Steam Tracing Calculation.xls

Steam Steam trac tracing ing simula simulatio tion n for determi determinin ning g Proce Process ss Flu Flu SI Unit Version  Author: J.A.B. de Lange Source: www.cheresources.com Press $tr $tr L L to acti%ate the macro that runs the simuation. e0treme, important important that the the references references in the 1utputs 1utputs section section an! th / It is e0treme, / It is aso %er, important to rea! the messages at the bottom of the screen Inputs Line Number  Pipe Length (m)

123 40

 Steam Specification Steam Pressure (kPa)

400

 Process Fui! Pipe Pipe NPS (inches) Pipe sche!ue Pipe materia "inimum aowabe fui! temperature temperature (#$)  Steam tracing a%aiabe &are'$emente! mount of %aiabe racers racer NPS (inches) racer Pipe "ateria Insuation Specifications Insuation "ateria Insuation hickness (mm) +missi%it, of insuation agging  mbient $on!itions mbient emperature (#$) -in! Veocit, (km'h)

8" STD Carbon steel 30

&are * ½" Stainless Steel

Rock Wool 40 kg/m³  0!4

1 10!8

Messages Solution converged to a satisfactory degree Hottest Hottest Surface Surface Tempe Temperatu rature re Accept Acceptable able for for Personnel Personnel Protect Protection, ion, insulat insulatii Insulation thickness thickness acceptable, acceptable, but refer to the second message for furthe furthe Steam pressure acceptable Process Fluid Fluid Temperatur Temperature e acceptable, acceptable, and above above Minimum Minimum Alloable Alloable Flui

id Temperature ssumptions: Sat#rate$ Steam is #se$% &ress#re $ro& along lengt' o( &i&e neglegible Resistance to 'eat trans(er t'ro#g' tracer &i&e )all material is neglegible 2ata sheet not be change!3 as this wi cause the program to respon! incorrect,. each time the simuation has been run3 before e%auating the outputs. 1uputs  1ther Information nnuus emperature (#$)

84!

 Steam Information Steam emperature (#$) Steam $onsumption (kg'h)

143!* 4

 Process Fui! Pipe Process Fui! emperature (#$) Pipe 1uter 7a!ius (mm) Pipe -a hickness (mm) Pipe Inner 7a!ius (mm) -a "ateria herma $on!ucti%it,3 k w3 (-'m;)  Steam racer Information racer 1uter 7a!ius (mm) Spacers 7e8uire!  Insuation Information herma $on!ucti%it,3 k (ins)3 (-'m;) emperature 7ange (#$) %erage Insuation emperature (#$)  1uter Surface Information 9ottest 1utsi!e Surface emperature (#$) Surface Fim $oefficient3 ho3 (-'m6?

>@?

>

0!04

0!04****

0!048*1

0!0248432 0!02124104+ 0!04* 0!048

0!0244*2+4+ 0!01

kw 1*!40**++ 2!82143 400!34432 10 21!******+ +!11843+3 herma con >4? >A6.* 0!032 0!0088001+ 0!0230+ 0!038 0!02+4144 0!02+8 0!02 0!04+ 0!03* 0!034* 0!038

Re(erence *

-in! spee! (m's)

(km'h) 0 1 2 3 4  * + 8  10 11

B 0 3!* +!2 10!8 14!4 18 21!* 2!2 28!8 32!4 3* 3!*

8 0 0!0 0!1 0!1 0!2 0!2 0!3 0!3 0!4 0!4 0! 0!

30!20102300 *!21838144

mbient em ,10 , ,8 ,+ ,* , ,4 ,3 ,2 ,1 0 1 2

12 13 14 1 1* 1+ 18 1 20

43!2 4*!8 0!4 4 +!* *1!2 *4!8 *8!4 +2

0!* 0!* 0!+ 0!+ 0!8 0!8 0! 0! 1

3 4  * + 8  10 11 12 13 14 1 1* 1+ 18 1 20 21 22 23 24 2 2* 2+ 28 2 30 31 32 33 34 3 3* 3+ 38 3 40 41 42 43 44 4 4* 4+ 48 4

0

Imperia Units %aiabe steam Latent 9eat (&U'bm) >=.=*5

Pipes Re(erence 1 Re(erence 2

are Cemente$

11 8

herma con!ucti%it,3 PFP3 kw3 (&U'fth#F) 44 >4 @64 !24321201* !82012+*+2 10!+*3142*2 31!1840 2!4*2+38302 2+!1132+ 231!*80012 231!0803004 22!2488024 *2!*3818* *2!*3818* *2!*3818*02 144!4218+8 14+!313*11 144!4218++2+ 4*!21*0*008 3!283*10* 34!**2040*0+

emperature3; Stainless steel Carbon steel Co&&er rass  5l#mini#m ron

emperature3 ; .iberglass .oam ;lass Calci#m silicate Rigi$

8 (&U'hft ) 0 !88+32*38 0!0 18!*+01*+1*8 0!1 0!1 0!2

,4 ,3 ,2 ,1 0 1

1 18 21 24 2+ 30 33 3* 3 42 4 48 1 4 + *0

0!2 0!3 0!3 0!4 0!4 0! 0! 0!* 0!* 0!+ 0!+ 0!8 0!8 0! 0! 1

2 3 4  * + 8  10 11 12 13 14 1 1* 1+ 18 1 20 21 22 23 24 2 2* 2+ 28 2 30 31 32 33 34 3 3* 3+ 38 3 40 41 42 43 44 4 4* 4+ 48

4 0 1 2 3 4  * + 8  *0 *1 *2 *3 *4 * ** *+ *8 * +0 +1 +2 +3 +4 + +* ++ +8 + 80 81 82 83 84 8 8* 8+ 88 8 0 1 2 3 4  * + 8

 100 101 102 103 104 10 10* 10+ 108 10 110 111 112 113 114 11 11* 11+ 118 11 120

 5mo#nt o( Tracers Tracers 1 2 3 4 

racer 12 ?" ½" =" 1" Re(erence Stainless Steel Carbon Steel

12 (Inches) 12 12 (mm) 0!*+2 1+!0*88 0!84 21!33* 1!0 2*!*+ 1!31 33!401 >

7eference 2

ucti%it,3 Insuation materia3 materia 3 kins >=4.* 6*?.A 0!033 0!034314 0!02 0!0+*44 0!04 0!0 0!02*20+ 0!02*4084 0!0+8 0!0*21 0!038 0!04 0!03*8 0!03 0!03 0!04

 

perature

6>6.* 6@A.* 646.* 0!03+ 0!04 0!044 0!02+ 0!0*4880*2 0!0+028 0!0* 0!0+ 0!082 0!02*+ 0!02*842 0!02+04 0!0*4 0!0*+4 0!0+04 0!042 0!04+ 0!04 0!041 0!0448 0!048 0!041 0!043* 0!04*

>#t&#ts 1uputs: &are  1ther Information nnuus emperature (#$)

84!

 Steam Information Information Steam emperature (#$) Steam $onsumption (kg'h)

143!*1232 +!21

 Process Fui! Pipe Process Fui! emperature (#$) Pipe 1uter 7a!ius (mm) Pipe -a hickness (mm)

56.>*@A=5?5 10!4 8!18

Pipe Inner 7a!ius (mm) -a "ateria herma $on!ucti%it,3 k w3 (-'m;)  Steam racer Information racer 1uter 7a!ius (mm)

101!3* 2!8

10!*+

Spacers 7e8uire!  Insuation Information herma $on!ucti%it,3 k (ins)3 (-'m;) emperature 7ange (#$) %erage Insuation emperature (#$)  1uter Surface Information Information 9ottest 1utsi!e Surface emperature (#$) Surface Fim $oefficient3 ho3 (-'m*.= 10!4 8!18 101!3* 2!8

10!*+

Spacers 7e8uire!  Insuation Information herma $on!ucti%it,3 k (ins)3 (-'m;) emperature 7ange (#$) %erage Insuation emperature (#$)  1uter Surface Information Information

0!040++ ,43 to 200-C +4!03

9ottest 1utsi!e Surface emperature (#$) Surface Fim $oefficient3 ho3 (-'m

7eference 2

ucti%it,3 Insuation materia3 materia 3 kins3 (&U'fth#F) >=4.* 6*?.A 0!033 0!034314 0!02 0!0+*44 0!04 0!0 0!02*20+ 0!02*4084 0!0+8 0!0*21 0!038 0!04 0!03*8 0!03 0!03 0!04

 

perature

6>6.* 6@A.* 646.* 0!03+ 0!04 0!044 0!02+ 0!0*4880*2 0!0+028 0!0* 0!0+ 0!082 0!02*+ 0!02*842 0!02+04 0!0*4 0!0*+4 0!0+04 0!042 0!04+ 0!04 0!041 0!0448 0!048 0!041 0!043* 0!04*

>#t&#ts

-.

1uputs: &are  1ther Information nnuus emperature (#F)  Steam Information Information

181!0

Steam emperature (#F) Steam $onsumption (bm'h)

20!14* 1!

 Process Fui! Pipe Process Fui! emperature (#F) Pipe 1uter 7a!ius (inches) Pipe -a hickness (inches) Pipe Inner 7a!ius (inches) -a "ateria herma $on!ucti%it,3 k w3 (&U'fth#F)  Steam racer Information racer 1uter 7a!ius (inches)

*6=.@@ 4!31 0!32 3! 30!*

0!42

Spacers 7e8uire!  Insuation Information herma $on!ucti%it,3 k (ins)3 (&U'fth#F) emperature 7ange (#F) %erage Insuation emperature (#F)  1uter Surface Information 9ottest 1utsi!e Surface emperature (#F) >

Surface Fim $oefficient3 ho3 (&U'ft h#F)

0!028 ,4 to 30-. 113!0

13!43 1!8

1uputs: $emente!  1ther Information nnuus emperature (#F)  Steam Information Steam emperature (#F) Steam $onsumption (bm'h)  Process Fui! Pipe Process Fui! emperature (#F) Pipe 1uter 7a!ius (inches) Pipe -a hickness (inches) Pipe Inner 7a!ius (inches) -a "ateria herma $on!ucti%it,3 k w3 (&U'fth#F)  Steam racer Information racer 1uter 7a!ius (inches)

Spacers 7e8uire!

23!

20!14* 40!03

>?.A5 4!31 0!32 3! 30!*

0!42

 Insuation Information herma $on!ucti%it,3 k (ins)3 (&U'fth#F) emperature 7ange (#F) %erage Insuation emperature (#F)  1uter Surface Information 9ottest 1utsi!e Surface emperature (#F) >

Surface Fim $oefficient3 ho3 (&U'ft h#F) L act (inches)

0!028 ,4 to 30-. 1*!1*

+! 2!0 2!**114

Cement 0!21 0!2*2 ?.>5>

6=A.* 0!04+ 0!0+*12*2 0!0*1 0!02+1*2 0!0+48 0!0 0!03 0!0

k1 k2

@>6.* 0!02 0!08241+ 0!0*3 0!02+21 0!08 0!0* 0!08 0!0

@@A.* 0!0+ 0!081*2 0!0** 0!02+182 0!08* 0!0+3 0!0*2 0!0

@46.* 0!0*2 0!0*34 0!0*8 0!02+08 0!03 0!08 0!0* 0!0*4

21!213148 0!4+821*3

acos66r1,r27/6r1@r277 0!*0402318 Starting Vaues 2iff   Ts#r( &i&e bare -C 21!43*+121* 21!43801+ 1!28140A,010 Ts#r( &i&e cement 23!4320143 23!432+8844 2!14034A,010 > 1!31118A,008 *.=>?64?6@ 8!*3*18A,008 Sol#tion conerge$ to a satis(actor $egree =.=A*A+C??A Sol#tion conerge$ to a satis(actor $egree

6.*

5@A.*

546.*

0!08* 0!0 0!0248 0!0242*3 , ,

0!028 0!023* ,

 

contin#e!

5=A.*

0!0* 0!022+83 ,

4>6.*

4@A.*

446.*

A>6.*

A46.*

=>6.*

0!0 0!104 0!0213 0!021003 , ,

0!108 0!02 ,

0!11* 0!01+++ ,

0!12* 0!0124 ,

0!13+ 0!01241 ,

;insInterp 0!038+08*3 0!0*13002 0!0224*+24 0!02*+*43 0!0*2214+*3 0!040++232+* 0!0404430882 0!040+2300*2

5=A.*

0!0* 0!022+83 ,

4>6.*

4@A.*

446.*

A>6.*

A46.*

=>6.*

0!0 0!104 0!0213 0!021003 , ,

0!108 0!02 ,

0!11* 0!01+++ ,

0!12* 0!0124 ,

0!13+ 0!01241 ,

;insInterp(-'m;) 0!0381432 0!0*43332*4 0!0308324+ 0!02*+88031 0!0*4*2*42+ 0!04481034++ 0!0423181 0!042*130*4

emp range 10 to 20-C ,43 to 20-C 10 to *0-C 10 to *0-C ,43 to 200-C ,43 to 200-C 10 to 20-C 10 to 20-C

emp range ;ins(&U'fth#F) 0 to 480-. 0!02204028 ,4 to 480-. 0!03+1*2+ 0 to 1200-. 0!0311428+* 0 to 1200-. 0!014+02 ,4 to 30-. 0!03+334+3 ,4 to 30-. 0!0288*+1 0 to 480-. 0!024+2*08 0 to 480-. 0!024**28

Steam abe SI Units pressure temp 9f kPa ; kD'kg *!8 311!84 1*2!18 13!+ 32!411 218!+ 20!*8 333!*+ 24! 2+!8 340!3 281!2 34!4+ 34!0* 302!83 41!3+ 34!844 321!04 48!2* 33!*1+ 33*!8* !1* 3*!*1 30!1 *2!0 3!*+ 3*3!4 *8! 3*2!+11 3+!0+ +!84 3*!233 38!*8 82!+4 3*+!+2 3!2 8!*3 3*!+ 404!+ *!3 3+1!+4 413!33 103!42 3+3!+22 421!4+ 110!32 3+! 42!1+ 11+!21 3++!283 43*!48 124!11 3+8!33 443!4 131!00 380!0* 40!11 13+! 382!01+ 4*! 144!+ 383!4*+ 4*2!*2 11!* 384!8* 4*8!3 18!8 38*!2 4+4!2 1*!48 38+!44 4+!* 1+2!3+ 388!+44 484! 1+!2+ 38!* 40!0* 18*!1* 31!128 4!18 13!0* 32!2*+ 4!83 1! 33!3+2 04!+2 20*!8 34!4 0!14 213!+4 3!44 13!* 220!*4 3*!11 1+!8 22+!3 3+!0* 22!1* 234!43 38!4+2 2*!3 241!32 3!422 30!3 248!22 400!344 34!2* 2!11 401!2 38!21 2*2!01 402!133 41!3 2*8!0 402!4 4!* 2+!8 403!844 4!14 282!* 404!*+2 2!8* 28! 40!48 *!3 2*!48 40*!28 !*1 303!38 40+!0+2 *3!1 310!2+ 40+!83 **!3 31+!1+ 408!4 *!*1 324!0* 40!33 +2!*3

Steam abe Imperia Units pressure temp 9(atent) psia !eg F &U'b 1 101!+4 *!+3 2 12*!0+ 4!03 3 141!4+ 10!42 4 12!* 120!2  1*2!24 130!2 * 1+0!0 138!03 + 1+*!84 144!83 8 182!8* 10!8+  188!2+ 1*!3 10 13!21 1*1!2* 11 1+!+ 1*!82 12 201!* 1+0!0 13 20!88 1+4 14 20!* 1++!+1 1 213!03 181!21 1* 21*!32 184!2 1+ 21!44 18+!** 18 222!41 10!** 1 22!24 13!2 20 22+!* 1*!2+ 21 230!+ 18! 22 233!0+ 201!44 23 23!4 203!88 24 23+!82 20*!24 2 240!0+ 208!2 2* 242!2 210!+ 2+ 244!3* 212! 28 24*!41 214! 2 248!4 21+ 30 20!34 218! 31 22!22 220!8 32 24!0 222!+ 33 2!84 224! 34 2+!8 22*!3 3 2!2 228 3* 2*0! 22!+ 3+ 2*2!8 231!4 38 2*4!1+ 233 3 2*!+2 234!* 40 2*+!2 23*!1 41 2*8!+4 23+!+ 42 2+0!21 23!2 43 2+1!* 240!* 44 2+3!0* 242!1 4 2+4!44 243! 4* 2+!8 244! 4+ 2++!14 24*!2

330!* 33+!8 344!+ 31!*4 38!4 3*!43 3+2!33 3+!22 38*!12 33!01 3!1 40*!80 413!+ 420! 42+!4 434!38 441!28 448!1+ 4!0+ 4*1!* 4*8!8* 4+!+ 482!* 48!4 4*!44 03!33 10!23 1+!12 24!02 30!1 3+!81 44!+0 1!* 8!4 *!3 +2!28 +!18 8*!0+ 2!+ !8* *0*!+* *13!* *20! *2+!44 *34!34 *41!23 *48!13 *!02 **1!2 **8!81

410!0*+ 410!+83 411!44 412!18 412!8+2 413!44 414!20* 414!8*1 41!0* 41*!13 41*!+*1 41+!383 41+!8 418!8 41!183 41!+*+ 420!344 420!1+ 421!4+8 422!033 422!8 423!128 423!**+ 424!2 424!+22 42!244 42!+* 42*!2*+ 42*!+*+ 42+!2*+ 42+!+* 428!244 428!+28 42!20* 42!*+8 430!1 430!*11 431!0+2 431!28 431!+8 432!422 432!8*+ 433!30* 433!+3 434!1+2 434!* 43!022 43!444 43!8*1 43*!2+8

+!8 +8!1 81!4 84!* 8+!8 0!+8 3!+ *!3* !1 *01!4 *04! *0+!2 *0!8 *12!41 *14!+ *1+!2 *20!08 *22!41 *24!+ *2+!2 *2!*2 *31!4 *34!2+ *3*!* *38!2 *41!2 *43!34 *4!*+ *4+!+* *4!8 *1! *4!2+ **!13 *8!23 **0!32 **2!41 **4!1 ***!3+ **8!4* *+0!32 *+2!18 *+4!28 *+*!14 *+8 *+!8* *81!+2 *83!8 *8!44 *8+!3 *8!1*

48 4 0 1 2 3 4  * + 8  *0 *1 *2 *3 *4 * ** *+ *8 * +0 +1 +2 +3 +4 + +* ++ +8 + 80 81 82 83 84 8 8* 8+ 88 8 0 1 2 3 4  * +

2+8!4 2+!+4 281!02 282!2+ 283! 284!+1 28! 28+!08 288!24 28!38 20! 21!*2 22!+1 23!+ 24!8* 2!1 2*! 2+!8 28! 2! 300! 301!* 302!3 303!8 304!83 30!++ 30*!* 30+!*1 308!1 30!41 310!2 311!1+ 312!04 312! 313!+ 314!* 31!43 31*!2* 31+!08 31+!8 318!* 31!4 320!28 321!0* 321!84 322!*1 323!3+ 324!13 324!88 32!*3

24+!* 248! 20!2 21! 22!8 24 2!2 2*!4 2+!* 28!8 2! 2*1!1 2*2!2 2*3!3 2*4!4 2*! 2**!* 2*+!* 2*8!+ 2*!+ 2+0!+ 2+1!+ 2+2!+ 2+3!+ 2+4!+ 2+!+ 2+*!* 2++!* 2+8! 2+!4 280!3 281!3 282!1 283 283! 284!8 28!+ 28*! 28+!4 288!2 28 28! 20!+ 21! 22!3 23!1 23! 24!+ 2! 2*!3

*+!+1 *82!*0 *8! **!3 +03!2 +10!18 +1+!08 +23!+ +30!8+ +3+!+* +44!** +1! +8!4 +*!34 ++2!24 ++!13 +8*!03 +2!2 +!82 80*!+1 813!*1 820!0 82+!4 834!2 841!1 848!08 84!8 8*1!8+ 8*8!++ 8+!** 882!* 88!4 8*!3 03!24 10!14 1+!03 23!3 30!82 3+!+2 44!*1 1!1 8!40 *!3 +2!1 +!0 8!8 2!88 !++ 100*!*+ 1013!*

43*!*83 43+!04 43+!44 43+!84 438!24 438!*8 43!0+8 43!4*+ 43!8 440!233 440!*1+ 440!8 441!3*+ 441!+3 442!10* 442!4+2 442!833 443!14 443!* 443!11 444!2*+ 444!*1+ 444!*+ 44!311 44!** 44* 44*!33 44*!*+8 44+!011 44+!344 44+!*+8 448!00* 448!333 448!**1 448!83 44!30* 44!*22 44!44 40!2* 40!+2 40!883 41!14 41!0* 41!811 42!11+ 42!422 42!+22 43!022 43!322 43!*1+

*0!+ *2!* *4!28 **!14 *+!++ *!*3 +01!2* +02!88 +04!+4 +0*!3+ +08 +0!*3 +11!2* +12!88 +14!1 +1*!14 +1+!++ +1!4 +20!+ +22!42 +24!0 +2!44 +2+!0+ +28!4+ +30!1 +31!4 +33!12 +34!2 +3!1 +3+!4 +38!3 +40!33 +41!* +43!3 +44!+ +4*!1 +4+!4 +48!4 +0!33 +1!+3 +3!12 +4!2 +!1 ++!08 +8!4+ +!8+ +*1!2* +*2!43 +*3!82 +*!22

8  100 101 102 103 104 10 10* 10+ 108 10 110 111 112 113 114 11 11* 11+ 118 11 120 121 122 123 124 12 12* 12+ 128 12 130 131 132 133 134 13 13* 13+ 138 13 140 141 142 143 144 14 14* 14+

32*!3* 32+!1 32+!82 328!4 32!2* 32!+ 330!*+ 331!3+ 332!0* 332!+ 333!44 334!11 334!+ 33!4* 33*!12 33*!+8 33+!43 338!08 338!+3 33!3+ 340!01 340!*4 341!2+ 341!8 342!1 343!13 343!+4 344!3 344! 34! 34*!1 34*!+4 34+!33 34+!2 348! 34!08 34!* 30!23 30!+ 31!3* 31!2 32!48 33!04 33! 34!14 34!* 3!23 3!++ 3*!31 3*!84

2+ 2+!8 28! 2!3 300 300!8 301! 302!2 303 303!+ 304!4 30!1 30!8 30*! 30+!2 30+! 308!* 30!3 30! 310!* 311!3 311! 312!* 313!2 313! 314! 31!2 31!8 31*!4 31+!1 31+!+ 318!3 31 31!* 320!2 320!8 321!4 322 322!* 323!2 323!8 324!4 32 32! 32*!1 32*!+ 32+!3 32+!8 328!4 32

1020!4* 102+!3 1034!2 1048!04 10*1!83 10+!*2 108!41 1103!2 111*! 1130!+8 1144!+ 118!3* 11+2!1 118!4 11!+3 1213!2 122+!31 1241!1 124!8 12*8!*8 1282!4+ 12*!2* 1310!0 1323!84 133+!*3 131!42 13*!21 13+ 1413!4+ 144+! 1482!42 11*! 11!3+ 18!8 1*20!32 1*4!8 1*8!2+ 1+23!+ 1+8!22 1+2!+ 182+!1+ 18*1!* 18*!12 130!* 1*!0+ 1! 2034!02 20*8! 220*!4 2344!3

43!1+ 44!211 44! 4!083 4!** 4*!222 4*!+8 4+!344 4+!84 48!444 48!83 4!22 4*0!0 4*0!+8 4*1!1 4*1!*1+ 4*2!128 4*2!*3 4*3!13 4*3!*3 4*4!133 4*4!*22 4*!111 4*!4 4**!0+2 4**! 4*+!01+ 4*+!483 4*8!*3 4*!+*+ 4+0!8+8 4+1!+2 4+3!03 4+4!04 4+!128 4+*!144 4++!144 4+8!133 4+!10* 480!0*1 481 481!28 482!844 483!+44 484!*33 48!11 48*!3+8 48+!233 40!44 43!+

+**!38 +*+!+8 +*8!4 ++1!+3 ++4!0* ++*!*1 ++!1+ +81!+3 +84!0* +8*!*2 +88!4 +1!2+ +3! +!2 +8!2 800!+ 802! 80!22 80+! 80!*4 811!+ 814!0* 81*!1 818!48 820!+ 822!*+ 824!+* 82*!8 831!+ 83+!0 842!2 84+!0 81!+4 8*!*2 8*1!28 8*!3 8+0!3 8+4!++ 8+!1 883!*1 88+!+ 82!21 8*!4 00!3 04!4 08!4 12!4 1*!4 31!2 4*!1+

148 14 10 12 14 1* 18 1*0 1*2 1*4 1** 1*8 1+0 1+2 1+4 1+* 1+8 180 182 184 18* 188 10 12 14 1* 18 200 20 210 21 220 22 230 23 240 24 20 2 2*0 2* 2+0 2+ 280 28 20 2 300 320 340

3+!38 3+!1 38!43 3!48 3*0!1 3*1!3 3*2! 3*3! 3*4!4 3*!3 3**! 3*+!4+ 3*8!42 3*!3+ 3+0!31 3+1!24 3+2!1* 3+3!08 3+3!8 3+4!88 3+!++ 3+*!* 3++!3 3+8!4 3+!2* 380!12 380!* 381!8 383!88 38!1 38+!1 38!88 31!8 33!+ 3!* 3+!3 3!1 400!+ 402!+2 404!44 40*!13 40+!8 40!4 411!0+ 412!*+ 414!2 41!81 41+!3 423!31 428!

32! 330!1 330!* 331!8 332!8 333! 33 33*!1 33+!1 338!2 33!2 340!2 341!2 342!2 343!2 344!2 34!2 34*!2 34+!2 348!1 34!1 30 30! 31! 32!8 33!+ 34!* 3! 3+!+ 3! 3*2!1 3*4!2 3**!2 3*8!3 3+0!3 3+2!3 3+4!2 3+*!1 3+8 3+! 381!+ 383!* 38!4 38+!1 388! 30!* 32!3 34 400! 40*!8

2482!2 2*20!1 2+8 28! 3033!8 31+1!+ 330!* 344+! 38!4 3+23!3 38*1!2 3!1 413+ 42+4! 4412!8 40!+ 4*88!* 482*! 4*4!4 102!3 240!2 3+8!1 1* *3! +1!8 2!+ *0*+!* *20! *343!4 *481!3 **1!2 *++!1 *8 +23!+ +84! +2!2 82+4 8*18!+ 8*3! 308!2 *3 +!+ 10342! 11032 11+21! 12411 13100! 13+0 144+! 11*

4*!+11 4!* 02!3+2 0!03 0+!*11 10!04 12!44 14!822 1+!0+8 1!2*+ 21!34 23!4*+ 2!483 2+!4 2!3*+ 31!244 33!0+2 34!8*1 3*!*11 38!328 40!00* 41!* 43!2*+ 44!8 4*!40* 4+!28 4!428 0! 2!3 3!++8 !1+8 *!*1 +!1+ *1!222 *4!41+ *+!44 +0!4+8 +3!3*1 +*!1*1 +8!883 81!22 84!04 8*!4 1!411 * *00!383 *04!+2 *08!4 *12!4*1 *1*!1+8

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