gradiente hidraulico ralf

8/20/2019 Gradiente Hidraulico Ralf

1/503

Nudo Cota Demanda Nudo Nudo Longitud

(l/s) Inicial Final (m)

1 100.00 0 1 1 2 500

2 95.00 60 2 2 3 400

3 95.00 40 3 4 3 200

4 95.00 30 4 5 4 400

5 95.00 30 5 2 5 200

6 95.00 40 6 6 5 600

0.00 0 1 6 300

! 0.00 0 ! 0 0 0

9 0.00 0 9 0 0 0

10 0.00 0 10 0 0 0

11 0.00 0 11 0 0 0

12 0.00 0 12 0 0 0

13 0.00 0 13 0 0 014 0.00 0 14 0 0 0

15 0 0 0

NT 7 " Nume$o de %u&e$ias 16 0 0 0NN 6 " Nume$o de Nudos 1 0 0 0NS 1 " Nume$o de Nudos con Cota 'ieomet$ica Conocida 1! 0 0 0

1 19 0 0 0

T 14.971 " %eme$atu$a

Solución :Primer Paso :

*at$i de Conecti+idad de Dimensi,n NT x NN " 7 x 6

Numero de Nudos1 2 3 4 5 6

1 -1 1 0 0 0 0 0 0 0 0 0 0 0


2/503

N u m e r o d e T u

b e r i a s

2 0 -1 1 0 0 0 0 0 0 0 0 0 03 0 0 1 -1 0 0 0 0 0 0 0 0 04 0 0 0 1 -1 0 0 0 0 0 0 0 05 0 -1 0 0 1 0 0 0 0 0 0 0 06 0 0 0 0 1 -1 0 0 0 0 0 0 07 -1 0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

A 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

Se!undo Paso :"ari# de Nudo sin $aos $imensión A12 % NT x NN " 7 x 5

Numero de Nudos2 3 4 5 6

1 1 0 0 0 0 0 0 0 0 0 0 0

d e T u b e r i a s

2 -1 1 0 0 0 0 0 0 0 0 0 0

3 0 1 -1 0 0 0 0 0 0 0 0 04 0 0 1 -1 0 0 0 0 0 0 0 05 -1 0 0 1 0 0 0 0 0 0 0 06 0 0 0 1 -1 0 0 0 0 0 0 07 0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

A12 % 0 0 0 0 0 0 0 0 0 0 0 0


3/503

N u m e r o

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

Tercer Paso :*at$i de Nudos sin Datos de Dimensi,n NN x NT " 6 x 7

Numero de Tuberias1 2 3 4 5 6 7

2 1 -1 0 0 -1 0 0 0 0 0 0 0 0

N u m e r o d e N u d o s

3 0 1 1 0 0 0 0 0 0 0 0 0 04 0 0 -1 1 0 0 0 0 0 0 0 0 05 0 0 0 -1 1 1 0 0 0 0 0 0 06 0 0 0 0 0 -1 1 0 0 0 0 0 0

A21 % 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0

&uaro Paso :*at$i %oologica de Cota 'ieomet$ica Conocida

1 ecto$ de Consumo en los nudos


4/503

1 -1

N u m e r o d e T u b e

r i a s

2 0

N u m e r o d e N u d

o s

1 0.000


r i a s

3 0 2 0.0604 0 3 0.0405 0 4 0.0306 0 5 0.030

7 -1 6 0.0400 0.000

A1' % 0 ( )m3*s+% 0.000 , )m3*s+%0 0.000

0 0.000

0 0.000

0 0.000

0 0.000

0 0.000

00

0

0

Seso Paso :" 7 - 7

Numero de Nudos1 2 3 4 5 6 7

1 1 0 0 0 0 0 0 0 0 0 0 0 0

T u b e r i a s

2 0 1 0 0 0 0 0 0 0 0 0 0 03 0 0 1 0 0 0 0 0 0 0 0 0 04 0 0 0 1 0 0 0 0 0 0 0 0 05 0 0 0 0 1 0 0 0 0 0 0 0 06 0 0 0 0 0 1 0 0 0 0 0 0 07 0 0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 0 0

&tencion de la *at$i Identidad )NT x NT+


5/503

%

N u m e r o d e 0 0 0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 0 0 1

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

Se/imo Paso :

Concide$ando DC m"2

N"m I " 2 I Numero de Tuberias1 2 3 4 5 6 7

1 2 0 0 0 0 0 0 0 0 0 0 0 0

N u m e r o d e T u b e r i a s

2 0 2 0 0 0 0 0 0 0 0 0 0 03 0 0 2 0 0 0 0 0 0 0 0 0 04 0 0 0 2 0 0 0 0 0 0 0 0 05 0 0 0 0 2 0 0 0 0 0 0 0 06 0 0 0 0 0 2 0 0 0 0 0 0 07 0 0 0 0 0 0 2 0 0 0 0 0 0

0 0 0 0 0 0 0 2 0 0 0 0 0% 0 0 0 0 0 0 0 0 2 0 0 0 0

0 0 0 0 0 0 0 0 0 2 0 0 0

0 0 0 0 0 0 0 0 0 0 2 0 0

0 0 0 0 0 0 0 0 0 0 0 2 0

0 0 0 0 0 0 0 0 0 0 0 0 2

0 0 0 0 0 0 0 0 0 0 0 0 0

Di7nici,n *at$i Diagonal )N+ de Dimensi,n )NT x NT+02

Nd8


6/503

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

cao Paso P&S $ TA&N:Primera eración

Calculo de la iscocidad Cinematica

% µ

"

ρ

% 1.1409

s % 0.00006

Tuberia , 8 $ e (i) () )m+ )m+ )m*s+

1 2 0.100 500.00 0.25 2.031!3216 44639!.465 0.0159345961 64.

2 3 0.100 400.00 0.15 5.65!!42421 4399.442 0.0166396!! 256

4 3 0.100 200.00 0.2 3.1!309!!61! 5599!.0!2 0.0161554665 !34.

5 4 0.100 400.00 0.15 5.65!!42421 4399.442 0.0166396!! 256

2 5 0.100 200.00 0.1 12.32395444 1115996.163 0.01!052626 29422

6 5 0.100 600.00 0.2 3.1!309!!61! 5599!.0!2 0.0161554665 2502.

1 6 0.100 300.00 0.25 2.031!3216 44639!.465 0.0159345961 404.

0 0 0.100 0.00 0 :DI/0; :DI/0; :DI/0;0 0 0.100 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 0.100 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 0.100 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 0.100 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 0.100 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 0.100 0.00 0 :DI/0; :DI/0; :DI/0;

(1.14 - 0.031 (%-15) < 0.0006! (% - 15)2) 10-6 m2/s

10-6 m2/s

)m3*s+


7/503

0 0 0.100 0.00 0 :DI/0; :DI/0; :D

0 0 0.100 0.00 0 :DI/0; :DI/0; :D

0 0 0.100 0.00 0 :DI/0; :DI/0; :D

0 0 0.100 0.00 0 :DI/0; :DI/0; :D

0 0 0.100 0.00 0 :DI/0; :DI/0; :D

Calculo de la *at$i 11

Numero de Tuberias

1 2 3 4 5 6 7

1 6.40!3 0 0 0 0 0 0 0 0 0


2 0 1155.24 0 0 0 0 0 0 0 0

3 0 0 !3.4255 0 0 0 0 0 0 0

4 0 0 0 25.64 0 0 0 0 0 0

5 0 0 0 0 2942.23 0 0 0 0 0

6 0 0 0 0 0 250.265 0 0 0 0

7 0 0 0 0 0 0 40.444 0 0 0

0 0 0 0 0 0 0 :DI/0; 0 0

A11 % 0 0 0 0 0 0 0 0 :DI/0; 0 0 0 0 0 0 0 0 0 0 :DI/0;

0 0 0 0 0 0 0 0 0 0 :

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

A11

% ;i= x ,

i=)n=>1+?@

i?)γ

i*,

i+


8/503

inalmene:

"


1 0.5 0 0 0 0 0 0 0 0 0 0 0


2 0 0.5 0 0 0 0 0 0 0 0 0 03 0 0 0.5 0 0 0 0 0 0 0 0 04 0 0 0 0.5 0 0 0 0 0 0 0 05 0 0 0 0 0.5 0 0 0 0 0 0 06 0 0 0 0 0 0.5 0 0 0 0 0 07 0 0 0 0 0 0 0.5 0 0 0 0 0

0 0 0 0 0 0 0 0.5 0 0 0 0

% 0 0 0 0 0 0 0 0 0.5 0 0 00 0 0 0 0 0 0 0 0 0.5 0 0

0 0 0 0 0 0 0 0 0 0 0.5 0

0 0 0 0 0 0 0 0 0 0 0 0.5

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

Numero de Tuberias

1 2 3 4 5 6 7

1 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0



B)nex+ [(21 Nd8-1

11-1

12)] [

21 N

d8-1 (=

a

11-1

10 >

n) < ? -

21 =

a]

Calculo de *at$ices o$ 'a$tes a$a el calculo del (B nex+

Nd8-1


9/503

N u m e r o d e T u

b e r i a s

4 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0




:DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0

% :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0:DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0











1 134.! 0.0 0.0 0.0 0.0 0.0 0.0 :DI/0; :DI/0; :DI/0

ero

d e T u b e r i a s

2 0.0 2310.5 0.0 0.0 0.0 0.0 0.0 :DI/0; :DI/0; :DI/0

3 0.0 0.0 166.9 0.0 0.0 0.0 0.0 :DI/0; :DI/0; :DI/0

4 0.0 0.0 0.0 1451.3 0.0 0.0 0.0 :DI/0; :DI/0; :DI/0

5 0.0 0.0 0.0 0.0 5!!4.5 0.0 0.0 :DI/0; :DI/0; :DI/0

6 0.0 0.0 0.0 0.0 0.0 500.6 0.0 :DI/0; :DI/0; :DI/0

7 0.0 0.0 0.0 0.0 0.0 0.0 !0.9 :DI/0; :DI/0; :DI/0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 :DI/0; :DI/0; :DI/0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 :DI/0; :DI/0; :DI/0

A11

-1

CND x CA11D

CND x CA D


10/503

0.0 0.0 0.0 0.0 0.0 0.0 0.0 :DI/0; :DI/0; :DI/0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 :DI/0; :DI/0; :DI/0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 :DI/0; :DI/0; :DI/0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 :DI/0; :DI/0; :DI/0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 :DI/0; :DI/0; :DI/00.0 0.0 0.0 0.0 0.0 0.0 0.0 :DI/0; :DI/0; :DI/0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 :DI/0; :DI/0; :DI/0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 :DI/0; :DI/0; :DI/0



N u m

e r o d e T u b e r i a s

















)CND x CA11D+>1

)CND x CA11D+>1


11/503


12/503

1 2 3 4 5 6 7

1 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;




4 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;5 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;



:DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;





1 1 14

1 6.40! 1 -100 0


2 115.52


2 0 0

3 !.34255 3 0 0

4 2.565 4 0 0

5 294.224 5 0 0

6 25.02 6 0 0

7 4.0444 7 -100 0

:DI/0; 0 0

:DI/0; 0 0

:DI/0; 0 0

:DI/0; 0 0

:DI/0; 0 0

:DI/0; 0 0

CA11

D C,D CA1'

D CBoD

E %


13/503


14/503

'a$a el calculo del Caudal se usa la ecuaci,n

" )CD > )CND CA11D+>1 CA11D+ C,D > ))CND CA11D+>1 )CA12D CB i ? 1D ? CA1'D CBoD++

esol+iendo o$ 'a$tes

CA12D CBi ?1D ? CA1'D CBoD )CND x CA11D+>1 . CA12D CBi ?1

1 1 1

1 95.00 1 -5.00 1 :DI


2 0.00


2 0.00


2 :DI

3 0.00 3 0.00 3 :DI

4 0.00 4 0.00 4 :DI

5 0.00 5 0.00 5 :DI

6 0.00 6 0.00 6 :DI

7 95.00 7 -5.00 7 :DI

0.00 0.00 :DI

0.00 0.00 :DI

0.00 0.00 :DI

0.00 0.00 :DI

0.00 0.00 :DI

0.00 0.00 :DI

0.00 0.00 :DI

0.00 0.00 :DI

0.00 0.00 :DI

0.00 0.00 :DI

0.00 0.00 :DI

0.00 0.00 :DI

Numero de Tuberias

1 2 3 4 5 6 7

&alculo de ,i ?1

,)i ? 1+

CA12D CBi ?1D

C)CND x CA11D+>1D+ CA11D


15/503


N u m e r o d e T u b

e r i a s




5 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/06 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0







:DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0:DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0








de

T u b e r i a s







CD > C)CND x CA11D+>1D+ CA11D


16/503

N :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :

:DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :



:DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; ::DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :




" )CD > )CND CA11D+>1 CA11 Tuberia

1 :DI/0; 1 -

N u m


2 :DI/0; 2 -

3 :DI/0; 4 -

4 :DI/0; 5 -

5 :DI/0; 2 -

6 :DI/0; 6 -

7 :DI/0; 1 -

:DI/0; 0 -

:DI/0; 0 -

:DI/0; 0 -

:DI/0; 0 -

:DI/0; 0 -

:DI/0; 0 -

:DI/0; 0 -

:DI/0; 0 -

:DI/0; 0 -

:DI/0; 0 -

:DI/0; 0 -

)CD > C)CND x CA11

D+>1D+ CA11

D+ . C,D ,)i ? 1+


17/503

Se!unda eraciónCalculo de la iscocidad Cinematica

% µ

"

ρ

% 1.140!9952

s % 0.00006

Tuberia , 8 $ e

(i) () )m+ )m+ )m*s+1 2 :DI/0; 500.00 0.25 :DI/0; :DI/0; :DI/0;

2 3 :DI/0; 400.00 0.15 :DI/0;

4 3 :DI/0; 200.00 0.2 :DI/0; :L@A;

5 4 :DI/0; 400.00 0.15 :DI/0; :DI/0; :DI/0;

2 5 :DI/0; 200.00 0.1 :DI/0; :DI/0; :DI/0;

6 5 :DI/0; 600.00 0.2 :DI/0; :DI/0; :DI/0;1 6 :DI/0; 300.00 0.25 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

(1.14 - 0.031 (%-15) < 0.0006! (% - 15)2) 10-6 m2/s

10-6 m2/s

)m3*s+


18/503

Calculo de la *at$i Nue+a B11

Numero de Tuberias

1 2 3 4 5 6 7

1 :DI/0; 0 0 0 0 0 0 0 0 0

N u m e r o d e T u

b e r i a s

2 0 :L@A; 0 0 0 0 0 0 0 0

3 0 0 :L@A; 0 0 0 0 0 0 0

4 0 0 0 :DI/0; 0 0 0 0 0 0

5 0 0 0 0 :DI/0; 0 0 0 0 0

6 0 0 0 0 0 :DI/0; 0 0 0 0

C 7 0 0 0 0 0 0 :DI/0; 0 0 0

o 0 0 0 0 0 0 0 :DI/0; 0 0

$ CA11DF % 0 0 0 0 0 0 0 0 :DI/0; 0 e 0 0 0 0 0 0 0 0 0 :DI/0

g 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

inalmene:

"

A11

%;i= x ,

i=)n=>1+?@

i?)γ

i*,

i+

B)nex+ [(21 Nd8-1

11-1

12)] [

21 N

d8-1 (=

a

11-1

10 >

n) < ? -

21 =

a]


dGin .&.,:Co$$egi$ la Condici,no$ la @&icaci,n de la*at$i BI " Identidad


19/503

1 2 3 4 5 6 71 0.5 0 0 0 0 0 0 0 0 0 0

N

u m e r o d e T u b e r i a s

2 0 0.5 0 0 0 0 0 0 0 0 03 0 0 0.5 0 0 0 0 0 0 0 04 0 0 0 0.5 0 0 0 0 0 0 0

5 0 0 0 0 0.5 0 0 0 0 0 06 0 0 0 0 0 0.5 0 0 0 0 0

C 7 0 0 0 0 0 0 0.5 0 0 0 0o 0 0 0 0 0 0 0 0.5 0 0 0

$ % 0 0 0 0 0 0 0 0 0.5 0 0e 0 0 0 0 0 0 0 0 0 0.5 0

g 0 0 0 0 0 0 0 0 0 0 0.5

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

Numero de Tuberias

1 2 3 4 5 6 7

1 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0

Tu

b e r i a s







:DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0

Nd8-1


20/503

N u m e r o











1 :DI/0; ::: ::: :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0

N u m e r o d e

T u b e r i a s






C 7 :DI/0; ::: ::: :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0o :DI/0; ::: ::: :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0

$ % :DI/0; ::: ::: :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0e :DI/0; ::: ::: :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0

g :DI/0; ::: ::: :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0

:DI/0; ::: ::: :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0




CND x CA11D

CND x CA11D


21/503

:DI/0; ::: ::: :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;

























)CND x CA11D+>1

)CND x CA11D+>1

CA21D . C)CND x CA11D+>1D


22/503

$ %

N u

m e r o d e T u


e 7 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;

g :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;


:DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;:DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;


Numero de Tuberias

1 2 3 4 5 6 7


N




C 4 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;

o 5 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;

$ % 6 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;e 7 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;






Numero de Tuberias

1 2 3 4 5 6 7


a s



CA21

D C)CND x CA11

D+>1D

)CA21

D C)CND x CA11

D+>1D+ . CA12

D

D C)CND x CA11

D+>1D+ CA12

D

> ))CA21

D C)CND x CA11

D+>1D+ CA12

D+>1


23/503

N u m e r o d e 7 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI

:DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI





1 1 14

1 :DI/0; 1 -100 0


r i a s

2 :DI/0;


r i a s

2 0 0


r i a s3 :DI/0; 3 0 0

4 :DI/0; 4 0 0

5 :DI/0; 5 0 0

6 :DI/0; 6 0 0

7 :DI/0; 7 -100 0

:DI/0; 0 0

:DI/0; 0 0

:DI/0; 0 0

:DI/0; 0 0

:DI/0; 0 0

:DI/0; 0 0

:DI/0; 0 0

:DI/0; 0 0

:DI/0; 0 0

:DI/0; 0 0

:DI/0; 0 0

:DI/0; 0 0

CA21D C)CND x CA11D+ 1D CA11D C,D ? CA1'D CBoD

CA11D C,D CA1'D CBoD

E %

CA21D C,D


24/503


2 :DI/0;


2 :DI/0;

3 :DI/0; 3 :DI/0;

4 :DI/0; 4 :DI/0;

5 :DI/0; 5 :DI/0;

6 :DI/0; 6 :DI/0;

7 :DI/0; 7 :DI/0;:DI/0; :DI/0;

:DI/0; :DI/0;

:DI/0; :DI/0;

:DI/0; :DI/0;

:DI/0; :DI/0;

> ))CA21D C)CND x CA11D+>1D+ CA12D+>1 . CA21D . C)CND x CA11D+>1D . CA11D C,D ? CA1'D CBo> - 2 :DI/0;

> - 3 :DI/0;

> - 4 :DI/0;

> - 5 :DI/0;

> - 6 :DI/0;

> - " :DI/0;

> - ! :DI/0;

> - 9 :DI/0;

> - 10 :DI/0;

> - 11 :DI/0;

> - 12 :DI/0;

> - 13 :DI/0;




B)nex+ %

&alculo de ,i ?1

,)i ? 1+


25/503

CA12D CBi ?1D ? CA1'D CBoD )CND x CA11D+>1 . CA11 1

1 95.00 1 -5.00

N u

m e r o d e T u b e r i a s

2 0.00

N u


2 0.00

N u

m e r o d e T u b e r i a s3 0.00 3 0.00

4 0.00 4 0.00

5 0.00 5 0.00

6 0.00 6 0.00

7 95.00 7 -5.00

0.00 0.00

0.00 0.00

0.00 0.00

0.00 0.00

0.00 0.00

0.00 0.00

0.00 0.00

0.00 0.00

0.00 0.00

0.00 0.00

0.00 0.00

0.00 0.00

Numero de Tuberias

1 2 3 4 5 6 7

1 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :

e r i a s





CA12

D CBi ?1

D

C)CND x CA11

D+>1D+ CA11

D


26/503

N u m e r o



















6 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0C 7 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0

o :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0

$ :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0

e :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0

g :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0






27/503


28/503

s % 0.00006

Tuberia , 8 $ e

(i) () )m+ )m+ )m*s+1 2 :DI/0; 500.00 0.25 :DI/0; :DI/0; :DI/0;

2 3 400.00 0.15 :L@A;

4 3 :DI/0; 200.00 0.2 :DI/0; :L@A;

5 4 :DI/0; 400.00 0.15 :DI/0; :DI/0; :DI/0;

2 5 :DI/0; 200.00 0.1 :DI/0; :DI/0; :DI/0;

6 5 :DI/0; 600.00 0.2 :DI/0; :DI/0; :DI/0;

1 6 :DI/0; 300.00 0.25 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;

0 0 :DI/0; 0.00 0 :DI/0; :DI/0; :DI/0;



1 :DI/0; 0 0 0 0 0 0 0 0 0 0 0 0

)m3*s+

A11 % ;i= x ,i=)n=>1+?@i?)γi*,i+

dGin .&.,:Co$$egi$ la Condici,na$a ala$ los +alo$esde la mat$i BNd8E-1


29/503


r i a s

2 0 :L@A; 0 0 0 0 0 0 0 0

3 0 0 :L@A; 0 0 0 0 0 0 0

4 0 0 0 :DI/0; 0 0 0 0 0 0

5 0 0 0 0 :DI/0; 0 0 0 0 0

6 0 0 0 0 0 :DI/0; 0 0 0 0

C 7 0 0 0 0 0 0 :DI/0; 0 0 0

o 0 0 0 0 0 0 0 :DI/0; 0 0

$ CA11DFF % 0 0 0 0 0 0 0 0 :DI/0; 0 e 0 0 0 0 0 0 0 0 0 :DI/0;

g 0 0 0 0 0 0 0 0 0 0 :

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

inalmene:

"


1 0.5 0 0 0 0 0 0 0 0 0 2 0 0.5 0 0 0 0 0 0 0 0 3 0 0 0.5 0 0 0 0 0 0 0

4 0 0 0 0 5 0 0 0 0 0 0

B)nex+ [(21 Nd8

-1 11

-1 12

)] [21

Nd8

-1 (=a

11-1

10 >

n) < ? -

21 =

a]


dGin .&.,:Co$$egi$ la Condici,no$ la @&icaci,n de la*at$i BI " Identidad

dGin .&.,:Co$$egi$ la @&icaci,n de la


30/503

C

N u m

e r o d e T u b e 7 0 0 0 0 0 0 0.5 0 0 0

o 0 0 0 0 0 0 0 0.5 0 0

$ % 0 0 0 0 0 0 0 0 0.5 0 e 0 0 0 0 0 0 0 0 0 0.5

g 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

Numero de Tuberias

1 2 3 4 5 6 7


N u m e r o d e T u b e r i a

s








% :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; ::DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :





Nd8-1

CA11F-1


31/503





1 :DI/0; ::: ::: :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;

N u m e r o d e T

u b e r i a s





6 :DI/0; ::: ::: :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;C 7 :DI/0; ::: ::: :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;

o :DI/0; ::: ::: :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;

$ % :DI/0; ::: ::: :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;e :DI/0; ::: ::: :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;

g :DI/0; ::: ::: :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;



:DI/0; ::: ::: :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;:DI/0; ::: ::: :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;






CND x CA11D

CND x CA11

D

)CND x CA11D+>1

dGin .&.,:Co$$egi$ la @&icaci,n dela *at$i B21 a$a$ealia$ la multilicaci,ncon BBN.B11E-1

dGin .&.,:Co$$egi$ la @&icaci,n de la*at$i B12 a$a $ealia$la multilicaci,n de la*at$i


32/503

N u m e r o d

e T u b e r i a s 3 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/

4 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/




:DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/

% :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/:DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/





:DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/:DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/




Numero de Tuberias

1 2 3 4 5 6 7


o d e T u b e r i a s



C 4 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/

o 5 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/

$ % 6 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/e 7 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/

g :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/

)CND x CA11

D+>1


CA21

D C)CND x CA11

D+>1D

dGin .&.,:Co$$egi$ la @&icaci,n dela *at$i B= a$a $ealia$la multilicaci,n de la*at$i

dGin .&.,:Co$$egi$ la @&icaci,nde la *at$i B10a$a $ealia$ lamultilicaci,n de la*at$i


33/503

:DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI


1 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI




C 4 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI

o 5 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI

$ % 6 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DIe 7 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI

g :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI







r o d e T u b e r i a s









)CA21

D C)CND x CA11

D+>1D+ . CA12

D

D C)CND x CA11

D+>1D+ CA12

D

> ))CA21

D C)CND x CA11

D+>1D+ CA12

D+>1

dGin .&.,:Co$$egi$ la @&icaci,nde la *at$i B21a$a $ealia$ la

multilicaci,n de la*at$i


34/503

1 1 14

1 ::: 1 -100 0

N u m


2 :::

N u m


2 0 0

3 ::: 3 0 0

4 ::: 4 0 0

5 ::: 5 0 0

6 ::: 6 0 0

7 ::: 7 -100 0

::: 0 0

::: 0 0

::: 0 0

::: 0 0

::: 0 0

::: 0 0

::: 0 0

::: 0 0

::: 0 0

::: 0 0::: 0 0

::: 0 0

CA21D . C)CND x CA11D+>1D . CA11D C,D ? CA1'D CBoD

1 1

1 ::: 1 :::

2 ::: 2 :::


CA21D C,D

dGin .&.,:Co$$egi$ la @&icaci,nde la *at$i B12 a$a$ealia$ lamultilicaci,n de la*at$i


35/503

N u m e r o

:::

N u m e r o

:::

::: :::

::: :::

::: :::

::: :::

> ))CA21D C)CND x CA11D+>1D+ CA12D+>1 . CA21D . C)CND x CA11D+>1D . CA11D C,D ? CA1'D C> - 2 :::

> - 3 :::

> - 4 :::

> - 5 :::

> - 6 :::

> - " :::

> - ! :::

> - 9 :::

> - 10 :::

> - 11 :::

> - 12 :::

> - 13 :::




CA12D CBi ?1D ? CA1'D CBoD )CND x CA11D+>1 . CA12D CBi ?1 1

1 ::: 1 ::: 1

s

2 :::

s

2 :::

s

2

3 ::: 3 ::: 3

B)nex+ %

&alculo de , i ?1

,)i ? 1+

CA12D CBi ?1D

dGin .&.,:

C i l @&i i, d l


36/503

N u m e r o d e T u b e r i 4 :::

N u m e r o d e T u b e r i 4 :::

N u m e r o d e T u b e r i

5 ::: 5 :::

6 ::: 6 :::

7 ::: 7 :::

::: :::

::: :::

::: :::

::: :::

::: :::

::: :::

::: :::

::: :::

::: :::

::: :::

::: :::

::: :::

Numero de Tuberias

1 2 3 4 5 6 7


m


2 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/3 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/








C)CND x CA11D+>1D+ CA11D

a $ a$a $ea a$ amultilicaci,n de la *at$i

dGin .&.,:Co$$egi$ la @&icaci,n de la*at$i B= $ecalculado a$a$ealia$ la multilicaci,n dela *at$i


37/503







Numero de Tuberias

1 2 3 4 5 6 7








C 7 :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;

o :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;

$ :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;

e :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0; :DI/0;












38/503

N u m e r o d

e T u b e r i a s

2 ::: 2 - 3

3 ::: 4 - 3

4 ::: 5 - 4

5 ::: 2 - 5

6 ::: 6 - 5

C 7 ::: 1 - 6

o ::: 0 - 0

$ ::: 0 - 0

e ::: 0 - 0

g ::: 0 - 0

::: 0 - 0

::: 0 - 0

::: 0 - 0

::: 0 - 0

::: 0 - 0

::: 0 - 0

::: 0 - 0

::: 0 - 0

&uara eraciónCalculo de la iscocidad Cinematica

% µ

"

ρ

% 1.140!9952

s % 0.00006

Tuberia , 8 $ e

(i) () )m+ )m+ )m*s+1 2 :L@A; 500.00 0.25 :L@A; :L@A; :L@A;

2 3 400.00 0.15 :L@A;

(1.14 - 0.031 (%-15) < 0.0006! (% - 15)2) 10-6 m2/s

10-6 m2/s

)m3*s+

dGin .&.,:Co$$egi$ la Condici,no$ la @&icaci,n de la*at$i BI " Identidad(>149)


39/503

4 3 :L@A; 200.00 0.2 :L@A; :L@A;

5 4 :L@A; 400.00 0.15 :L@A; :L@A; :L@A;

2 5 :L@A; 200.00 0.1 :L@A; :L@A; :L@A;

6 5 :L@A; 600.00 0.2 :L@A; :L@A; :L@A;

1 6 :L@A; 300.00 0.25 :L@A; :L@A; :L@A;

0 0 :L@A; 0.00 0 :L@A; :L@A; :DI/0;

0 0 :L@A; 0.00 0 :L@A; :L@A; :DI/0;0 0 :L@A; 0.00 0 :L@A; :L@A; :DI/0;

0 0 :L@A; 0.00 0 :L@A; :L@A; :DI/0;

0 0 :L@A; 0.00 0 :L@A; :L@A; :DI/0;

0 0 :L@A; 0.00 0 :L@A; :L@A; :DI/0;

0 0 :L@A; 0.00 0 :L@A; :L@A; :DI/0;

0 0 :L@A; 0.00 0 :L@A; :L@A; :DI/0;

0 0 :L@A; 0.00 0 :L@A; :L@A; :DI/0;

0 0 :L@A; 0.00 0 :L@A; :L@A; :DI/0;

0 0 :L@A; 0.00 0 :L@A; :L@A; :DI/0;0 0 :L@A; 0.00 0 :L@A; :L@A; :DI/0;


Numero de Tuberias

1 2 3 4 5 6 71 :L@A; 0 0 0 0 0 0 0 0 0 0 0

T u b e r i a s

2 0 :L@A; 0 0 0 0 0 0 0 0 0 0

3 0 0 :L@A; 0 0 0 0 0 0 0 0 0

4 0 0 0 :L@A; 0 0 0 0 0 0 0 0

5 0 0 0 0 :L@A; 0 0 0 0 0 0 0

6 0 0 0 0 0 :L@A; 0 0 0 0 0 0

C 7 0 0 0 0 0 0 :L@A; 0 0 0 0 0

o 0 0 0 0 0 0 0 :DI/0; 0 0 0 0

A11

% ;i= x ,

i=)n=>1+?@

i?)

γi*,

i+

dGin .&.,:Co$$egi$ la Condici,na$a ala$ los +alo$esde la mat$i BNd8E-1(>259)


40/503

$ CA11DFF %

N u m e r o d e 0 0 0 0 0 0 0 0 :DI/0; 0 0

e 0 0 0 0 0 0 0 0 0 :DI/0; 0

g 0 0 0 0 0 0 0 0 0 0 :DI/0;

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

inalmene:

"


1 0.5 0 0 0 0 0 0 0 0 0 0


2 0 0.5 0 0 0 0 0 0 0 0 0 3 0 0 0.5 0 0 0 0 0 0 0 0

4 0 0 0 0.5 0 0 0 0 0 0 0 5 0 0 0 0 0.5 0 0 0 0 0 0 6 0 0 0 0 0 0.5 0 0 0 0 0

C 7 0 0 0 0 0 0 0.5 0 0 0 0 o 0 0 0 0 0 0 0 0.5 0 0 0

$ % 0 0 0 0 0 0 0 0 0.5 0 0 e 0 0 0 0 0 0 0 0 0 0.5 0

g 0 0 0 0 0 0 0 0 0 0 0.5

0 0 0 0 0 0 0 0 0 0 0

B)nex+ [(21 Nd8-1

11-1

12)] [

21 N

d8-1 (=

a

11-1

10 >

n) < ? -

21 =

a]


Nd8-1

dGin .&.,:

Co$$egi$ la @&icaci,n de la*at$i BN a$a $ealia$ lamultilicaci,n con B11


41/503

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

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56/503

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57/503

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