LABORATORIO N°1
METODO HARDY CROSS
9.19)$ 9.19)$ll sis siste tema ma de tuberi tuberias as en %arale %aralelo lo&& most mostra rado do en la 'gura 'gura 9 los caudales en las dos ramas del circuito uli*ando el metodo
DATOS Q = 456 Lt / seg
0,456 m3/seg
tuberia
Long. (m)
diam. (m)
c
1
1 50 0
0. 3
120
2
900
0. 4
120
METODO DE HARDY CROSS Malla 1
tuberia
ki
Q (lt/seg)
1
01.2
11 !
2
1 1.4 4
"340
#
∆Q I=
3.7434!"3
9.20 9.20 $l agua agua -u,e -u,e atra atrae ess del del sist sistem ema a most mostra rado do en la 'gur 'gura a9 & la la elea eleacio cion n es de !0.0 !0.0 metr metros os , la altu altura ra de de %resi %resion on de 45. 45. de la red de tuberias& la altura de %resion en
6 uberia
L(m)
(m)
c
1
900
0. 5
100
2
900
0. 5
100
3
1 20 0
0. !
100
4
1 20 0
0. 4
100
5
1 20 0
0. 4
100
!
900
0. 4
100
900
0. 3
100
1 20 0
0. 4
100
9
1 20 0
0. 3
100
10
1 20 0
0. 3
100
11
900
0. 4
100
12
900
0. 3
100
MLL 1
78$
L (m)
d (cm)
12
9 00
50
4
12 00
40
!
9 00
40
3
12 00
!0
2
9 00
50
5
12 00
40
9 00
30
4
12 00
40
!
9 00
40
9
12 00
30
11
9 00
40
12 00
40
. 00
9 00. 00
30 .00
10
12 00
30
12
9 00
30
9
12 00
30
: 2
: 3
: 4
:
6 uberia
L(m)
(m)
c
1
900
0. 5
100
2
900
0. 5
100
3
1 20 0
0. !
100
4
1 20 0
0. 4
100
5
1 20 0
0. 4
100
!
900
0. 4
100
900
0. 3
100
1 20 0
0. 4
100
9
1 20 0
0. 3
100
10
1 20 0
0. 3
100
11
900
0. 4
100
12
900
0. 3
100
MLL 1
78$
L (m)
d (cm)
12
9 00
50
4
12 00
40
!
9 00
40
3
12 00
!0
2
9 00
50
5
12 00
40
9 00
30
4
12 00
40
!
9 00
40
9
12 00
30
11
9 00
40
12 00
40
. 00
9 00. 00
30 .00
10
12 00
30
12
9 00
30
9
12 00
30
: 2
: 3
: 4
:
9.21)La 9.21)La red de tuberias tuberias most mostrada rada en la 'gura 'gura 9.1& re%re re%resent sent tuberias
DATOS#
uberia
L(m)
(m)
c
1
!00
0. 3
120
2
!00
0. 3
120
3
!00
0. 3
120
4
400
0.2 5
120
5
400
0.2 5
120
!
400
0.2 5
120
400
0.2 5
120
!00
0. 3
120
9
!00
0. 3
120
10
!00
0. 3
120
9.5!)
MLL
M
L (m)
d (cm)
1
10 00
50
4
12 00
40
!
10 00
30
3
12 00
!0
2
10 00
50
5
12 00
40
10 00
40
4
12 00
40
!
10 00
30
9
12 00
30
11
10 00
40
12 00
40
10 00
40
10
12 00
30
12
10 00
30
9
12 00
30
:
:
: =
:
9.5)
MLL
M
L (m)
d (cm)
1
! 10
!1
5
9 15
3 .1
! 10
45 .
4
915
!1
2
!10
!1
!
915
3.1
9
!10
45.
5
915
3.1
3
!10
3.1
915
!1
10
!10
45.
!
915
3.1
!10
45.
12
915
3.1
15
!10
!1
11
915
45.
9
!10
45.
13
915
3.1
1!
!10
45.
12
915
3.1
10
!10
45.
14
915
45.
1
!10
3.1
13
915
3.1
:
:
: =
: =
: =
:
$;ercicios en clases
MLL
78$
>
Q(l/s)
1
1154.5
33
4
45012
!
!
4!!
"2
3
1539
"3
2
4!!
12
5
45012
2
4!!
"13
4
45012
"!
ESTUDIANTE
GUIDO RODOLFO BURVEGA QUIROZ
REGISTRO
212056190
GRUPO
CIV 230-B
.1!& determinar %ara QING. 45!PALENQUE lt / seg (caudal total )& DOCENTE ESPADA GERMAN e +ard, cross
ki 01.2!94!9022 11.43559!3534
?L (m)
?L/Q
Q@
?L@
14.9
0.123!2 119.22243493
15.9093220!
"1!.1
0.0435 "33!.25!502
"15.2
"1.21
0.1515
0.0193220!
RES$%ESTA # Q& = &&!,7 Lt/seg Q = 336," Lt/seg
.1& en el ue se conocen ciertos caudales& como se indica en la 'gura.$n el %unt 0 metros. La eleacion en es de 30.00 metros. eterminar& los caudales atrae
ki
Qi (lt/s)
55.995315
1!0
55.995315
120
30.143!54
240
221.2!124519!
40
221.2!124519!
0
1!5.94!29339
0
!3.!2!5!20019
!0
221.2!124519!
1!0
9.1!493359
40
9.1!493359
40
1!5.94!29339
0
!3.!2!5!20019
40
<
>
Q (L/s)
?L (m)
?L/Q
AQ
100
55&9
1!0
1&9
0&012
12&!4
100
221.2!
40
0.5
0.014
12.!01
100
1!5.95
"0
"1.55
0.019
12.!01
100
30.1
"240
"2.19
0.009
12.!01
"1.2
0.055
100
55.9
120
1.11
0.009
5.333
100
221.2!
0
2.0
0.02!
5.333
100
!3.!3
"!0
"3.0
0.0!2
5.333
100
221.2!
"40
"0.5
0.014
5.333
"1.10
0.111
100
1!5.95
0
1.55
0.019
19.299
100
9.1
40
2.33
0.05
19.299
100
1!5.95
"0
"1.55
0.019
19.299
100
221.2!
"1!0
".4!
0.04
19.299
"5.13
0.144
100.00
!3.!3
!0.00
3.0
0.0!
"4.!
100
9.1
40
2.33
0.05
"4.5
100
!3.!3
"40
"1.5
0.044
"4.5
100
9.1
"40
"2.33
0.05
"4.5
1.95
0.222
un sistema de en;uagado %or c+orro de agua. eterminar el caudal de agua ue
ki 320.510!09 320.510!09 320.510!09 519.23510!5! 519.23510!5! 519.23510!5! 519.23510!5! 320.510!09 320.510!09 320.510!09
ue se muestra en la 'gura 9.35. 6e su%one <120 %ara todas las tuberias
<
>
Q (L/s)
?L (m)
(?L/Q)
AQ
120
44.39
200
2.2!
0.011
25.224
120
15.91
50
0.!2
0.012
25.224
120
534.1
"100
"4.99
0.050
25.224
120
21.92
"300
"1.5!
0.005
25.224
"3.!
0.09
120
44.39
150
1.33
0.009
".549
120
15.91
50
0.!2
0.012
".549
120
131.!0
"25
"0.2
0.029
".549
120
15.91
"50
"0.41
0.00
".549
0.1
0.05
120
534.1
100
.55
0.05
"!.425
120
!41.02
25
0.0
0.02
"!.425
120
131.!0
"100
"1.23
0.012
"!.425
120
15.91
"200
"5.32
0.02
"!.425
1.!9
0.142
120
131.!0
25
0.14
0.00!
10.0!!
120
!41.02
25
0.0
0.02
10.0!!
120
534.1
"5
"1.39
0.01
10.0!!
120
!41.02
"25
"1.!!
0.0!!
10.0!!
"2.21
0.119
e se muestra en la 'gura 9.3!. 6e su%one ue <120 %ara todas.
<
>
Q (L/s)
?L (m)
(?L/Q)
AQ
120
10.2
141.5
0.2
0.002
!.103
120
152.!1
31.5
0.25
0.00
!.103
120
41.9!
"0.5
"0.31
0.004
!.103
120
15.42
"141.5
"0.41
0.003
"0.20
0.01
!.103
120
10.2
110
0.1
0.002
"3.5
120
152.!1
40
0.40
0.010
"3.5
120
41.9!
"4
"0.15
0.003
"3.5
120
152.!1
"31.5
"0.25
0.00
"3.5
0.1!
0.023
120
101.4
0
0.4
0.011
"!.19
120
15.42
13.4
0.01
0.000
"!.19
120
41.9!
"35
"0.0
0.002
"!.19
120
152.!1
"40
"0.40
0.010
"!.19
0.2
0.023
120
41.9!
0.5
0.31
0.004
4.332
120
152.!1
11.
0.04
0.004
4.332
120
10.2
"14.15
0.00
0.000
4.332
120
!2.94
"0.5
"0.4
0.00
4.332
"0.12
0.015
120
41.9!
4
0.15
0.003
"4.409
120
152.!1
10.55
0.03
0.003
"4.409
120
41.9!
"25.95
"0.05
0.002
"4.409
120
152.!1
"11.
"0.04
0.004
"4.409
0.10
0.012
120
41.9!
35
0.0
0.002
3.5!1
120
!2.94
4.4
0.23
0.005
3.5!1
120
101.4
"3!.5
"0.2!
0.00
3.5!1
120
152.!1
"10.55
"0.40
0.03
3.5!1
"0.34
0.052
?L
?L/Q
BQ
QCQoDBQ
?LC(m)
?LC/QC
2.10
0.0!
2.11
35.11
2.35
0.0
3.49
0.5
2.11
!.42
3.9!
0.!2
"5.
0.22
2.11
"24.9
"5.05
0.20
"3.45
0.09
2.11
"34.9
"3.10
0.09
"3.3
0.9!
"1.4
0.9
1.31
0.11
1.!9
13.!9
1.!
0.12
0.4!
0.23
1.!9
3.!9
1.42
0.3
"1.52
0.12
1.!9
"11.31
"1.1
0.10
"3.49
0.5
1.!9
"!.42
"3.9!
0.!2
"3.24
1.04
"2.04
1.23
QE QDAQ
?LE (m)
?LE/QE
AQE
QEE QEDAQE
12&!4
2&1
0&013
&5
10&22
4.2!
0.
0.01
.!21
55.49
"!.!99
"1.0
0.021
.!21
".252
"22.399
"1.9
0.009
.!21
"219.
"0.3
0.059
125.333
1.20
0.010
"0.!0
124.25
5.333
2.33
0.02
"0.!0
4.25
"49.910
"2.!3
0.053
"0.!0
"5.23
"4.2!
"0.
0.01
"0.!0
"55.49
0.12
0.10!
!.!99
1.0
0.021
"1.25
.252
!4.05!
5.5
0.0
"1.25
54.92!
"!0.01
"0.93
0.015
"1.25
"!2.52!
"140.01
"5.
0.042
"1.25
"142.52!
0.5!
0.1!5
49.91
2.!3
0.05
.31
5.2
35.243
1.4
0.052
.305
42.54
"44.5
"2.15
0.04
.305
"3.452
"!4.05!
"5.5
0.0
.305
"54.92!
"3.24
0.240
circula %or cada tuberia. 6e su%one <120 %ara todas la
MLL
M
L (m)
1
!00
5
400
!00
4
400
:
2
!00
!
400
9
!00
5
400
:
3
!00
400
10
!00
!
400
:
QE QDAQ
?LE (m)
(?LE/QE)
AQE
QEE QEDAQE
225.224
2.2
0.013
.29
233.054
2.3
1.5
0.019
.29
.259
"!.351
"3.3
0.055
.29
"9.4!
"24.!
"2.01
0.00
.29
"2!!.94!
"1.35
0.093
142.451
1.21
0.00
3.343
145.94
42.451
0.4!
0.011
3.343
45.94
"42.!15
"0.3
0.009
3.343
"4.1!4
"2.3
"1.5
0.019
3.343
".259
"0.29
0.04
!.351
3.3
0.055
2.954
9.4!
.509
0.09
0.011
2.954
2.51
"10!.425
"2.09
0.020
2.954
".40
"20!.425
".53
0.041
2.954
"1.40
"!.
0.12
42.!15
0.3
0.009
.92
4.1!4
35.0!!
1.30
0.03
.92
43.95
"!4.934
"3.39
0.052
.92
"5!.042
".509
"0.09
0.011
.92
"2.51
"1.0
0.110
QE QDAQ
?LE (m)
(?LE/QE)
AQE
QEE QEDAQE
14.!03
0.30
0.002
"3.459
144.144
41.4!1
0.42
0.010
"3.459
34.9
"5.449
"0.22
0.004
"3.459
"!4.521
"135.39
"0.3
0.003
"3.459
"13.5!
0.12
0.019
10!.142
0.1!
0.002
3.025
109.1!
3!.142
0.33
0.009
3.025
39.1!
"5!.19
"0.20
0.004
3.025
"49.425
"41.4!1
"0.42
0.010
3.025
"34.9
"0.14
0.024
5.!99
0.52
0.009
2.!13
!3.1
2.1
0.00
0.000
2.!13
9.224
"41.19
"0.11
0.003
2.!13
"3.55
"4!.19
"0.52
0.011
2.!13
"43.55
"0.11
0.023
.939
0.3
0.005
"3.40
2.15
1!.132
0.0
0.005
"3.40
12.392
"9.1
0.00
0.000
"3.40
"13.55
"!0.221
"0.35
0.00!
"3.40
"!!.54
0.11
0.015
49.9
"0.1!
"0.003
2.553
4.2
!.141
0.01
0.002
2.553
33.!94
"30.359
"0.0
0.002
2.553
"2.0!
"20.540
"0.12
0.00!
2.553
10.52
"0.33
0.00
34.230
0.0
0.002
"!.151
31.19
51.9!1
0.2!
0.005
"!.151
45.10
"32.939
"0.1
0.00!
"!.151
"39.090
"2.50
0.00
0.001
"!.151
"3!.23
0.1!
0.014
BQC
QCCQoCDBQC
?LCC(m)
?LCC/QCC
BQCC
1.02
3!.13
2.4
0.0
0.5
1.02
!.54
4.09
0.!3
0.5
1.02
"23.
"4.!
0.20
0.5
1.02
"33.
"2.93
0.09
0.5
"1.04
0.9
0.90
14.59
1.
0.13
0.45
0.90
4.59
2.13
0.4!
0.45
0.90
"10.41
"1.01
0.10
0.45
0.90
"!.54
"4.09
0.!3
0.45
"1.09
1.31
?LEE (m)
?LEE/QEE
AQEE
QEEE QEEDAQEE
?LEEE (m)
2&35
0&0133
"0&29
19&443
2&33
1.05
0.019
"0.3
49.9!!
0.
"1.45
0.019
"0.3
"2.3!
"1.!5
"1.!
0.00
"0.3
"220.552
"1.
0.09
0.0!0
1.19
0.010
4.5
129.43
1.2
2.30
0.02
4.5
9.43
2.54
"3.45
0.0!0
4.5
"52.31!
"2.
"1.05
0.019
4.5
"49.9!!
"0.
"1.02
0.115
1.45
0.019
4.11
2.3!
1.!5
4.19
0.0!
4.11
!0.4!
5.01
"0.9
0.01!
4.11
"5.15
"0.5
"!.02
0.042
4.11
"13.15
"5.!5
"1.3!
0.153
3.45
0.0!
"0.5
52.32
2.
2.!1
0.0!1
"0.49
41.99
2.53
"1.55
0.041
"0.49
"3.201
"1.!0
"4.19
0.0!
"0.49
"!0.4!
"5.01
0.33
0.239
"0.33
0.0
0.1!
"1.21
d (cm)
<
>
Q (L/s)
?L (m)
30
120
320.51
200
1!.32
25
120
519.24
100
.33
30
120
320.51
"100
"3.00
25
120
519.24
"200
"3.05 "1!.39
30
120
320.51
100
4.53
25
120
519.24
50
2.03
30
120
320.51
"100
"1.!
25
120
519.24
"100
"1.35 3.4!
30
120
320.51
50
1.2!
25
120
519.24
50
2.03
30
120
320.51
"50
"3.00
25
120
519.24
"50
"1.50 "1.20
?LEE (m)
(?LEE/QEE)
AQEE
QEEE QEEDAQEE
?LEEE (m)
3.00
0.013
1!.505
249.559
3.40
1.3
0.020
1!.505
99.123
2.19
"!.14
0.0!9
1!.505
"5.012
"4.43
"1.90
0.00
1!.505
"250.441
"1.!9
"3.31
0.109
1.2!
0.009
4.!42
150.43!
1.33
0.53
0.011
4.!42
50.43!
0.!3
"0.4
0.010
4.!42
"4.!3
"0.4
"1.3
0.020
4.!42
"99.123
"2.19
"0.43
0.050
!.14
0.0!9
2.041
5.012
4.43
0.9
0.031
2.041
2!.4!2
0.
"1.1!
0.015
2.041
"5.429
"1.10
"!.45
0.03!
2.041
"15.429
"!.31
"0.5
0.151
0.4
0.010
4.151
4.!3
0.4
1.9
0.045
4.151
4.109
2.34
"2.5
0.04!
4.151
"51.91
"2.24
"0.9
0.031
4.151
"2!.4!2
"0.
"1.02
0.132
"0.53
"0.0
"2.21
"0.20
?LEE (m)
(?LEE/QEE)
AQEE
QEEE QEEDAQEE
?LEEE (m)
0.29
0.002
2.09
14!.241
0.29
0.31
0.009
2.09
3.9!!
0.3
"0.2!
0.004
2.09
"!0.94
"0.24
"0.40
0.003
"0.0
0.01
0.1
0.002
"1.92
10.25
0.1
0.3
0.010
"1.92
3.25
0.35
"0.1!
0.003
"1.92
"53.2!2
"0.1
"0.31
0.009
"1.92
"3.9!!
"0.3
0.0
0.023
0.!3
0.010
"1.441
!0.234
0.5!
0.00
0.000
"1.441
5.3
0.00
"0.10
0.003
"1.441
"40.025
"0.11
"0.4!
0.011
"1.441
"45.025
"0.49
0.0!
0.023
0.32
0.004
1.94!
!.012
0.3!
0.05
0.004
1.94!
14.33
0.0!
0.00
0.000
1.94!
"11.!13
0.00
"0.42
0.00!
1.94!
"!3.1
"0.3
"0.05
0.015
"0.35
"0.005
51.94
12.153
"0.94
0.29
0.009
51.94
5.!
1.!2
0.00
0.000
51.94
49.1
"0.1!
"0.03
"0.003
51.94
!0.90
"0.!
"0.09
0.001
0.0
0.002
.29!
3.1!9
0.09
0.21
0.005
.29!
53.10!
0.2
"0.25
0.00!
.29!
"31.94
"0.1
"0.33
0.009
.29!
"0.91
"1.4!
"0.30
0.022
QCCCQoCCDBQCC
2.09
"13!.59
"0.39 0.04
"0.05
"0.04
0.03
"0.34
"1.2!
?LCCC(m)
?LCCC/QCCC
BQCCC
QCCCCQoCCCDBQCCC
3!.0
2.55
0.0
0.29
3!.99
!.!!
4.23
0.!4
0.29
!.!9
"23.30
"4.4
0.19
0.29
"23.01
"33.30
"2.4
0.09
0.29
"33.01
"0.52
0.9
15.04
1.99
0.13
0.2!
15.29
5.04
2.53
0.50
0.2!
5.30
"9.9!
"0.93
0.09
0.2!
"9.0
"!.!!
"4.23
0.!4
0.2!
"!.!9
"0.!4
1.3!
?LEEE/QEEE
AQEEE
QE QEEEDAQEEE
?LE (m)
?LE /QE
0&0134
3&049
12&492
2&41
0&0135
0.01
3.040
53.41
0.9
0.01
0.020
3.040
"9.243
"1.52
0.019
0.00
3.040
"21.511
"1.3
0.00
0.04
0.059
0.059 0.010
"0.411
129.02
1.2
0.010
0.02
"0.411
9.02
2.52
0.02
0.055
"0.411
"55.45
"3.20
0.05
0.01
"0.411
"53.41
"0.9
0.01
"0.39
0.114
0.110 0.020
"0.553
9.243
1.52
0.019
0.03
"0.553
5.202
4.51
0.09
0.015
"0.553
"5.2!
"0.!
0.015
0.041
"0.553
"13.2!
"5.!9
0.041
"0.52
0.154
0.15 0.05
2.3
55.4!
3.20
0.0!
0.0!0
2.31
44.530
2.4
0.0!4
0.042
2.31
"35.40
"1.40
0.039
0.03
2.31
"5.202
"4.51
0.09
0.12
0.240
0.240
?L/Q
AQ
QE QDAQ
?LE (m)
(?LE/QE)
0.02
23.932
223.932
20.12
0.090
0.03
23.932
139.94
13.!5
0.09
0.030
23.932
"95.!1
"4.1
0.044
0.15
23.932
"1!.0!
"20.9
0.119
.1
0.350
0.30 0.045
"15.9!3
4.03
3.2
0.039
0.041
"15.9!3
34.03
1.00
0.029
0.01
"15.9!3
"115.9!3
"5.95
0.051
0.013
"15.9!3
"139.94
"13.!5
0.09
"15.32
0.21
0.11 0.025
19.549
45.!1
1.0!
0.023
0.041
19.549
!9.549
3.5
0.054
0.0!0
19.549
"30.451
"0.50
0.01!
0.350
19.549
"30.451
"0.1
0.02
3.49
0.120
0.4!
(?LEEE/QEEE)
AQEEE
QE QEEEDAQEEE
?LE (m)
(?LE /QE )
0.014
2.9
252.35
3.4
0.014
0.022
2.9
94.00
2.02
0.021
0.059
2.9
"0.9
"5.09
0.0!3
0.00
2.9
"24.!43
"1.!!
0.00
"1.25
0.105
0.102 0.009
.120
15.55!
1.45
0.009
0.012
.120
5.55!
0.0
0.014
0.010
.120
"41.399
"0.3!
0.009
0.022
.120
"94.00
"2.02
0.021
"0.13
0.053
0.053 0.059
.53
0.9
5.09
0.0!3
0.029
.53
34.199
1.24
0.03!
0.015
.53
"!!.4!
"0.
0.013
0.03!
.53
"1!!.4!
"5.5
0.034
"0.30
0.14
0.139 0.010
0.4!
41.399
0.3!
0.009
0.049
0.4!
4.955
2.42
0.049
0.043
0.4!
"51.045
"2.1
0.043
0.029
0.4!
"34.199
"1.24
0.03!
"0.!4
0.13
0.131
(?LEEE/QEEE)
AQEEE
QE QEEEDAQEEE
?LE (m)
(?LE /QE )
0.002
"1.30
144.942
0.29
0.002
0.010
"1.30
3!.5!1
0.34
0.009
0.004
"1.30
"!3.1!3
"0.25
0.004
0.003
"1.30
"13.05
0.01
"0.40
0.003
"0.03
0.01
0.002
1.11
10.31
0.1
0.002
0.009
1.11
3.31
0.3
0.010
0.003
1.11
"50.9!
"0.1
0.003
0.010
1.11
"3!.5!1
"0.34
0.009
0.03
0.024
0.024 0.009
0.
!2.413
0.!0
0.010
0.000
0.
.90!
0.00
0.000
0.003
0.
"39.145
"0.10
0.003
0.011
0.
"44.145
"0.4
0.011
0.02
0.023
0.023 0.005
"1.19
3.1
0.34
0.005
0.004
"1.19
13.149
0.05
0.004
0.000
"1.19
"12.01
0.00
0.000
0.00!
"1.19
"!5.25!
"0.40
0.00!
"0.02
0.015
0.015 "0.00
"31.44
95.30
"0.55
"0.00!
0.019
"31.44
54.235
0.0
0.013
"0.003
"31.44
1.35
"0.02
"0.001
"0.014
"31.44
30.53!
"0.24
"0.00
"0.12
"0.002
"0.00! 0.003
21.5
!0.20!
0.23
0.004
0.005
21.5
4.955
0.52
0.00
0.005
21.5
"9.945
"0.02
0.002
0.01
21.5
"2.!0
"0.20
0.00
0.53
0.020
0.031
?LCCCC(m)
?LCCCC/QCCCC
BQCCCC
QCCCCCQoCCCCDBQCCCC
?LCCCCC(m)
2.59
0.0
0.1
3.1!
2.!1
4.2
0.!4
0.1
!.3
4.32
"4.3
0.19
0.1
"22.4
"4.31
"2.0
0.0
0.1
"32.4
"2.
"0.31
0.9
"0.15
2.05
0.13
0.13
15.42
2.0
2.
0.52
0.13
5.43
2.90
"0.
0.09
0.13
"9.5
"0.!
"4.2
0.!4
0.13
"!.3
"4.32
"0.32
1.39
"0.19
AQE
Q QE DAQE
?L (m)
?L /Q
AQ
"0&319
12&12
2&40
0&013!
1&15!
"0.352
51.23
0.91
0.01
1.15
"0.352
"1.40
"1.!0
0.020
1.15
"0.352
"21.!4
"1.3
0.00
1.15
"0.13
0.059
1.2
130.900
1.30
0.010
"0.13
1.2
90.900
2.!2
0.029
"0.13
1.2
"53.349
"2.9
0.05!
"0.13
1.2
"51.23
"0.91
0.01
"0.13
0.04
0.112
1.11
1.40
1.!0
0.020
"0.200
1.11
59.295
4.2
0.01
"0.200
1.11
"5!.45
"0.1
0.014
"0.200
1.11
"13!.45
"5.55
0.041
"0.200
0.0!
0.15!
"0.2
53.35
2.9
0.0!
1.04
"0.21
44.24
2.1
0.0!3
1.03!
"0.21
"35.52
"1.42
0.040
1.03!
"0.21
"59.295
"4.2
0.01
1.03!
"0.4!
0.240
AQE
QEE QEDAQE
?LEE (m)
(?LEE/QEE)
AQEE
"13.4!9
210.4!3
1.94
0.05
.030
"13.4!9
.312
5.3
0.0!!
.030
"13.4!9
"93.394
"3.99
0.043
.030
"13.4!9
"19.53
"23.94
0.12!
.030
"4.1!
0.320
3.114
122.151
!.5!
0.054
"4.20
3.114
2.151
4.01
0.05!
"4.20
3.114
".49
"2.5
0.03
"4.20
3.114
".312
"5.3
0.0!!
"4.20
1.9
0.212
"15.!92
43.394
0.9
0.022
"1.95
"15.!92
53.5
2.33
0.043
"1.95
"15.!92
"4!.143
"1.0
0.023
"1.95
"15.!92
"4!.143
"1.5
0.03
"1.95
0.4!
0.12
AQE
Q QE DAQE
?L (m)
(?L /Q )
AQ
!.43
25.94
3.!4
0.014
1.01
!.43
99.942
2.23
0.022
1.01
!.43
"5.44
"4.4
0.059
1.01
!.43
"241.20!
"1.5
0.00
1.01
"0.19
0.102
1.29!
15.52
1.4
0.009
2.952
1.29!
5.52
0.4
0.014
2.952
1.29!
"42.!25
"0.3
0.009
2.952
1.29!
"99.942
"2.23
0.022
2.952
"0.30
0.055
1.114
5.44
4.4
0.059
3.434
1.114
32.91
1.15
0.035
3.434
1.114
"!5.32
"0.!
0.013
3.434
1.114
"1!5.32
"5.!
0.034
3.434
"0.90
0.142
2.522
42.!25
0.3
0.009
0.33
2.522
51.4
2.!5
0.051
0.33
2.522
"4.523
"1.9
0.041
0.33
2.522
"32.91
"1.15
0.035
0.33
"0.10
0.13!
AQE
Q QE DAQE
?L (m)
(?L /Q )
AQ
0.!
145.!99
0.29
0.002
"0.4
0.!
3.99
0.3!
0.009
"0.4
0.!
"!1.!4
"0.24
0.004
"0.4
0.!
"13.301
"0.39
0.003
0.02
0.01
"0.4
"0.!
10.01
0.1
0.002
0.40
"0.!
3.01
0.35
0.009
0.40
"0.!
"52.34!
"0.1
0.003
0.40
"0.!
"3.99
"0.3!
0.009
0.40
"0.02
0.024
"0.54
!1.114
0.5
0.009
0.32
"0.54
!.!!
0.00
0.000
0.32
"0.54
"39.!
"0.11
0.003
0.32
"0.54
"44.!
"0.49
0.011
0.32
"0.01
0.023
0.0
5.09!
0.35
0.005
"0.43
0.0
13.4!
0.0!
0.004
"0.43
0.0
"12.104
0.00
0.000
"0.43
0.0
"!4.01
"0.39
0.00!
"0.43
0.01
0.015
"29.3
!!.!3
"0.2
"0.004
21.9
"29.3
24.501
0.1!
0.00
21.9
"29.3
"11.999
"0.01
0.001
21.9
"29.3
0.105
0.00
0.000
21.9
"0.13
0.003
"14.3!
45.149
0.14
0.003
"10.90
"14.3!
!0.595
0.35
0.00!
"10.90
"14.3!
"24.305
"0.10
0.004
"10.90
"14.3!
"12.30!
"0.04
0.004
"10.90
0.34
0.01
?LCCCCC/QCCCCC
BQCCCCC
QCCCCCCQoCCCCCDBQCCCCC
?LCCCCCC(m)
?LCCCCCC/QCCCCCC
0.0
0.0
3.25
2.!2
0.0
0.!4
0.0
!.3
4.32
0.!4
0.19
0.0
"22.!
"4.2
0.19
0.0
0.0
"32.!
"2.!
0.0
"0.10
0.9
0.9
0.14
0.0
15.49
2.10
0.14
0.53
0.0
5.51
2.9
0.54
0.09
0.0
"9.49
"0.5
0.09
0.!4
0.0
"!.3
"4.32
0.!4
"0.09
1.41
1.40
Q E Q DAQ
?L E (m)
?L E/Q E
AQ E
Q EE Q EDAQ E
13&32
2&43
0&013
"0&121
13&20
52.59
0.95
0.01
"0.129
51.52
"0.04
"1.55
0.019
"0.129
"0.!3
"21!.05
"1.1
0.00
"0.129
"21!.34
0.01
0.0!0
130.1!
1.30
0.010
0.!9
131.413
90.1!
2.!1
0.029
0.!9
91.413
"54.5!
"3.10
0.05
0.!9
"53.!1
"52.59
"0.95
0.01
0.!9
"51.52
"0.15
0.114
0.04
1.55
0.019
0.!!
0.!3
5.059
4.!4
0.00
0.!!
5.55
"5!.!5
"0.2
0.014
0.!!
"55.91
"13!.!5
"5.5
0.041
0.!!
"135.91
"0.20
0.155
54.5
3.10
0.0!
"0.11
53.!
45.24
2.93
0.0!5
"0.110
45.14
"34.1!
"1.34
0.039
"0.110
"34.2!
"5.059
"4.!4
0.00
"0.110
"5.55
0.05
0.240
You're Reading a Preview Unlock full access with a free trial.
Download With Free Trial
Q E Q DAQ
?L E (m)
(?L E/Q E)
AQ E
Q EE Q EDAQ E
259.12
3.!
0.014
2.!20
2!2.431
9.00
2.15
0.022
2.!20
100.152
".90
"4.5
0.0!1
2.!20
"5.51
"240.1
"1.5
0.00
2.!20
"23.5!9
"0.50
0.104
1!1.04
1.53
0.009
0.45
1!2.29
!1.04
0.92
0.015
0.45
!2.29
"40.055
"0.34
0.009
0.45
"40.!!!
"9.00
"2.15
0.022
0.45
"100.152
"0.05
0.055
.90
4.5
0.0!1
0.41
5.51
35.42
1.3!
0.03
0.41
35.23
"!2.299
"0.
0.012
0.41
"!1.1
"1!2.299
"5.4!
0.034
0.41
"1!1.1
"0.13
0.145
40.055
0.34
0.009
1.0!
40.!!!
51.59
2.!9
0.052
1.0!
52.94!
"4.141
"1.95
0.041
1.0!
"4.054
"35.42
"1.3!
0.03
1.0!
"35.23
"0.2
0.139
Q E Q DAQ
?L E (m)
(?L E/Q E)
AQ E
Q EE Q EDAQ E
145.229
0.29
0.002
0.2
145.502
3.130
0.34
0.009
0.2
3.!51
"!2.!51
"0.25
0.004
0.2
"!2.11
"13.1
"0.39
0.003
0.2
"13.49
"0.01
0.01
10.099
0.1
0.002
"0.25
10.52
3.099
0.3!
0.009
"0.25
3.52
"51.513
"0.1
0.003
"0.25
"52.013
"3.130
"0.34
0.009
"0.25
"3.!51
0.01
0.024
!1.901
0.59
0.010
"0.20
!1.431
.41
0.00
0.000
"0.20
!.9!9
"39.30
"0.11
0.003
"0.20
"39.5!
"44.30
"0.4
0.011
"0.20
"44.5!
0.01
0.023
4.2!3
0.34
0.005
0.25
4.!3
13.412
0.05
0.004
0.25
13.!!4
"12.53
0.00
0.000
0.25
"12.2!
"!4.!
"0.40
0.00!
0.25
"!4.319
"0.01
0.015
.29
"0.4
"0.005
"50.!5
3.3
4!.4!9
0.52
0.011
"50.!5
"4.1
9.9!9
"0.01
"0.001
"50.!5
"40.!
22.50
"0.14
"0.00!
"50.!5
"2.392
"0.09
"0.001
34.!9
0.0
0.002
.41
42.39
49.!91
0.24
0.005
.41
5.104
"35.209
"0.21
0.00!
.41
"2!.9!
"45.1
"0.50
0.011
.41
13.2
"0.3
0.024
BQCCCCCC
QCCCCCCCQoCCCCCCDBQCCCCCC 0.05
3.30
0.05
!.5
0.05
"22.1
0.05
"32.1
0.03
15.53
0.03
5.54
0.03
"9.4!
0.03
"!.5
You're Reading a Preview Unlock full access with a free trial.
Download With Free Trial
You're Reading a Preview Unlock full access with a free trial.
Download With Free Trial
?L EE (m)
(?L EE/Q EE)
AQ EE
Q EEE Q EEDAQ EE
?L EEE (m)
(?L EEE/Q EEE)
3.4
0.014
0.39
2!2.29
3.5
0.014
2.24
0.022
0.39
99.33
2.20
0.022
"4.51
0.0!0
0.39
"!.49
"4.!2
0.0!0
"1.53
0.00!
0.39
"23.11
"1.53
0.00!
"0.0
0.103
"0.20
0.103
1.54
0.009
1.213
1!3.492
1.5!
0.010
0.93
0.015
1.213
!3.492
0.9!
0.015
"0.35
0.009
1.213
"39.!14
"0.34
0.00
"2.24
0.022
1.213
"99.33
"2.20
0.022
"0.12
0.055
"0.02
0.055
4.51
0.0!0
1.39!
!.49
4.!2
0.0!0
1.31
0.03
1.39!
3!.41
1.40
0.03
"0.!
0.012
1.39!
"!0.422
"0.3
0.012
"5.43
0.034
1.39!
"1!0.422
"5.35
0.033
"0.3
0.143
"0.05
0.144
0.35
0.009
0.1!1
39.!14
0.34
0.00
2.9
0.053
0.1!1
53.10
2.1
0.053
"1.
0.040
0.1!1
"4!.93
"1.!
0.040
"1.31
0.03
0.1!1
"3!.41
"1.40
0.03
"0.04
0.13
"0.12
0.139
You're Reading a Preview Unlock full access with a free trial.
Download With Free Trial
"0.39
0.003
"0.1
0.01
0.01
0.1
0.002
0.14
0.3!
0.009
"0.1
"13.!!
"0.39
0.003
0.00
0.01
10.995
0.1
0.002
0.14
3.995
0.3!
0.009
0.003
0.14
"51.12
"0.1
0.003
"0.35
0.009
0.14
"3.33
"0.35
0.009
"0.01
0.024
0.00
0.024
0.5
0.009
0.11
!1.1!
0.59
0.010
0.00
0.000
0.11
.241
0.00
0.000
"0.11
0.003
0.11
"39.452
"0.11
0.003
"0.4
0.011
0.11
"44.452
"0.4
0.011
0.00
0.023
0.00
0.023
0.35
0.005
"0.1!
4.4!2
0.34
0.005
0.05
0.004
"0.1!
13.50
0.05
0.004
0.00
0.000
"0.1!
"12.443
0.00
0.000
"0.39
0.00!
"0.1!
"!4.591
"0.40
0.00!
0.00
0.015
0.00
0.015
"0.10
"0.003
3!.!!
4.3
"0.34
"0.005
0.01
"0.001
3!.!!
32.4!
0.2
0.00
"0.11
0.003
3!.!!
"4.014
0.00
0.000
"0.21
0.00
3!.!!
.429
"0.02
"0.003
"0.41
0.00!
"0.10
0.001
0.12
0.003
"15.0
2.201
0.05
0.002
0.33
0.00!
"15.0
42.30
0.1
0.004
"0.13
0.005
"15.0
"42.592
"0.30
0.00
"0.0!
"0.004
"15.0
"3.5
"0.3
0.010
0.2
0.009
"0.43
0.023
AQ
Q E Q DAQ
?L E (m)
"0.123
21!.09
1.93
"0.123
9.21
!.9
"0.123
"!.19
"3.44
"0.123
"13.291
"22.50 "0.04
0.21
119.42
!.29
0.21
!9.42
3.3
0.21
"0.52
"3.04
0.21
"9.21
"!.9 0.02
0.101
3!.19
0.!9
0.101
52.90
2.2!
0.101
"4.093
"1.12
0.101
"4.093
"1.2 0.00
AQ EEE
QE Q EEEDAQ EEE
?LE (m)2
(?LE /QE )3
AQE 4
Q QE DAQE
1.02
2!3.900
3.
0.014
0.1!0
2!4.0!0
1.02
100.223
2.24
0.022
0.1!0
99.5
1.02
"5.9
"4.53
0.0!0
0.1!0
"!.290
1.02
"23!.100
"1.52
0.00!
0.1!0
"235.940
"0.03
0.103
0.15
1!3.!
1.5!
0.010
0.49
1!4.15
0.15
!3.!
0.9
0.015
0.49
!4.15
0.15
"39.2
"0.34
0.009
0.49
"39.451
0.15
"100.223
"2.24
0.022
0.49
"99.5
"0.05
0.05!
0.201
5.9
4.53
0.0!0
0.50
!.290
0.201
3!.220
1.3
0.03
0.50
3!.23
0.201
"!0.220
"0.3
0.012
0.50
"59.!50
0.201
"1!0.220
"5.34
0.033
0.50
"159.!50
"0.15
0.143
0.453
39.2
0.34
0.009
0.0!
39.451
0.453
53.5!0
2.5
0.053
0.0!
53.!2
0.453
"4!.440
"1.3
0.039
0.0!
"4!.33
0.453
"3!.220
"1.3
0.03
0.0!
"3!.23
"0.02
0.139
You're Reading a Preview Unlock full access with a free trial.
Download With Free Trial
You're Reading a Preview Unlock full access with a free trial.
Download With Free Trial
You're Reading a Preview Unlock full access with a free trial.
Download With Free Trial
?L (m)5
(?LE /QE )!
AQE
Q QE DAQE
?L (m)9
0.29
0.002
0.04
145.405
0.1
0.35
0.009
0.04
3.49
0.01
"0.25
0.004
0.04
"!2.33
"0.04
