01.25663706143596permeability of vacuumN/A^2_N/_A^2q1.6021773319e- chargeC_coulem1.7588196211e- charge / massC/kg_coul/_kgme (_Me)9.109389731electron rest masskg_kgmn (_Mn)1.674928627neutron rest masskg_kgmp (_Mp)1.672623127proton rest masskg_kgm1.883532728muon rest masskg_kgpe1836.152701mass p+ / mass e-1re2.8179409215classical e- radiusm_mq206.768262mass / mass e-102.0678346115magnetic flux quantumWb_WbB (_b)9.274015424Bohr magnetonJ/T_J/_Te9.284770124e- magnetic momentJ/T_J/_TN5.050786627nuclear magnetonJ/T_J/_Tp1.4106076126p+ magnetic momentJ/T_J/_T4.490451426 magnetic momentJ/T_J/_Ta0 (_Rb)5.2917724911Bohr radiusm_mR (_Rdb)1.09737315347Rydberg constant1/m_m^1brc13.7417749161st radiation constantWm^2_W*_m^2brc2.014387692nd radiation constantmK_m*_Kbrc30.002897756Wien displacementmK_m*_K5.670518Stefan-Boltzmann constantW/(m^2K^4)_W/(_m^2*_K^4)c2.4263105812e- Compton wavelengthm_mn1.3195911015n Compton wavelengthm_mp1.3214100215p+ Compton wavelengthm_mSP101325standard pressurePa_PaST273.15standard temperatureK_KVm22.41410molar vol. ideal gas at STPliters/mol_l/_molmwa0.02897Molar Mass of Dry Airkg/mol_kg/_molNA (_Na)6.022136723Avogadro's number/mol_mol^1Rm (_Rc)8.314510Molar ideal gas constantJ/(molK)_J/(_mol*_K)Mea5.97624Mass of the Earthkg_kgrea6.376Mean radius of earthm_m.F()(f(t)*^(**t),t,,)Fourier Transformf(t)1/(2*)*(F()*^(**t),,,)Inverse Fourier Transformf(t)F()Transformationg(t)G()Transformationa*f(t)+b*g(t)a*F()+b*G()Linearityf(t)F()Symmetry(t)1Time Unit Pulsef(t-t0)^(**t0)*F()Time Shiftingf(a*t)1/abs(a)*F(/a)Time Scaling(f(t),t)**F()Time Differentiation(f(),,,t)1/(*)*F()+*F(0)*()Time Integration12**()Frequency Unit Pulse^(*0*t)*f(t)F(-0)Frequency Shiftingt*f(t)*(F(),)Frequency Differentiation1/(*t)*f(t)+*f(0)*(t)(F(),,,)Frequency Integration(f()*g(t-),,,)F()*G()Convolutionf(t)*g(t)1/(2*)*(F(y)*G(-y),y,,)Modulationconj(f(t))conj(F())Complex Conjugate(conj(f(t))*g(t),t,,)1/(2*)*(conj(F())*G(),,,)Parseval's Theorem(abs(f(t))^2,t,,)1/(2*)*(abs(F())^2,,,)Energy Relation12**()Constant(t)1Unit Impulse(t-t0)^(**t0)Shifted Unit Impulseu(t)*()+1/(*)Unit Stept*u(t)**((),)-1/^2Unit Rampu(t+T)-u(t-T)2*T*sin(*T)/(*T)Rectangular Pulse1-2*abs(t)/TT/2*(sin(*T/4)/(*T/4))^2Triangular, abs(t)