MNIRH_TP3

UNIVERSIDAD NACIONAL AGRARIA LA MOLINA ESCUELA DE POSTGRADO MAESTRIA EN RECURSOS HIDRICOS

SEMESTRE

: 20 2015 – I

DOCENTE

: Ing. José Arapa Q.

ALUMNO

: Ag!"o Ta#a Ro$!r% &!nr'.

CURSO

: Mé%o"os n(ér)*os !n )ng!n)!r+a "! r!*rsos #+"r)*os.

TEMA

: In%!gra*),n N(ér)*a.

CODI-O

: 201502/

MOLINA  LIMA – ER 2015

Maestría en recursos Hídricos - Universidad Nacional Agraria la Molina

Indice.

1. Ap3)*an"o Ap3)*an"o 3os (é%o"o (é%o"oss "! )n%!gr )n%!gra*),n a*),n "! S)(pson S)(pson 14 14 ' S)(pson S)(pson 46 46 "!%!r()na "!%!r()narr 3os 3os r!s3%a"os n(ér)*os *on ss r!sp!*%)7as r!pr!s!n%a*)on!s %a$3ar!s "! 3as s)g)!n%!s 8n*)on!s "! 839o -ra"a3(!n%! ar)a"o: ar)a"o:...................................................................2 a;

<n*),n <n*),n "! <39o <39o -ra"a3( -ra"a3(!n%! !n%! a ar)a"o *on p!n")!n p!n")!n%! %! pos)%)7a pos)%)7a S =>;......................2

$; <n*),n <n*),n "! <39o <39o -ra"a3( -ra"a3(!n%! !n%! a ar)a"o *on p!n")!n p!n")!n%! %! n!ga%)7a n!ga%)7a S =;. =;......................4 2. Ap3)*an"o Ap3)*an"o 3os (é%o"o (é%o"oss "! )n%!gr )n%!gra*),n a*),n "! S)(pson S)(pson 14 14 ' S)(pson S)(pson 46 46 "!%!r()na "!%!r()narr 3os 3os r!s3%a"os n(ér)*os ' ss r!sp!*%)7as r!pr!s!n%a*)on!s gra8)*as "! 3as s)g)!n%!s 8n*)on!s "! %ranspor%! "! S!")(!n%os !n Ssp!ns),n "! E)ns%!)n =1?50;:............................................6 I 1= 0.216

I 2= 0.216

A

Z − 1

1

∫(

(1 − A )Z A A

Z −1

1

∫(

( 1− A )Z A

1− y

y 1 − y

y

z

) dy

.......................................................................6

z

)

ln ( y ) dy

...............................................................8

. Un *ana3 *ana3 %rap!@o %rap!@o)"a3 )"a3 *on: $B6 26 26 So0.00 So0.001B 1B ' n0.0256 n0.0256 %ranspo %ranspor%a r%a n n *a"a3 *a"a3 12 (4s (4s s! p)"!:..................................... ......................................................... ........................................ ...................................... .................. .............. .... 9 a;

D!%!r()nar D!%!r()nar !3 %)ran% %)ran%!! *r)%)*o *r)%)*o (!")an%! (!")an%! !3 (!%o"o (!%o"o "! n!%on n!%on Rap#son Rap#son.........................9

$; D!%!r()nar D!%!r()nar !3 %)ran% %)ran%!! nor(a3 nor(a3 (!")an% (!")an%!! !3 (é%o"o (é%o"o "! 3a s!*an%! s!*an%!...................................9 *; Ca3*3ar Ca3*3ar ' gra8)*ar gra8)*ar !3 !3 p!r8)3 p!r8)3 "!3 r!(an r!(anso so =839o =839o gra"a3( gra"a3(!n%! !n%! 7ar)a" 7ar)a"o;6 o;6 *r!a"o *r!a"o por por na pr!sa F! !($a3sa !3 aga #as%a na pro8n")"a" "! 1.5 ( )n(!")a%a(!n%! "!%rGs "! 3a pr!sa. S! spon! F! !3 !H%r!(o "! agas arr)$a "!3 p!r8)3 !s )ga3 a na pro8n")a" 1 (a'or F! 3a pro8n")"a" nor(a3. E3 *o!8)*)!n%! "! !n!rg+a !s 1.1. !(p3!ar !3 (é%o"o "! )n%!gra*),n ......................................................... ........................................ ...................................... .................. 9 ")r!*%a o Ka#(!%!88...................................... "; E3a$ E3a$or orar ar !3 a3g a3gor or)% )%(o (o !n !n Ma%3 Ma%3a$ a$...........................................................................9

17


1. Ap3)*a Ap3)*an"o n"o 3os (é%o"os (é%o"os "! )n%!gra* )n%!gra*),n ),n "! S)(pson S)(pson 14 ' S)(pso S)(pson n 46 46 "!%!r( "!%!r()na )narr 3os r!s3%a"os n(ér)*os *on ss r!sp!*%)7as r!pr!s!n%a*)on!s %a$3ar!s "! 3as s)g)!n%!s 8n*)on!s "! 839o -ra"a3(!n%! ar)a"o: ar)a"o: a; <n*),n <n*),n "! <39o -ra"a -ra"a3(!n% 3(!n%!! ar)a"o ar)a"o *on *on p!n")!n%! p!n")!n%! pos)%)7a pos)%)7a S =>;. u

∫ 1−duu

F ( u , N ) )=

N

0

S)(pson 14 %CODIGO FUNCION DE FLUJO GRADUALMENTE VARIADO (FGV) S(+) % REGLA DE SIMPSON 1/3 funct!n "FGV# funct!n "FGV# $ f&''13(uNn) N$nu*t,(N)$".1/(10. $".1/(10. N N .). .).##f$n2n()4$5-6$u7$(64)/nFP$5f!, $188n1 f!, $188n1 0$4+97 FP$FP+f(0)n: FI$5f!, $88n f!, $88n 0$4+97PARA O2cu2! f!, $18115 f!, $18115 u$uu+9:u- u()$uf!, ?$1815 f!, ?$1815 N?$NN+?9:N- N(?)$N?%CODIGO FUNCION DE FLUJO GRADUALMENTE VARIADO (FGV) S(+) T4624f&''13(?)$f&''13(uN?@5)% REGLA DE SIMPSON 3/ n: funct!n "FGV# funct!n "FGV# $ f&''3(uNn) n: N$nu*t,(N)R$"u. T4624f&''13 #-R$"5 N-R# $".1/(10. $".1/(10. N N .). .).##S)(pson 4 f$n2n()4$5-6$u7$(64)/nFR$5f!, $1838n1 f!, $1838n1 0$4+97 FR$FR+f(0)n: FS$5f!, $838n1 f!, $838n1 0$4+97 FS$FS+f(0)n: FT$5f!, $3838n3 f!, $3838n3 0$4+97 FT$FT+f(0)n: FGV$(397/)9(f(4)+39(FR+FS)+9FT+f(6))-

17


%CODIGO PARA O2cu2! f!, $18115 f!, $18115 u$uu+9:u- u()$uf!, ?$1815 f!, ?$1815 N?$NN+?9:N- N(?)$N?T4624f&''3(?)$f&''3(uN?@5)n: n: R$"u. T4624f&''3 #-R$"5 N-R#

$; <n*),n <n*),n "! <39o -ra"a -ra"a3(!n% 3(!n%!! ar)a"o ar)a"o *on *on p!n")!n%! p!n")!n%! n!ga%)7a n!ga%)7a S =;. u

∫ 1+duu

F ( u , N )=

N

0

S)(pson 14 %CODIGO FUNCION DE FLUJO GRADUALMENTE VARIADO (FGV) S() % REGLA DE SIMPSON 1/3 funct!n "FGV# funct!n "FGV# $ f&'n13(uNn) N$nu*t,(N)$".1/(1+0. $".1/(1+0. N N .). .).##f$n2n()4$5-6$u7$(64)/nFP$5f!, $188n1 f!, $188n1 0$4+97 FP$FP+f(0)n: FI$5%CODIGO PARA O2cu2! FGV$(7/3)9(f(4)+;9FP+9FI+f(6))f!, $18115 f!, $18115 u$uu+9:u- u()$uf!, ?$1815 f!, ?$1815 N?$NN+?9:N- N(?)$N?T4624f&'n13(?)$f&'n13(uN?@5)n: n: R$"u. T4624f&'n13 #-R$"5 N-R#

17


S)(pson 4

%CODIGO FUNCION DE FLUJO GRADUALMENTE VARIADO (FGV) S() % REGLA DE SIMPSON 3/ funct!n "FGV# funct!n "FGV# $ f&'n3(uNn) N$nu*t,(N)$".1/(1+0. $".1/(1+0. N N .). .).##f$n2n()4$5-6$u7$(64)/nFR$5f!, $1838n1 f!, $1838n1 0$4+97 FR$FR+f(0)n: FS$5f!, $838n1 f!, $838n1 0$4+97 FS$FS+f(0)n: FT$5f!, $3838n3 f!, $3838n3 0$4+97 FT$FT+f(0)%CODIGO PARA O2cu2! f!, $18115 f!, $18115 u$uu+9:u- u()$uf!, ?$1815 f!, ?$1815 N?$NN+?9:N- N(?)$N?T4624f&'n3(?)$f&'n3(uN?@5)n: n: R$"u. T4624f&'n3 #-R$"5 N-R#

2. Ap3)*a Ap3)*an"o n"o 3os (é%o"os (é%o"os "! )n%!gra* )n%!gra*),n ),n "! S)(pson S)(pson 14 ' S)(pso S)(pson n 46 46 "!%!r( "!%!r()na )narr 3os r!s3 r!s3%a" %a"os os n(ér) n(ér)*os *os ' ss r!sp! r!sp!*%) *%)7as 7as r!pr! r!pr!s!n s!n%a* %a*)on )on!s !s gra8)* gra8)*as as "! 3as s)g)! s)g)!n%! n%!ss 8n*)on!s "! %ranspor%! "! S!")(!n%os !n Ssp!ns),n "! E)ns%!)n =1?50;:

17


Z −1

1

z y − I =0.216 ∫ ( ) dy (1− A )Z A y

A

1

1

S)(pson 14 % FUNCION INTEGRAL I1 DE TRANSPORTE DE SEDIMENTOS EN % SUSPENSION DE EINSTEIN (1B@5) % REGLA DE SIMPSON 1/3 funct!n I1$ntn13I1(An) funct!n I1$ntn13I1(An) $(5=19A(1))/((1A))$nu*t,()$".((1)/). $".((1)/).   .. ..##f$n2n()4$A-6$17$(64)/nIP1$5f!, $188n1 f!, $188n1 $4+97 IP1$IP1+f()n: S)(pson 4 II1$5f!, $88n f!, $88n $4+97 II1$II1+f()n: % FUNCION INTEGRAL I1 DE TRANSPORTE DE SEDIMENTOS EN I1$(7/3)9(f(4)+;9IP1+9II1+f(6))% SUSPENSION DE EINSTEIN (1B@5) I1$9I1% REGLA DE SIMPSON 3/ funct!n I1$ntn3I1(An) funct!n I1$ntn3I1(An) $(5=19A(1))/((1A))% FUNCION INTEGRAL I1 DE TRANSPORTE DE SEDIMENTOS EN $nu*t,()% SUSPENSION DE EINSTEIN (1B@5) $".((1)/). $".((1)/).   .. ..##% REGLA DE SIMPSON 1/3 f$n2n()% GRAFICO 4$A-6$1c2! 422 7$(64)/nc24,-c2cIR1$5f!, $1838n1 f!, $1838n1 % V42!, uu$5=51-NN$=5nc42 $4+97:u$5=51-:N$5=% Int,&42! : c>2cu2! IR1$IR1+f()f!, $1815 f!, $1815 n: u$95=55551- u()$uIS1$5f!, ?$885 f!, ?$885 f!, $838n1 f!, $838n1 &?$?95=1-&(?)$&? $4+97 I1(?)$ntn13I1(u&?15) n: IS1$IS1+f()n: n: IT1$57!2: !n f!, $3838n3 f!, $3838n3 $I1(8) $4+97-ra8)*o '2!t(u.*. '2!t(u .*.) ) IT1$IT1+f()$I1(8;)n: '2!t(u.c. '2!t(u .c.) ) I1$(397/)9(f(4)+39(IR1+IS1)+9IT1+f(6))$I1(8)I1$9I1'2!t(u.,. '2!t(u .,.) ) $I1(8)'2!t(u.6. '2!t(u .6.) ) $I1(815)'2!t(u.. '2!t(u ..) ) $I1(81)'2!t(u.6. '2!t(u .6.) ) $I1(81)'2!t(u.. '2!t(u ..) ) ,: !n

17


% FUNCION INTEGRAL I1 DE TRANSPORTE DE SEDIMENTOS EN % SUSPENSION DE EINSTEIN (1B@5) 1 Z − 1 z % REGLA DE SIMPSON 1/3 A 1 − y I 2 =− ( y ) dy 0.216 ln funct!n I1$ntn13I1(An) funct!n I1$ntn13I1(An) Z y A ( − ) 1 A $(5=19A(1))/((1A))$nu*t,()$".((1)/). $".((1)/).   .. ..##f$n2n()4$A-6$17$(64)/nIP1$5f!, $188n1 f!, $188n1 $4+97 IP1$IP1+f()n: II1$5f!, $88n f!, $88n $4+97 II1$II1+f()n: I1$(7/3)9(f(4)+;9IP1+9II1+f(6))I1$9I1-

∫(

)

17


% FUNCION INTEGRAL I DE TRANSPORTE DE SEDIMENTOS EN % SUSPENSION DE EINSTEIN (1B@5) % REGLA DE SIMPSON 3/ funct!n I$ntn3I(An) funct!n I$ntn3I(An) $(5=19A(1))/((1A))$nu*t,()$".(2!()9((1)/). $".(2!()9((1)/).  .). .).##f$n2n()4$A-6$17$(64)/nIR$5f!, $1838n1 f!, $1838n1 $4+97 IR$IR+f()n: IS$5f!, $838n1 f!, $838n1 $4+97-rG8)*o IS$IS+f()n: IT$5% FUNCION INTEGRAL I DE TRANSPORTE DE SEDIMENTOS EN f!, $3838n3 f!, $3838n3 % SUSPENSION DE EINSTEIN (1B@5) $4+97% REGLA DE SIMPSON 1/3 IT$IT+f()% GRAFICO n: c2! 422 I$(397/)9(f(4)+39(IR+IS)+9IT+f(6))c24,-c2cI$9Iuu$5=51-NN$=5- % V42!, nc42 :u$5=51-:N$5=- % Int,&42! : c>2cu2! f!, $1815 f!, $1815 u$95=55551- u()$uf!, ?$885 f!, ?$885 &?$?95=1-&(?)$&? I(?)$ntn13I(u&?15)n: $I(815)n: '2!t(u.. '2!t(u ..) ) 7!2: !n $I(81)$I(8)'2!t(u.6. '2!t(u.*.) .6.) '2!t(u.*. '2!t(u )) $I(81)$I(8;)'2!t(u.. '2!t(u.c.) ..) '2!t(u.c. '2!t(u )) ,: !n $I(8)'2!t(u.,. '2!t(u .,.) ) $I(8)'2!t(u.6. '2!t(u .6.) )

17


c24,-c2c

. UnH$1-<$-$*ana3 *ana3 %rap!@o)"a3 %rap!@o)"a3 *on: *on: $B6 26 26 So0.001B So0.001B ' n0.025 n0.02566 %ranspor%a %ranspor%a n *a"a3 *a"a3 12 (4s (4s s!C$H/B=1p)"!: L$,t(1+)a;$1=K@D!%!r()na D!%!r()narr !3 %)ran%! %)ran%! *r)%)*o *r)%)*o (!")an (!")an%! %! !3 (!%o"o (!%o"o "! n!%on n!%on Rap#son Rap#son E,,$5=551A$(<+9)9P$<+99LT$<+99F$A3/TC72 46(F)$E,, 72 46(F)$E,, D$(39A9T99A3)/T $F/D A$(<+9)9 P$<+99L T$<+99 F$A3/TCn: V$H/AD$A/TNF$V/,t(B=19D)EN$+V/(B=19)VNFEN

17


 $ 5=;; V $ =3KB@ NF $ 1=5555 EN $ 5=BK35 

$; D!%!r()na D!%!r()narr !3 %)ran%! %)ran%! nor(a3 nor(a3 (!")an% (!")an%!! !3 (é%o"o (é%o"o "! 3a s!*an% s!*an%!. !. c2c-c24, H$1<$$N$5=5@S$5=551C$(H9N/S5=@)3L$,t(1+)$1=K@-$1=K@51E,,$5=551A$(<+9)9-A$(<+9)9P$<+99L-P$<+99LF$A@/PC-F$A@/PC72 46 72 46 (F)$E,, 3$(F9())/(FF) $-$3 A$(<+9)9-A$(<+9)9 P$<+99L-P$<+99L F$A@/PC-F$A@/PCn: T$<+99V$H/AD$A/TNF$V/,t(B=19D)EN$+V/(9B=1)VNFEN

17


 t,4ntn  $ 1=5@ V $ 1=3; NF $ 5=;15 EN $ 1=13@ 

*; Ca3*3 Ca3*3ar ar ' gra8)* gra8)*ar ar !3 p!r8)3 p!r8)3 "!3 r!(an r!(anso so =839o =839o gra"a gra"a3(! 3(!n%! n%! 7ar)a"o 7ar)a"o;6 ;6 *r!a"o *r!a"o por na pr!sa F! !($a3sa !3 aga #as%a na pro8n")"a" "! 1.5 ( )n(!")a%a(!n%! "!%rGs "! 3a pr!sa. S! spon! F! !3 !H%r!(o "! agas arr)$a "!3 p!r8)3 !s )ga3 a na pro8n")"a" 1 (a'or F! 3a pro8n")"a" nor(a3. E3 *o!8)*)!n%! "! !n!rg+a !s 1.1. !(p3!ar !3 (é%o"o "! )n%!gra*),n ")r!*%a o Ka#(!%!88. Q=

12

So=

0.0016

b=

6

α =

1.1

z=

2

Y2=

1.5

n=

0.025

Prof.

1%

T

F

1. T)ran T)ran%! %! *r)% *r)%)*o )*o por N!%o N!%on n rapso rapson. n. ITER A

Y

A

P

D

1

1.9

18.62

14.4970583

13.6

460.000213

900.501696

2

1.38 1.3891 9173 7341 41

12.1 12.194 9464 6466

12.2 12.212 1257 5723 23

11.55 1.5566 6693 9366

142. 142.23 2395 9543 43

391. 391.81 8155 5597 97

3

1.02 1.0261 6146 4666 66

8.26 8.2628 2833 3386 86

10.5 10.589 8906 0674 74

10.1 10.104 0458 5866 66

41.1 41.151 5121 2143 43

182. 182.72 7223 2371 71

4

0.80 0.8009 0934 3496 96

6.08 6.0886 8603 0342 42

9.58 9.5818 1890 9005 05

9.20 9.2037 3739 3986 86

9.84 9.8449 4955 5517 17

100. 100.55 5550 5062 62

5

0.70 0.7030 3028 2885 85

5.20 5.2066 6672 7224 24

9.14 9.1440 4040 4061 61

8.81 8.8121 2115 1541 41

1.33 1.3388 8815 1525 25

74.0 74.057 5753 5384 84

6

0.68 0.6849 4950 5081 81

5.04 5.0480 8020 2009 09

9.06 9.0631 3193 9315 15

8.73 8.7398 9803 0324 24

0.03 0.0395 9533 3367 67

69.7 69.7111243 124399

7

0.68 0.6843 4383 8377

5.04 5.0430 3064 6434 34

9.06 9.0606 0656 5697 97

8.73 8.7375 7534 3482 82

3.79 3.7917 17E E05 05

69.5 69.577 7754 5493 93

8

0.68 0.6843 4383 8316 16

5.04 5.0430 3059 5957 57

9.06 9.0606 0654 5453 53

8.73 8.7375 7532 3264 64

3.49 3.4987 87E E111

69.5 69.577 7742 4209 09

17


9

0.6844

5.0 5.04305957

9.06065453

8.73753264

0

69.5774209

2. D!%!r()na D!%!r()narr !3 %)ran%! %)ran%! nor(a3 nor(a3 (!")an%! (!")an%! !3 (é%o"o (é%o"o "! s!*an%! s!*an%!.. I!

Yo

Y1

Ao

A1

1

1

8

8.1002

2

1.01

1.01 1.0746442 4 1.0647402 4 1.0658098 5 1.0658300 8 1.0658300 4 1.0658300 4

3 1.0746 1.0746442 44244 4 1.0647 1.0647402 40244 5 1.0658 1.0658098 09855 6 1.0658 1.0658300 30088 7 1.0658 1.0658300 30044 8 1.0658 1.0658300 30044

1.0658

Fo

F1

10.472136 10.5168573

123.075827

106.587504

8.75 8.7575 7585 8591 91 10.5 10.516 1685 8573 73 10.8 10.805 0595 9551 51

106 106.5 .587 8750 5044

19.2 19.284 8457 5758 58

8.75 8.7575 7585 8591 91 8.65 8.6557 5785 8501 01 10.8 10.805 0595 9551 51 10.7 10.761 6166 6631 31

19.2 19.284 8457 5758 58

2.3 2.334 3485 8595 9522

8.65 8.6557 5785 8501 01 8.6 8.666 6676 7604 0422 10.7 10.761 6166 6631 31 10. 10.76 7664 6446 4666

2.3 2.334 3485 8595 9522

0.0 0.043 4333 3347 4722

8.66 8.6667 6760 6042 42 8.66 8.6669 6968 6802 02 10.7 10.766 6644 4466 66 10.76 10.7665 6537 37

0.0 0.043 4333 3347 4722

0.00 0.0001 0100 0009 09

8.66 8.6669 6968 6802 02 8.66 8.6669 6967 6754 54 10.7 10.766 6653 5377 10.7 10.766 6653 5368 68

0.00 0.0001 0100 0009 09

4.2 4.275 758E 8E0 099

8.66 8.6669 6967 6754 54 8.66 8.6669 6967 6754 54 10.7 10.766 6653 5368 68 10.7 10.766 6653 5368 68

4.2 4.275 758E 8E0 099

4.5 4.547 475E 5E1 133

8.666 8.66696 9675 7544 8.66 8.6669 6967 6754 54 10.7 10.766 6653 5368 68 10.7 10.766 6653 5368 68

4.5 4.547 475E 5E1 133

0

8.10 8.1002 02

Po

Yn =

1.0658

Yn " 1% =

1.0758

P1

T#r$n& nor'$( Yn =

1.0658

Y)*b =

T#r$n& +r##+o Y+ =

0.6844

,- =

T#r$n& #n#+#o Y1 =

1.0758

T#r$n& f#n$( Y2 =

1.5000

/'&ro & r$'o =

0.2147

0.0212  = 3.439 / = 3.681

20

=

2.963

!



845.55896

17.7489219

0

0.255

827.810038

18.648788

17.7489219

0.199

0.263

809.16125

18.2222624

36.3977099

1.45

0.209

0.2775

790.938987

18 18.4384731

54.6199723

1.33

1.42

0.2195

0.293

772.500514

19 19.6304921

73.0584455

1.3940

1.31

1.40

0.231

0.304

752.870022

15.7974815

92.6889376

1.3727

1.29

1.37

0.2435

0.3535

737.072541

23 23.9252275

108.486419

1.3515

1.27

1.34

0.2575

0.342

713.147313

21 21.8276226

132.411646

1.3303

1.25

1.32

0.273

0.357

691.319691

21.6582267

154.239269

1.3091

1.23

1.29

0.29

0.382

669.661464

24.0831836

175.897496

1.2879

1.21

1.27

0.3095

0.4005

645.57828

24 24.0131373

199.980679

1.2667

1.19

1.24

0.331

0.431

621.565143

25.0357604

223.993817

--

=-*-n

=/*

F/

F

1.5000

1.41

1.53

0.181

0.245

1.4788

1.39

1.50

0.1895

1.4576

1.37

1.48

1.4364

1.35

1.4152



17


1.2455

1.17

1.21

0.355

0.467

596.529383

29.4182297

249.029577

1.2243

1.15

1.19

0.384

0.494

567.111153

29.6287205

278.447807

1.2031

1.13

1.16

0.417

0.542

537.482432

35.3434773

308.076527

1.1819

1.11

1.14

0.457

0.581

502.138955

37.5992144

343.420005

1.1607

1.09

1.11

0.506

0.652

464.539741

48.0938387

381.019219

1.1395

1.07

1.09

0.569

0.713

416.445902

56.6021755

429.113058

1.1182

1.05

1.06

0.656

0.838

359.843727

87.4434881

485.715233

1.0970

1.03

1.04

0.79

0.967

272.400238

159.611058

573.158721

1.0758

1.01

1.01

1.089

1.419

112.78918

P&n#&n&

--



0.00000

1.5000

0.00

0.02840

1.5072

17.75

0.05824

1.5158

36.40

0.08739

1.5238

54.62

0.11689

1.5321

73.06

0.14830

1.5423

92.69

0.17358

1.5463

108.49

0.21186

1.5634

132.41

0.24678

1.5771

154.24

0.28144

1.5906

175.90

0.31997

1.6079

199.98

0.35839

1.6251

223.99

0.39845

1.6439

249.03

0.44552

1.6698

278.45

0.49292

1.6960

308.08

0.54947

1.7313

343.42

0.60963

1.7703

381.02

0.68658

1.8260

429.11

0.77714

1.8954

485.72

0.91705

2.0141

573.16

1.17243

2.2483

732.77

732.769779

17


-ra8)*a "!3 p!r8)3 "! r!(anso.

Perfl de Remanso 2.$"

2.""

1.$"

1.""

".$"

"."" "

d%

1""

2""

#" "

4" "

$""

6""

7""

8""

E3a$orar !3 a3gor)%(o !n Ma%3a$.

17

MNIRH_TP3

Recommend Documents