ࡱ> &%  !"#$()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root Entry Fj-a7UWorkbook?MBD00067ACFFP UP UOle A 1F!Solution!Picture 2 FMicrosoft Equation 2.0 DS Equation Equation.29q@@?HlGG T=eD f.1՜.+,0HP X`hp x CompObjfEquation Native \SummaryInformation('DocumentSummaryInformation8 @\pMechanical Engineering Dept. Ba==h,_8X@"1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1Arial1 Arial1 Arial1 Arial1Arial1 Arial1 Arial1 Arial"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)7*2_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)?,:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_) 0.000                + ) , *  # ! " " "p""@ @ # !p""@ @  " "8     # ! 8 ``i̜̙3f3333f3ffff333ff333f33f33BBB\`2Solver Problem D;'3e:$f:$+ solver_adj):$:$" solver_cvgMbP? solver_drv solver_est solver_itrd solver_lin solver_neg solver_num solver_nwt  solver_opt:5" solver_preư> solver_scl solver_sho solver_timd" solver_tol? solver_typ solver_valsum_sq:5 Ta;'3 Tp;'3`i;3  "3`K* VjجK@=3`K* VjجK ;| osxVMHTQ>89c: ~O@3q!49F.G'F|L $Di"-*E6qvp,dP_ܟiXv==|CZZr*7q#<?V"WvLB5P5|X TU.2MQkqlzseIWSʵ+TUqlp-0+p"h;Ԭ]4#f FFw4ƣc2:ƨ3ǚx°A e‰ a⭓?Y-)5C >GIDtp|4``-k dL2MO'"Qsƥ?I[vDc]bev?%$RrxX5P>w2vm;gF 41(R~SuC>|6[͗ЌsY4c+;&eǏ3&aWj?Zc(οe̞Ό7r%IY >=甩rB8?sk5eҘ=9pL,R湼iũE_-X^lwƜqזWlmeMpj8#%Zr5@k րk`*)Iӓ:L l78~Е1Rʔ9jDν'ӦzXCa[y%9G{`<[PZj4J&̥l~sҍrpG[HNcm/ҍn>9G8Ŋ-h;/ aoZBABu#Q8OGoʏT yؿ ;iV3  @@   Distance (cm)Temperature (C)e =f =Distance Temp ActualTemp Predicted(Tp-Ta) (Tp-Ta)^2R^2 ==1-sum_sq/DEVSQ(Ta)sum_sq =Ta (K)Tp (K)(K)(K2) D (cm)G n @ 6$  dMbP?_*+%&A&#Prepared by Steve Mayes &D&RPage &PM\\ICARUS\HP_OfficeXXLetterTHP LaserJet 8000 Series PCL 6. \ ƣQp1 P 4C0T (kAch"2Ň(4*`  YX3ȡ!OGgcJFrņFGKL>{kha~ hk:9`>2ѵiqs7GD1R,-.0`ΈÑ{_.!!t>!Q^L; ZwpկRAnDǕgXpr&΂з It Ujx8%q \1Wt!\el75BTd%Aa_Ґw_\CA?[`m *qn$JTU~q2 irZJq(e)ƑUގ *zT VjR82Q[dTʹNz1k,7Ȩi@8vζF( j)}T&ˬ+x>Y6]i[)iŚ4St9 ِ8Aqs澇N aZB,h1h8cT[ 4`l˩acURmWͯҭD.偌EqKjb&֏! N #,9 qڕtV4IuS!1ԮU"LXX??U} } } } $ 6            @@@c@"@At@&@̔@ .@a@ 2@@ 5@a@ 8@@ ;@&@>@ A@@5AB@yAC@W)(T#  $  % & , ' ( ) * + , - . / 01234 5 $$ƯdL? $$e / /~ 0>@0@0'0UGР@0(0~0ޖ6@/(0fЗq@1(~ 1@@1@1'1`Φc@1(1Ut0(1zP @2(~ 2B@2ףp=J@2'2P"IN~@2(2g@x@1(2K,ql=A3(~ 3C@3QŲ@3'39$@3(3<8a2(3+*@5(4 5 5 #5QFA/ %'3*~ h@FFj R(  p  6NMM?I- ]`\  @&A Page &PM\\ICARUS\HP_Office,,LetterTHP LaserJet 8000 Series PCL 6.\ ƣQp1 P 4C0T (kAch"2Ň(4*`  YX3ȡ!OGgcJFrņFGKL>{kha~ hk:9`>2ѵiqs7GD1R,-.0`ΈÑ{_.!!t>!Q^L; ZwpկRAnDǕgXpr&΂з It Ujx8%q]ɺs_-NuV9_$AXt^JCe9(TEp9 !oCTZ\%u2@qH(P Ur4Av_*\^W)DȲuҙ\gAP 'j %Tb儺y eNvX$i6OjyIff7Vy1:& oCl1ɮnCQ _cU=ɭi1Ydqkfnf@e>HCʷËvVusb:s0ƧL e.,J`4`kkMaNURXW0̬ͯGFw bɗKzx6:9l3©]46Pˇ;MV׵+mb@"d,,??3?k3d23 M NM4  3QQ ;Q ;Q3_4E4 ss3QQQQ3_  NM  d4JK4  3QQ ;'3Q ;Q3_ M NM  d4E4 ss3Q .Non-linear regressionQQQ3_4JK4 3QQQQ3_  NM  d4JK4D$% MP+3O&Q4$% MP+3O&Q4FA 3O]q 3*D@43*@X@@@i@N4%  i@M 3OY&Q  Distance (cm)'4% QBMZ3Ok&Q "Temperature (C)'4523  NM43d" 3_ M NM  d444% NT @M3OM& Q V)Temperature versus Distance from the Wall'4% g @ *?3O$=& P  $ * , - 6Q p6Default Power Trendline T = 0.3132 D2.4839 R2 = 0.6223'4% 5 3@M*?3O=&P( .0 19Q v9Calculated Power Correlation T = 0.001 D4.2944 R2 = 0.993'4% 9N@ *?3O[";&P-.7Q r7Default Linear Trendline T = 154.6 D - 1681 R2 = 0.7299'44 eee   PA ?A@Picture 2@"]H  dnvEquationzzz  s 8nv @Text 3N=#]@nvD h<iAssumed form for the relationship between temperature and distance Below are the predicted values (Tp)<uh  >ov  @Text 4P-p.]@ov <Coefficient of Determination:<zz  s 8Tov @Text 5K<i]@Tov =<>This is the data generated by an experiment (Data Series #1):<d=zz  s 8ov @Text 6#`&]@ov< Z0<[The red cells are the ones Solver changes in order to minimize the value in the blue cell.<0&!w6<>Zzz  s 8ov @Text 7(,i]@ov yp<zTo start Solver use the menu sequence: Tools|Solver. Note how the red and blue cells use Excels Insert|Name capabilities.<p0 &&'(,- .!`a g hby  >Dpv  @Text 8A7A]@Dpvt `<Try changing the values e and f to some other starting value (you usually insert a guess here to start the solution process). Watch how Solver works to minimize the value in the cell named sum_sq. Why is the power correlation calculated above so much better than the Excel's default power trendline? The above graph demonstrates that some care should be used in employing default trendlines.<` !S%X&0>@7  Solver Problem  WorksheetsUG FMicrosoft Excel WorksheetBiff8Excel.Sheet.89qOh+'0HPd  Steve MayesMechanical Engineering Dept.sofMicrosoft Excel@̛߾@HUGb) s&" WMFC? |||lRb) EMF|@    !" !" !  " !  S'%    &% 6% Ld!??% "6"% Ld"""!??% 363% Ld333!??% D6D% LdDDD!??% U6U% LdUUU!??% f6f% Ldfff!??% w6w% Ldwww!??% 6% Ld!??% 6% Ld!??% 6% Ld!??% 6% Ld!??% 6% Ld!??% 6S% LdRR!??% y6y% Ldyyy!??% 6% Ld!??% R6R% LdRRR!??'%  Ld!??'%  ( &% 6% Ld!??% 6% Ld!??%  ( &% 6% Ld!??% 6% Ld!??% % RpArial #-wl #v qS0`vВ ߔArialPDYVw #\Б`v#0 #dv%    TT !AA LP1   ( &% 6% Ld!??   TT #2AA #LP2   % #6#% Ld###!??   TT 4CAA 4LP3   % 464% Ld444!??   TT ETAA ELP4   % E6E% LdEEE!??   TT VeAA VLP5   % V6V% LdVVV!??   TT gvAA gLP6   % g6g% Ldggg!??   TT xAA xLP7   % x6x% Ldxxx!??   TT AA LP8   % 6% Ld!??   TT AA LP9   % 6% Ld!??   TXAALP10   % 6% Ld!??   TXAALP11   % 6% Ld!??   TTFNAAFLPA    % 6% Ld!??   TTAALPB    % &" WMFC |\|z6z% Ldzzz!??   TTAALPC    % 6% Ld!??% % " !% %   S   T"VreAA"V LhDistance (cm)  TVeAAVLlTemperature (C)  TTGgMvAAGgLP3TpgvAAgLX100.07TTGxMAAGxLP6TdxAAxLT1.52TTGMAAGLP9TpAALX209.45TXCPAACLP11TlAALX13.31TXCPAACLP15TlAALX94.11TXCPAACLP18TpAALX263.78% % " !% %   S% '%     ( &% 6R% LdQ8!??% "6R"% Ld"Q""8!??% 36R3% Ld3Q338!??% D6RD% LdDQDD8!??% U6RU% LdUQUU8!??% f6Rf% LdfQff8!??% w6Rw% LdwQww8!??% 6R% LdQ8!??% 6R% LdQ8!??% 6R% LdQ8!??% 6R% LdQ8!??% 6R% LdQ8!??% 6% Ld!??% y6y% Ldyyy!??% 6% Ld!??% R6R% LdRRR!??% % " !%   SS 0  % %   % % !&% '% % % % " !% % %   % % % " !% % %   % % % " !% % %   KRp Arial -wإ  qS00< P ArialfwģwYVw \<0 #0 dv% Rp  Arial+-wإ T  qS0<   ArialfwģwYVw \< #0 dv% % % Rp  Arial #-wإ p qS0< @  ArialfwģwYVw \< #0 dv% % % % % Rp  Arial #-wإ  qS0 <   Arial@YVw \<  #0 dv% Rp  Arial #-wإ h qS0< \ Arial@YVw \< #0 dv% Rp Arial ,VwVww@ yFw L qS0<  Arial@YVw \< #0 dv% % % % % % % % % % % Rp Arial #&" WMFC |<|-wإ  qS0<   ArialfwģwYVw \< #0 dv% % Rp Arial ,VwVww@ yFw 0 qS0< L Arial@YVw \< #0 dv% % % % % % % % % % % Rp Arial #-wإ 4   qS0 <  Arial@YVw 4\<  #0 4dv% Rp Arial #-wإ 8  qS0 <  Arial@YVw \<  #0 dv% Rp Arial ,VwVww@ yFw   qS0 < @ Arial@YVw 3\<  #0 3dv% % % % % % % % % % % % " !% % %   K&% ( '% (     +E% % % " !% % %   K% ( % (   V0,LRB8686BB8&% B8  668666B6B8&% ( B86B% ?6E?6E?g6Eg?;6E;?6E?6E?6E?6E?c6Ec?86E8Bg66gBj6Bdj6dj6dj6d<j6<d{j6{dj6dj6d6j66d% % % " !% % %   F% % % " !% % %   ?5=% % % " !% % %   ?5:% hb'% &% (     V0h_kbheebh_% % % " !% % %   ?5:f  V0cfifc% % % " !% % %   ?5:^  V0[^a^[% % % " !% % %   ?5:f  V0cfifc% % % " !% % %   ?5:b  V0_beb_% % % " !% % %   ?5:#[  V0#X&[#^ [#X% % % " !% % %   ?5:IT  V0IQLTIWFTIQ% % % " !% % %   ?5:n<  V0n9q<n?k<n9% % % " !% % %   ?5:2  V0/252/% % % " !% % %   ?5:   V0  % % % " !% % %   ?5:  V0% % % " !% % %   ?5:  V0% % % " !% % %   ?5:*?  V0*<-?*B'?*<% % % " !% % %   ?5:% % % " !% % %   ?5=% % % " !% % %   K% % % " !% % %   F% % % " !% % %   B8:% % % " !% % %   B87% ( &% ( hf   6kf6of6sf6wf6{f6f6f6f6ee6e6e6e6e6e6d6d6d6d6cc6c6c6b6b6b&" WMFC ||6a6a6a6``6`6_6_6^6^6]6]6\6\6[[6[6Z6 Y6 Y6X6W6W6V6!U!U6%T6)T6-S61R65Q69P6=O6AN6EM6IMIM6LL6PK6TI6XH6\G6`F6dE6hD6lC6pBpB6t@6x?6|>6=6;6:6967666646362606/6-6+6*6(6''6%6#6!6 6666666666 6 66666 666666"6&6*&% ( hg6kg6og6sg6wg6{g6g6g6f6ff6f6f6f6f6f6f6f6f6f6ff6f6f6f6f6f6e6e6e6ee6e6d6d6d6d6c6c6c6b6bb6a6a6 a6 `6_6_6^6]6!]!]6%\6)[6-Z61Y65X69W6=V6AU6ET6ISIS6LQ6PP6TN6XM6\K6`J6dH6hF6lD6pBpB6t@6x>6|;696764616.6,,6)6%6"666666 666666666666666666666 66}6u6l6b6"Y6&O6*E&% ( h6*% % % " !% % %   B8:% % % " !% % %   K% % % % % % " !% % %   ,   TDAA)LTemperature versus Distance from the Wall             % % % % " !% % %   K% % % " !% % %   K% % % " !% % %   K% % % % % % % % % % % % % % % % " !% % %   -6j % % % % % %   TAA0L|Default Power Trendline   '% Ld>!??% % TAAC LdT = 0.3132 D % TpAAALX2.4839% TTAAVLPR % TTAATLP2% TAAV L` = 0.6223% % % % " !% % %   K% % % % % % % % ( % % % % % % % % " !% % %   YZ % % % % % %   TAA[]LCalculated Power Correlation    '% Ld[k!??% % TAAp LdT = 0.001 D % TpAAnLX4.2944% TTAALPR % TTAALP2% T|AAL\ = 0.993% % % % " !% % %   K% % % % % % ( % %T&WMFC|| % % % % % % " !% % %   Q: % % % %   TAAL|Default Linear Trendline '% Ld!??% % TAALpT = 154.6 D - 1681 TTAA&LPR % TTAA$LP2% TAA& L` = 0.7299% % % % " !% % %   K% % % % " !% % %   K (   TlAALX-2000TlAALX-1000TTAA4`LP0TdAA"4LT1000TdAA" LT2000TdAA"LT3000Td #AA"LT4000Td #AA"LT5000Td p#}AA"\LT6000Td E#RAA"1LT7000% % % " !% % %   K% % % " !% % %   K  TTAA?pLP0TTAA~pLP5TXAApLP10TXAApLP15TXAA6pLP20TXAAupLP25TXAApLP30TXAApLP35TXAA0pLP40% % % " !% % %   K% % % % % % " !% % %    b  TAA  LhDistance (cm)  % % % % " !% % %   K% % % % % " !% % %   0  Rp Arial00wL0!wL84w0!w !Z%  % j,wYVw 4\hw#0 4dv% TAA.LlTemperature (C)  % ( % % % % " !% % %   K% % % " !% % %   K&% ( %     +E% % ( " !  K" S!  " !  " % % '% &% +!&K% ( % ( % %   %   % $'K% % % %     T$'6AA$'!LThis is the data generated by an T$8GAA$8Lexperiment (Data Series #1):   " !  S% % K@0 SS  % " !  S'%   ( &% 6S% LdRS!??% 6% Ld!??% "   S  '' ' ,S-  -- @ !-""- @ !"-33- @ !3-DD- @ !D-UU- @ !U-ff- @ !f-ww- @ !w-- @ !-- @ !-- @ !-- @ !-- @ !-S- @ !R-yy- @ !y-- @ !-RR- @ !R-  @ !- -- @ !-- @ !- -- @ !-- @ !--Arial-  2  1 -- @ !  2 # 2 -##- @ !#  2 4 3 -44- @ !4  2 E 4 -EE- @ !E  2 V 5 -VV- @ !V  2 g 6 -gg- @ !g  2 x 7 -xx- @ !x  2 8 -- @ !  2 9 -- @ !  2 10 -- @ !  2 11 -- @ !  2 FA  -- @ !  2 B  -zz- @ !z  2 C  -- @ !-"System-'-- ,S  2 V" Distance (cm)  2 VTemperature (C)   2 gG32 g100.07 2 xG6 2 x1.52 2 G92 209.45 2 C112 13.315 2 C152 94.115 2 C182 263.78--'-- ,S--   -R- @ !8-""R- @ !8"-33R- @ !83-DDR- @ !8D-UUR- @ !8U-ffR- @ !8f-wwR- @ !8w-R- @ !8-R- @ !8-R- @ !8-R- @ !8-R- @ !8-- @ !-yy- @ !y-- @ !-RR- @ !R--'- ,S,S - -  --- - ---'-- -  ---'-- -  ---'-- -  ,SArial- Arial--- Arial----- Arial- Arial- Arial----------- Arial-- Arial----------- Arial- Arial- Arial------------'-- -  ,S- -    0---'-- - ,S-  -  $,L L ,,L- L,L  ,L,-  ,-)/)/{){/O)O/$)$/)/)/)/w)w/L)L/{,{ ~,x,~kxk~x~x~&x&~exe~x~x~ x ---'-- -  ,S---'-- -  ,SI)---'-- -  ,SI)- vR- -   $RsUvRyOvRs---'-- - ,SI)zw $wwzzw}tzww---'-- - ,SI)r $oruro---'-- - ,SI)z $wz}zw---'-- - ,SI)v $svyvs---'-- - ,SI)o  $ lo r o l---'-- - ,SI)h3 $3e6h3k0h3e---'-- - ,SI)PX $XM[PXSUPXM---'-- - ,SI)F~ $~CF~I{F~C---'-- - ,SI) $"---'-- - ,SI) $---'-- - ,SI) $---'-- - ,SI)S $PSVSP---'-- - ,SI)---'-- - ,SI)---'-- - ,S---'-- - ,S---'-- - ,SL,---'-- - ,SL,-  - zR zUzYz]zazezizmzqyuyyy}yyyxxxxwwwvvvuuuttssrrqqppoonmmlkkji hhgfed#c'b+a/a3`6_:]>?><;975420.,*)'%#!   -  {R{U{Y{]{a{e{i{mzqzuzyz}zzzzzzzzzzzzzyyyyyxxxxwwwvvuuutssrqq ponmlk#j'i+h/g3e6d:b>aB_F^J\NZRXVVZT^RbOfMjKnHrEvBz@~=963/+($  vm cY-  R---'-- -  ,SL,---'-- -  ,S------'-- -  ,  E2 (l)Temperature versus Distance from the Wall             ----'-- -  ,S---'-- -  ,S---'-- -  ,S----------------'-- -  , ------ *2 DDefault Power Trendline   - @ !R- -2 W T = 0.3132 D -2 U2.4839- 2 jR - 2 h2-2 j = 0.6223----'-- -  ,S-------- --------'-- -  , ------ 12 qECalculated Power Correlation    - @ !E- -2 s T = 0.001 D -2 4.2944- 2 R - 2 2-2  = 0.993----'-- -  ,S------ --------'-- -  , ---- +2 Default Linear Trendline - @ !$- -"2 'T = 154.6 D - 1681  2 :R - 2 82-2 : = 0.7299----'-- -  ,S----'-- -  ,S   2 -200092 -10009 2 t0 2 H 1000 2  2000 2 3000 2 4000 2 5000 2 p 6000 2 E 7000---'-- -  ,S---'-- -  ,S  2 )0 2 h5 2 10 2 15 2  20 2 _25 2 30 2 35 2 40---'-- -  ,S------'-- -  , 2  Distance (cm)  ----'-- -  ,S-----'-- -  ,  Arial- 2 BTemperature (C)  - ----'-- -  ,S---'-- -  ,S-  -   0-- ' ,S' ' '--- - L&!- - - -  - -,K'$----  92 '$!This is the data generated by an 12 8$experiment (Data Series #1):   ' ,S--,S -' ,S-  -S- @ !S-- @ !-'CompObj f