I
nd
o
ne
s
ia
n J
o
urna
l o
f
E
lect
rica
l En
g
ineering
a
nd
Co
m
pu
t
er
Science
Vo
l.
23
,
No
.
2
,
A
u
g
u
s
t
2
0
2
1
,
p
p
.
1
1
1
0
~
1
1
1
9
I
SS
N:
2
5
0
2
-
4
7
5
2
,
DOI
: 1
0
.
1
1
5
9
1
/ijeecs.v
23
.i
2
.
pp
1
1
1
0
-
1
1
1
9
1110
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ee
cs.ia
esco
r
e.
co
m
Numerica
l inves
ti
g
a
tion o
n t
he b
eh
a
v
io
r of combin
in
g
open
-
cha
nnel f
lo
w
No
r
Azni
Sh
a
ha
ri
1
,
No
r
Arif
H
us
a
ini
No
rwa
za
2
,
I
s
k
a
nd
a
r
Sh
a
h M
o
hd
Z
a
wa
wi
3
,
Nuris
ha
A
drina
M
o
h
d K
a
ma
rul
4
,
Aim
i Sa
id
5
1,
2,
4,
5
F
a
c
u
lt
y
o
f
Co
m
p
u
ter an
d
M
a
th
e
m
a
ti
c
a
l
S
c
ien
c
e
s Un
iv
e
rsiti
Te
k
n
o
lo
g
i
M
ARA
,
Ca
wa
n
g
a
n
Ne
g
e
ri
S
e
m
b
il
a
n
,
Ka
m
p
u
s
S
e
re
m
b
a
n
,
M
a
lay
sia
3
F
a
c
u
lt
y
o
f
C
o
m
p
u
ter a
n
d
M
a
th
e
m
a
ti
c
a
l
S
c
ien
c
e
s,
Ko
m
p
lek
s Al
-
Kh
a
wa
rizm
i,
Un
iv
e
rsiti
Te
k
n
o
lo
g
i
M
ARA
,
S
h
a
h
Ala
m
,
S
e
lan
g
o
r
,
M
a
lay
sia
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
No
v
3
0
,
2
0
2
0
R
ev
is
ed
J
u
l 7
,
2
0
2
1
Acc
ep
ted
J
u
l 1
4
,
2
0
2
1
Op
e
n
-
c
h
a
n
n
e
l
flo
w
is
k
n
o
wn
a
s
f
l
u
id
flo
w
with
a
n
o
p
e
n
a
tmo
sp
h
e
ri
c
su
rfa
c
e
.
It
h
a
s
b
e
c
o
m
e
a
n
im
p
o
rta
n
t
iss
u
e
e
sp
e
c
ially
wh
e
n
m
e
a
su
rin
g
t
h
e
flo
w
ra
te
a
n
d
d
e
p
t
h
o
f
wa
ter
a
s
p
a
rt
o
f
e
n
v
ir
o
n
m
e
n
tal
m
a
n
a
g
e
m
e
n
t
sc
h
e
m
e
s.
M
a
n
y
e
ffo
rts
h
a
v
e
b
e
e
n
m
a
d
e
b
y
t
h
e
p
re
v
i
o
u
s
re
se
a
rc
h
e
rs
to
in
v
e
stig
a
te
t
h
e
b
e
h
a
v
i
o
r
o
f
wa
ter
flo
w.
Ho
we
v
e
r,
m
o
st
stu
d
ies
o
n
wa
ter
flo
w
h
a
v
e
o
n
l
y
b
e
e
n
c
a
rried
o
u
t
in
a
stra
ig
h
t
p
rism
a
ti
c
m
a
in
c
h
a
n
n
e
l,
e
it
h
e
r
in
a
trap
e
z
o
id
a
l
a
n
d
re
c
tan
g
u
lar
t
y
p
e
o
f
c
h
a
n
n
e
l
se
c
ti
o
n
with
late
ra
l
b
ra
n
c
h
o
f
a
n
g
le
o
f
9
0
o
.
In
th
is
stu
d
y
,
t
h
e
g
e
n
e
ra
l
e
q
u
a
ti
o
n
s
o
f
c
o
m
b
in
i
n
g
o
p
e
n
-
c
h
a
n
n
e
l
fl
o
w
fo
r
trap
e
z
o
id
a
l
a
n
d
V
-
sh
a
p
e
d
c
h
a
n
n
e
ls
a
re
m
o
d
ifi
e
d
in
th
e
f
o
rm
o
f
n
o
n
li
n
e
a
r
p
o
ly
n
o
m
ial
e
q
u
a
ti
o
n
s.
Th
e
p
r
o
p
o
se
d
e
q
u
a
ti
o
n
s
a
re
so
lv
e
d
u
sin
g
Ne
wto
n
-
Ra
p
h
s
o
n
p
ro
c
e
d
u
re
to
d
e
term
in
e
th
e
u
p
str
e
a
m
flo
w
d
e
p
th
.
All
th
e
c
o
m
p
u
t
a
ti
o
n
s
a
n
d
a
n
a
ly
sis
o
f
t
h
e
b
e
h
a
v
i
o
r
o
f
wa
ter
flo
w
d
e
p
th
i
n
flu
e
n
c
e
d
b
y
F
ro
u
d
e
n
u
m
b
e
r
a
n
d
flo
w
ra
te
ra
ti
o
a
re
p
e
rfo
rm
e
d
u
si
n
g
g
ra
p
h
ica
l
u
se
r
in
terfa
c
e
,
wh
ich
is
d
e
sig
n
e
d
i
n
M
ATLAB
so
f
twa
re
.
Co
m
p
a
ra
ti
v
e
a
n
a
ly
sis
sh
o
ws
th
a
t
th
e
m
o
d
ifi
e
d
e
q
u
a
ti
o
n
s
a
g
re
e
we
ll
w
it
h
th
e
e
x
p
e
rime
n
tal
d
a
ta
a
s
re
p
o
rted
i
n
th
e
li
tera
tu
re
.
T
h
e
trap
e
z
o
i
d
a
l
c
h
a
n
n
e
l
d
e
m
o
n
stra
tes
t
h
e
h
i
g
h
e
st
v
a
lu
e
o
f
f
l
o
w
d
e
p
th
a
s
t
h
e
F
ro
u
d
e
n
u
m
b
e
r
a
n
d
f
lo
w
ra
te
ra
ti
o
in
c
re
a
se
;
th
u
s
,
it
h
a
s
p
o
ten
t
ial
to
a
v
o
id
wa
ter o
v
e
rfl
o
w.
K
ey
w
o
r
d
s
:
C
h
an
n
el
ju
n
ctio
n
Mo
m
en
tu
m
p
r
in
cip
le
Nu
m
er
ical
m
eth
o
d
V
-
s
h
ap
ed
c
h
an
n
el
W
ater
f
lo
w
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
No
r
Azn
i Sh
ah
ar
i
Facu
lty
o
f
C
o
m
p
u
ter
an
d
Ma
th
em
atica
l Scie
n
ce
s
Un
iv
er
s
iti T
ek
n
o
lo
g
i M
AR
A
(
UiT
M)
C
awa
n
g
an
Neg
er
i Sem
b
ilan
,
Kam
p
u
s
Ser
em
b
an
E
m
ail:
n
o
r
az
n
i@
u
itm
.
ed
u
.
m
y
1.
I
NT
RO
D
UCT
I
O
N
W
ater
f
lo
w
is
a
m
ajo
r
n
atu
r
al
elem
en
t
th
at
af
f
ec
ts
o
u
r
p
o
p
u
latio
n
s
,
co
m
m
u
n
ities
,
an
d
ec
o
s
y
s
tem
s
.
T
h
e
h
y
d
r
a
u
lic
b
e
h
av
io
r
o
f
o
p
en
-
ch
a
n
n
el
f
lo
w
d
e
p
en
d
s
o
n
th
e
s
y
s
tem
e
n
v
ir
o
n
m
en
ts
s
u
ch
as
th
e
s
tr
u
ctu
r
e
elem
en
ts
o
f
th
e
ch
an
n
el
an
d
f
l
o
w
co
n
d
itio
n
,
wh
ich
ca
n
b
e
d
i
v
id
ed
in
to
t
h
r
ee
ty
p
es:
cr
itical
f
lo
w,
s
u
p
er
cr
itical
f
lo
w
an
d
s
u
b
cr
itical
f
lo
w
[
1
]
.
On
e
o
f
th
e
m
o
s
t
im
p
o
r
tan
t
s
tr
u
ctu
r
al
elem
en
ts
o
f
th
e
s
y
s
tem
th
at
ca
n
b
e
co
n
s
id
er
ed
is
th
e
t
y
p
e
o
f
ch
a
n
n
el’
s
ju
n
ctio
n
.
T
h
e
f
l
o
w
b
e
h
a
v
e
s
d
i
f
f
e
r
e
n
t
l
y
at
t
h
e
c
h
a
n
n
e
l
j
u
n
c
t
i
o
n
d
u
e
t
o
m
a
n
y
c
o
m
p
l
e
x
p
a
r
a
m
e
t
e
r
s
a
n
d
v
a
r
i
ab
l
e
s
t
h
a
t
m
u
s
t
b
e
c
o
n
s
i
d
e
r
e
d
.
T
h
e
e
s
t
i
m
at
e
d
i
n
c
r
e
a
s
e
i
n
t
h
e
u
p
s
t
r
e
a
m
f
l
o
w
d
e
p
t
h
a
s
a
r
e
s
u
l
t
o
f
l
a
t
e
r
al
f
l
o
w
i
s
o
n
e
o
f
t
h
e
i
m
p
o
r
t
a
n
t
p
a
r
a
m
e
t
e
r
s
i
n
t
h
e
c
h
a
n
n
e
l
j
u
n
c
t
i
o
n
f
l
o
w
[
2
]
.
T
h
e
c
h
a
n
n
e
l
j
u
n
c
t
i
o
n
c
a
n
b
e
e
it
h
e
r
a
c
o
m
b
in
i
n
g
c
h
a
n
n
e
l
j
u
n
c
t
i
o
n
[2
]
-
[
6]
o
r
a
d
i
v
i
d
i
n
g
c
h
a
n
n
e
l
j
u
n
c
ti
o
n
[
1
]
,
[7
]
-
[
14]
.
T
h
e
r
e
ar
e
m
an
y
ty
p
es
o
f
c
h
an
n
el
s
ec
tio
n
s
th
at
ca
n
b
e
u
s
ed
f
o
r
th
e
in
v
esti
g
atio
n
o
f
o
p
en
c
h
an
n
el
f
lo
w
s
y
s
tem
s
.
T
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
N
u
merica
l in
ve
s
tig
a
tio
n
o
n
th
e
b
eh
a
vio
r
o
f c
o
mb
in
in
g
o
p
e
n
-
ch
a
n
n
el
flo
w
(
N
o
r
A
z
n
i S
h
a
h
a
r
i
)
1111
m
o
s
t
co
m
m
o
n
ch
a
n
n
el
s
ec
tio
n
s
o
f
o
p
en
c
h
an
n
els
in
clu
d
e
t
h
o
s
e
th
at
ar
e
tr
ap
ez
o
id
al,
r
ec
t
an
g
u
lar
,
tr
ian
g
u
lar
,
V
-
s
h
ap
ed
,
an
d
s
em
i
-
cir
cu
lar
.
T
h
e
th
eo
r
y
o
f
m
o
m
e
n
tu
m
p
r
in
cip
le
a
n
d
m
ass
co
n
tin
u
i
ty
eq
u
atio
n
h
as
b
ee
n
ap
p
lied
to
th
e
d
ev
elo
p
m
e
n
t
o
f
th
e
b
e
h
av
io
r
o
f
wate
r
f
lo
w
to
esti
m
ate
t
h
e
ch
an
n
el
ju
n
ctio
n
’
s
u
p
s
tr
ea
m
an
d
d
o
wn
s
tr
ea
m
d
ep
th
r
atio
.
Acc
o
r
d
i
n
g
to
[
2
]
u
s
ed
th
e
m
o
m
en
tu
m
p
r
in
cip
le
eq
u
atio
n
a
n
d
f
o
u
n
d
th
at
t
h
e
i
n
cr
ea
s
e
in
th
e
f
l
o
w
d
ep
th
ca
n
b
e
p
r
ed
icted
wh
en
th
er
e
ar
e
u
n
d
is
tu
r
b
ed
f
lo
w
co
n
d
itio
n
s
in
th
e
c
h
an
n
els.
M
o
s
t
o
f
t
h
e
e
q
u
atio
n
s
o
f
r
ig
h
t
-
an
g
led
an
d
s
h
o
r
t
b
r
a
n
ch
ch
an
n
els
with
eq
u
al
wid
th
h
av
e
b
ee
n
d
e
v
elo
p
e
d
u
s
in
g
m
a
s
s
,
m
o
m
en
tu
m
an
d
en
er
g
y
co
n
s
er
v
atio
n
to
d
eter
m
in
e
th
e
u
p
s
tr
ea
m
d
e
p
th
at
t
h
e
ju
n
ctio
n
[
1
0
]
,
[
1
5
]
,
[
1
6
]
.
In
[
1
7
]
ap
p
lied
t
h
e
m
o
m
en
tu
m
p
r
in
cip
le
an
d
m
as
s
co
n
tin
u
ity
,
d
is
tin
ct
f
r
o
m
th
e
p
r
ev
io
u
s
s
tu
d
y
,
i.e
with
o
u
t
ass
u
m
in
g
eq
u
ality
o
f
th
e
u
p
s
tr
ea
m
d
ep
th
an
d
wid
th
.
T
h
eir
m
o
d
el
p
io
n
ee
r
e
d
th
e
d
e
v
elo
p
m
en
t o
f
a
g
en
er
al
n
o
n
lin
ea
r
m
o
d
el
b
ased
o
n
th
e
th
eo
r
y
o
f
m
o
m
en
t
u
m
wit
h
m
o
r
e
p
h
y
s
ical
ef
f
e
cts
s
u
ch
as
b
o
u
n
d
a
r
y
f
r
ictio
n
f
o
r
ce
s
an
d
n
o
n
-
r
ig
h
t
-
a
n
g
le
ju
n
ctio
n
.
R
ash
wan
[
9
]
v
er
if
ied
t
h
e
m
o
d
el
o
f
t
wo
c
o
n
tr
o
l
v
o
lu
m
es
u
s
in
g
th
e
ap
p
r
o
ac
h
o
f
s
h
o
wn
in
[
1
7
]
an
aly
tically
f
o
r
s
u
b
cr
itical
d
i
v
id
in
g
s
tead
y
f
lo
w.
Fu
r
t
h
er
m
o
r
e,
[
1
8
]
p
r
esen
ted
a
c
o
m
p
a
r
is
o
n
with
th
e
1
D
d
y
n
am
ic
m
o
d
el
p
r
o
p
o
s
ed
b
y
[
1
7
]
with
th
e
2
D
m
o
d
el,
wh
ile
[
1
9
]
m
a
d
e
a
co
m
p
ar
is
o
n
with
t
h
e
3
D
m
o
d
el.
Mo
s
t
o
f
th
e
b
r
an
c
h
in
g
ch
a
n
n
el
f
lo
w
s
tu
d
ies
h
av
e
b
ee
n
co
n
d
u
cte
d
with
a
r
ig
id
b
o
u
n
d
ar
y
a
n
d
90
o
b
r
an
c
h
in
g
an
g
le.
No
r
m
ally
,
th
e
s
tu
d
y
o
n
ch
a
n
n
el
ju
n
ctio
n
in
v
o
l
v
es
a
m
ai
n
ch
an
n
el
th
at
is
a
s
tr
aig
h
t
p
r
is
m
atic
ch
an
n
el
with
9
0
o
o
r
n
o
t
9
0
o
b
r
a
n
ch
in
g
an
g
le.
Ho
w
ev
er
,
[
1
6
]
-
[
1
9
]
d
er
iv
e
d
a
m
o
d
el
with
d
if
f
er
e
n
t
b
r
an
ch
i
n
g
ju
n
ctio
n
an
g
les
.
Ho
wev
er
,
th
e
c
h
an
n
els o
f
n
atu
r
al
allu
v
ial
r
iv
er
s
ar
e
u
s
u
ally
n
o
n
p
r
is
m
atic
an
d
o
f
ten
cu
r
v
ed
[
2
0
]
.
Mo
s
t
o
f
th
e
s
tu
d
ies
ar
e
f
o
cu
s
ed
o
n
ce
r
tain
ty
p
es
o
f
c
r
o
s
s
-
s
ec
tio
n
al
s
h
ap
e
an
d
b
r
an
ch
in
g
an
g
le.
Fo
r
in
s
tan
ce
,
in
[
2
1
]
elab
o
r
ated
o
n
th
e
in
f
l
u
en
ce
o
f
th
e
c
r
o
s
s
-
s
ec
tio
n
al
s
h
ap
e
(
s
em
i
cir
cu
l
ar
,
r
ec
tan
g
u
lar
an
d
tr
ap
ez
o
id
al)
o
f
th
e
s
ep
ar
atio
n
zo
n
e
in
a
9
0
°
ju
n
c
tio
n
u
s
in
g
lar
g
e
-
e
d
d
y
s
im
u
latio
n
m
o
d
els
to
s
im
u
late
th
e
co
m
p
lex
tu
r
b
u
len
t
f
lo
w.
Pan
d
ey
an
d
Mish
r
a
[
2
2
]
ap
p
lie
d
th
e
m
o
m
en
tu
m
p
r
in
cip
le
e
q
u
atio
n
to
b
u
ild
a
m
ath
em
atica
l
m
o
d
el
o
f
th
e
b
eh
av
io
r
o
f
wate
r
f
l
o
w
f
o
r
tr
ap
ez
o
id
al
a
n
d
r
ec
tan
g
u
lar
cr
o
s
s
-
s
ec
tio
n
al
s
h
ap
e
ch
an
n
el
j
u
n
ctio
n
p
r
o
b
lem
s
wit
h
3
0
o
an
d
9
0
o
b
r
an
ch
i
n
g
a
n
g
le
s
.
T
h
ey
f
o
u
n
d
o
u
t
th
at,
in
o
r
d
er
to
p
ass
th
e
s
am
e
wate
r
d
is
ch
ar
g
e
v
alu
e
with
th
e
s
am
e
b
o
tto
m
wid
th
an
d
f
lo
w
d
ep
th
th
r
o
u
g
h
th
e
m
ain
c
h
a
n
n
el,
th
e
d
e
p
th
r
atio
f
o
r
a
r
ec
ta
n
g
u
lar
ch
an
n
el
wo
u
l
d
b
e
h
i
g
h
er
th
a
n
th
at
o
f
th
e
tr
a
p
ez
o
id
al
ch
a
n
n
el.
I
n
r
ec
en
t
y
e
ar
s
,
Mo
h
d
Z
awa
wi
et
a
l.
[
2
3
]
im
p
r
o
v
ed
t
h
e
g
e
n
er
al
eq
u
atio
n
o
f
d
iv
id
in
g
o
p
en
-
ch
an
n
el
f
lo
w
f
r
o
m
[
2
2
]
to
in
v
esti
g
ate
th
e
am
o
u
n
t
o
f
r
iv
er
f
lo
w
r
ate
at
d
if
f
er
e
n
t
b
if
u
r
ca
tio
n
an
g
les.
Ho
wev
er
,
m
o
s
t
ex
is
tin
g
g
en
er
al
eq
u
atio
n
s
o
f
o
p
e
n
-
ch
a
n
n
el
f
lo
w
with
v
ar
io
u
s
p
ar
am
eter
s
ar
e
co
m
p
licated
to
b
e
s
o
lv
ed
.
I
n
o
r
d
er
to
d
eter
m
in
e
th
e
f
lo
w
d
ep
th
,
it
is
ess
en
ti
al
to
d
ev
elo
p
a
s
im
p
lifie
d
v
er
s
io
n
o
f
f
lo
w
eq
u
atio
n
s
th
at
ca
n
b
e
s
o
lv
ed
n
u
m
er
ically
.
T
h
er
e
f
o
r
e,
th
e
ai
m
o
f
th
is
s
tu
d
y
is
to
d
e
r
iv
e
t
h
e
eq
u
atio
n
s
o
f
co
m
b
in
in
g
f
l
o
w
f
o
r
t
r
ap
ez
o
id
al
an
d
V
-
s
h
ap
e
ch
an
n
els
in
th
e
f
o
r
m
o
f
p
o
ly
n
o
m
ial
eq
u
atio
n
s
with
d
eg
r
ee
5
an
d
s
o
lv
e
it
u
s
i
n
g
New
to
n
-
R
ap
h
s
o
n
p
r
o
ce
d
u
r
e
[
2
4
]
,
[
2
5
]
.
T
h
e
ef
f
ec
ts
o
f
Fro
u
d
e
n
u
m
b
er
a
n
d
f
lo
w
r
ate
r
atio
o
n
f
lo
w
d
ep
th
f
o
r
b
o
th
ty
p
es
o
f
ch
a
n
n
els
ar
e
in
v
esti
g
ated
.
Fu
r
th
er
d
is
cu
s
s
io
n
s
o
n
f
o
r
m
u
latio
n
a
n
d
im
p
lem
en
tatio
n
ar
e
p
r
esen
ted
in
th
e
n
ex
t
s
ec
tio
n
s
.
2.
M
AT
H
E
M
AT
I
CA
L
F
O
RM
UL
A
T
I
O
NS
T
h
is
s
ec
tio
n
d
escr
ib
es
th
e
m
ath
em
atica
l
f
o
r
m
u
latio
n
an
d
t
h
eo
r
etica
l
s
tu
d
y
o
n
th
e
b
eh
a
v
io
r
o
f
th
e
co
m
b
in
in
g
f
lo
w
i
n
tr
ap
ez
o
id
a
l
an
d
V
-
s
h
a
p
ed
c
h
an
n
els.
T
h
e
co
m
b
in
i
n
g
ju
n
ctio
n
allo
ws
th
e
wate
r
f
lo
w
f
r
o
m
two
b
r
an
ch
c
h
an
n
els
t
o
a
s
in
g
l
e
m
ain
ch
an
n
el.
T
h
e
b
eh
av
io
r
o
f
c
o
m
b
in
in
g
f
lo
w
is
d
ete
r
m
in
ed
b
y
a
p
p
ly
in
g
th
e
m
ass
co
n
tin
u
ity
a
n
d
m
o
m
e
n
tu
m
p
r
in
ci
p
le
with
t
h
e
f
o
llo
win
g
ass
u
m
p
tio
n
s
:
th
e
wate
r
f
l
o
w
is
o
n
e
d
im
en
s
io
n
al
an
d
p
ar
allel
to
th
e
ch
a
n
n
el
w
alls
,
v
elo
city
is
u
n
if
o
r
m
ly
d
is
tr
ib
u
ted
im
m
e
d
iately
alo
n
g
t
h
e
ch
an
n
el
b
ef
o
r
e,
in
s
id
e
an
d
af
ter
th
e
ju
n
ctio
n
,
th
e
f
r
ictio
n
o
f
th
e
ch
an
n
el
wall
ac
tin
g
u
p
o
n
th
e
wate
r
f
lo
w
is
d
is
r
eg
ar
d
ed
,
ex
ter
n
al
f
o
r
ce
s
ac
tin
g
u
p
o
n
t
h
e
wate
r
f
lo
w,
i
n
clu
d
in
g
win
d
,
ar
e
d
is
r
eg
ar
d
ed
,
an
d
th
e
f
lo
w
d
ep
th
s
in
b
r
an
ch
ch
an
n
els ar
e
eq
u
al
ju
s
t b
ef
o
r
e
th
e
ju
n
ctio
n
.
T
h
e
s
ch
em
atic
lay
o
u
t
a
n
d
g
eo
m
etr
ic
d
etails
u
s
ed
f
o
r
t
h
is
s
tu
d
y
ar
e
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
e
wate
r
is
ass
u
m
ed
to
f
lo
w
f
r
o
m
th
e
b
r
a
n
ch
c
h
an
n
el
(
ch
a
n
n
el
1
a
n
d
c
h
an
n
el
2
)
to
t
h
e
m
ai
n
c
h
an
n
el
(
ch
a
n
n
el
3
)
,
wh
er
e
q
is
th
e
f
lo
w
r
ate
o
f
th
e
w
ater
f
lo
w,
b
is
th
e
b
o
tto
m
wid
th
o
f
th
e
ch
an
n
el
s
ec
tio
n
,
is
th
e
an
g
le
o
f
th
e
b
r
an
ch
ch
an
n
el
to
th
e
a
x
is
o
f
th
e
m
ain
c
h
an
n
el,
y
is
th
e
f
lo
w
d
ep
th
o
f
th
e
wate
r
f
lo
w,
T
is
t
h
e
to
p
wid
th
o
f
th
e
cr
o
s
s
-
s
ec
tio
n
al
ar
ea
o
f
t
h
e
wate
r
,
z
is
th
e
s
id
e
s
lo
p
e
v
alu
e
o
f
t
h
e
ch
a
n
n
el
a
n
d
is
th
e
s
id
e
s
lo
p
e
an
g
le
o
f
th
e
ch
an
n
el
f
r
o
m
th
e
h
o
r
izo
n
t
al
lin
e.
E
ac
h
p
ar
am
eter
with
s
u
b
s
cr
ip
ts
1
,
2
,
an
d
3
in
d
icate
s
th
e
p
ar
am
eter
th
at
b
elo
n
g
s
to
ch
an
n
el
1
,
ch
an
n
e
l
2
,
an
d
ch
an
n
el
3
,
r
esp
ec
tiv
ely
.
T
h
e
s
u
m
m
ar
y
o
f
th
e
c
h
an
n
els’
co
m
p
o
n
en
t
eq
u
atio
n
s
is
s
h
o
wn
in
T
a
b
le
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
23
,
No
.
2
,
Au
g
u
s
t 2
0
2
1
:
1
1
1
0
-
1
1
1
9
1112
Fig
u
r
e
1
.
Sch
em
atic
la
y
o
u
t o
f
co
m
b
in
in
g
f
lo
w
ju
n
ctio
n
T
ab
le
1
.
C
h
an
n
els’
co
m
p
o
n
en
t
eq
u
atio
n
C
h
a
n
n
e
l
c
o
m
p
o
n
e
n
t
s
Tr
a
p
e
z
o
i
d
a
l
V
-
sh
a
p
e
d
To
p
W
i
d
t
h
(
)
2
T
y
b
z
y
=+
(
)
2
T
y
z
y
=
C
r
o
ss
-
se
c
t
i
o
n
a
l
A
r
e
a
2
()
A
y
b
y
z
y
=+
2
()
A
y
z
y
=
W
e
t
t
e
d
P
e
r
i
met
e
r
(
)
(
)
1
2
2
21
w
P
y
b
y
z
=
+
+
(
)
(
)
1
2
2
21
w
P
y
y
z
=+
H
y
d
r
a
u
l
i
c
R
a
d
i
u
s
(
)
2
1
2
2
2
(
1
z
)
H
b
y
z
y
Ry
by
+
=
++
(
)
1
2
2
2
(
1
z
)
H
zy
Ry
=
+
H
y
d
r
o
st
a
t
i
c
F
o
r
c
e
o
n
t
h
e
H
o
r
i
z
o
n
t
a
l
S
t
r
i
p
(
a
t
a
n
y
se
c
t
i
o
n
)
o
f
t
h
e
C
r
o
ss
-
S
e
c
t
i
o
n
a
l
A
r
e
a
(
)
2
23
b
z
y
P
y
y
=+
(
)
3
3
zy
Py
=
2.
1
.
Sim
pli
f
ied
equa
t
io
n o
f
wa
t
er
f
lo
w
f
o
r
V
-
s
ha
ped
c
ha
nn
el
T
h
e
co
n
tin
u
o
u
s
-
m
o
m
en
tu
m
p
r
in
cip
le
m
o
d
el
b
ased
o
n
ass
u
m
p
tio
n
s
o
f
th
is
s
tu
d
y
is
d
e
f
in
ed
b
y
1
1
−
3
+
=
(
3
3
−
2
2
2
−
1
1
1
)
.
(
1
)
So
lv
e
f
o
r
L
.
H.
S
o
f
(
1
)
,
wh
er
e
3
1
1
3
=
zy
P
,
3
3
3
3
=
zy
P
an
d
P
is
a
d
if
f
er
e
n
ce
b
etwe
en
t
h
e
p
r
ess
u
r
e
f
o
r
ce
at
th
e
ju
n
ctio
n
o
n
th
e
m
ain
ch
an
n
els
an
d
th
e
p
r
ess
u
r
e
f
o
r
ce
r
ig
h
t
b
ef
o
r
e
th
at.
Sin
ce
it
is
ass
u
m
ed
th
at
th
er
e
is
n
o
h
y
d
r
au
lic
ju
m
p
at
th
e
j
u
n
ct
io
n
,
th
en
,
3
(
1
3
−
3
3
)
.
(
2
)
T
ak
in
g
R
.
H.
S o
f
(
1
)
a
n
d
u
s
in
g
th
e
d
ef
in
itio
n
o
f
f
lo
w
r
ate,
th
e
n
(
3
3
3
−
2
2
2
2
−
1
1
1
1
)
=
3
2
3
[
1
−
{
2
2
3
2
(
2
3
)
2
+
1
2
3
2
(
1
3
)
1
}
]
.
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
N
u
merica
l in
ve
s
tig
a
tio
n
o
n
th
e
b
eh
a
vio
r
o
f c
o
mb
in
in
g
o
p
e
n
-
ch
a
n
n
el
flo
w
(
N
o
r
A
z
n
i S
h
a
h
a
r
i
)
1113
T
h
e
Fro
u
d
e
n
u
m
b
er
,
3
o
f
c
h
an
n
el
3
is
d
ef
in
ed
as
3
=
3
3
√
3
3
.
B
y
s
u
b
s
titu
tin
g
3
in
to
(
3
)
,
th
e
f
o
llo
win
g
eq
u
atio
n
s
ar
e
o
b
tain
ed
:
3
2
3
=
3
2
(
3
3
3
2
)
(
3
3
)
=
(
3
2
3
3
3
)
(
3
2
3
)
=
3
2
(
3
2
3
)
=
3
2
(
3
2
)
2
2
3
=
3
2
3
3
2
.
(
4
)
R
ed
u
ce
th
e
co
m
p
le
x
ity
o
f
th
e
eq
u
atio
n
b
y
u
s
in
g
r
atio
v
a
r
iab
l
es.
L
et
1
3
=
an
d
1
3
=
1
2
3
2
=
2
an
d
21
=
yy
g
iv
es
2
3
=
2
2
3
2
=
2
.
Fro
m
th
e
d
ef
in
itio
n
s
o
f
co
n
tin
u
ity
an
d
r
atio
v
ar
ia
b
le,
2
3
=
an
d
,
y
iel
d
s
3
2
3
3
2
[
1
−
1
2
(
2
2
+
(
1
−
)
2
1
)
]
.
(
5
)
T
ak
in
g
(
2
)
eq
u
al
with
(
5
)
,
3
(
1
3
−
3
3
)
=
3
2
3
3
2
[
1
−
1
2
{
2
2
+
(
1
−
)
2
1
}
]
.
(
6
)
T
h
er
ef
o
r
e,
th
e
g
en
er
al
eq
u
atio
n
o
f
th
e
b
eh
a
v
io
r
o
f
wate
r
f
lo
w
at
th
e
co
m
b
in
i
n
g
ch
a
n
n
el
ju
n
ctio
n
(
V
-
s
h
ap
ed
)
is
d
ef
in
e
d
b
y
,
1
3
(
3
−
1
)
=
1
2
3
2
[
1
−
1
2
(
2
2
+
(
1
−
)
2
1
)
]
.
(
7
)
E
x
p
an
d
i
n
g
(
7
)
,
1
3
3
−
1
3
=
3
2
2
−
3
2
2
2
(
1
−
)
2
1
.
(
8
)
T
h
en
,
ex
p
an
d
(
8
)
an
d
r
ea
r
r
a
n
g
e
it to
f
o
r
m
a
p
o
l
y
n
o
m
ial
e
q
u
a
tio
n
:
2
3
5
−
2
3
2
−
3
2
2
+
3
2
(
1
−
)
2
1
=
0
.
T
h
er
ef
o
r
e,
th
e
s
im
p
lifie
d
e
q
u
a
tio
n
o
f
c
o
m
b
in
in
g
f
lo
w
f
o
r
V
-
s
h
ap
ed
ch
an
n
el
is
g
iv
en
b
y
(
)
=
2
3
5
+
.
2
+
(
9
)
wh
er
e,
(
)
=
0
,
(
3
)
=
−
(
2
3
+
3
2
)
,
(
3
,
,
1
)
=
3
2
(
1
−
)
2
1
.
2.
2
.
Sim
pli
f
ied
equa
t
io
n o
f
wa
t
er
f
lo
w
f
o
r
t
ra
pe
zo
ida
l c
ha
nn
el
T
h
e
g
en
er
al
eq
u
atio
n
o
f
th
e
b
eh
av
io
r
o
f
wate
r
f
lo
w
at
th
e
co
m
b
in
in
g
ch
an
n
el
ju
n
ctio
n
(
tr
ap
ez
o
id
al)
p
r
o
p
o
s
ed
b
y
[
2
2
]
is
d
ef
i
n
ed
as f
o
llo
ws:
(
1
+
2
3
)
[
1
2
(
2
−
1
)
+
3
3
(
3
−
1
)
]
=
3
2
(
1
+
3
)
2
[
1
−
(
1
+
3
)
{
2
(
2
+
3
)
2
+
(
1
−
)
2
(
1
+
3
)
1
}
]
(
1
0
)
wh
er
e
3
=
3
3
,
1
=
1
3
,
2
=
2
3
.
E
x
p
an
d
i
n
g
(
1
0
)
,
y
ield
s
−
3
2
(
1
+
3
)
3
2
(
2
+
3
2
)
2
−
3
2
(
1
+
3
)
3
(
1
−
)
2
(
1
+
3
2
)
1
=
3
3
(
1
+
2
3
)
3
+
1
2
(
1
+
2
3
)
2
−
1
2
(
1
+
2
3
)
−
3
3
(
1
+
2
3
)
−
3
2
(
1
+
3
)
2
(
1
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
23
,
No
.
2
,
Au
g
u
s
t 2
0
2
1
:
1
1
1
0
-
1
1
1
9
1114
As
s
h
o
wn
in
(
1
1
)
ca
n
n
o
t
b
e
s
o
lv
ed
f
o
r
an
y
v
alu
e
o
f
a
n
g
les
1
an
d
2
u
n
less
o
n
e
o
f
th
em
is
at
90
o
Hen
ce
,
we
n
ee
d
to
elim
in
ate
o
n
e
o
f
th
e
tr
ig
o
n
o
m
etr
y
in
th
e
eq
u
atio
n
.
Fro
m
th
e
ca
s
e
s
tu
d
y
,
we
ass
u
m
e
th
e
m
ain
f
lo
w
is
f
r
o
m
c
h
an
n
el
1
t
o
ch
an
n
el
3
an
d
c
o
n
s
id
er
0
1
0
9
0
an
d
0
2
90
=
.
In
(
1
1
)
is
m
u
ltip
lied
b
o
th
s
id
es with
2
13
r
r
r
b
y
k
y
+
to
g
et
t
h
e
(
1
2
)
:
−
3
2
(
1
+
3
)
3
(
1
−
)
2
1
=
[
3
3
(
1
+
2
3
)
3
+
1
2
(
1
+
2
3
)
2
−
1
2
(
1
+
2
3
)
−
3
3
(
1
+
2
3
)
−
3
2
(
1
+
3
)
2
]
(
1
+
3
2
)
(1
2
)
No
w,
ex
p
an
d
th
e
eq
u
atio
n
a
n
d
r
ea
r
r
an
g
e
it to
f
o
r
m
a
p
o
ly
n
o
m
ia
l e
q
u
atio
n
.
3
2
3
(
1
+
2
3
)
5
+
[
1
3
3
(
1
+
2
3
)
+
3
2
(
1
+
2
3
)
]
4
+
1
2
(
1
+
2
3
)
3
+
[
−
3
2
(
1
+
2
3
)
−
3
2
3
(
1
+
2
3
)
−
3
2
(
1
+
3
)
2
3
]
2
+
[
−
1
2
(
1
+
2
3
)
−
1
3
3
(
1
+
2
3
)
−
3
2
(
1
+
3
)
2
1
]
+
3
2
(
1
+
3
)
3
(
1
−
)
2
1
=
0
.
(
1
3
)
T
h
er
ef
o
r
e,
th
e
s
im
p
lifie
d
o
f
(
1
3
)
is
(
1
4
)
(
)
=
.
5
+
.
4
+
ℎ
.
3
+
.
2
+
.
+
,
(
1
4
)
wh
er
e,
(
)
=
0
,
(
3
)
=
3
2
3
(
1
+
2
3
)
,
(
3
,
1
)
=
[
1
3
+
1
2
]
(
3
)
(
1
+
2
3
)
,
ℎ
(
3
,
1
)
=
1
2
(
1
+
2
3
)
,
(
3
,
3
)
=
(
−
3
)
[
(
3
3
+
1
2
)
(
1
+
2
3
)
+
3
2
(
1
+
3
)
2
]
,
(
3
,
1
,
3
)
=
(
−
1
)
[
(
3
3
+
1
2
)
(
1
+
2
3
)
+
3
2
(
1
+
3
)
2
]
,
(
3
,
3
,
,
1
)
=
3
2
(
1
+
3
)
3
(
1
−
)
2
1
.
2.
3
.
G
ra
ph
ica
l
us
er
inte
rf
a
ce
(
G
UI)
in M
AT
L
A
B
pro
g
ra
m
m
ing
T
h
e
g
r
ap
h
ical
u
s
er
in
ter
f
ac
e
(
GUI
)
u
s
in
g
MA
T
L
AB
p
r
o
g
r
am
m
in
g
h
as
b
ee
n
u
s
ed
in
th
i
s
s
tu
d
y
to
ca
lcu
late
th
e
d
o
m
ain
d
ata
an
d
co
m
p
ar
e
th
e
b
eh
av
io
r
o
f
wate
r
f
lo
w
b
ased
o
n
th
e
g
r
ap
h
.
GUI
is
d
iv
id
ed
in
t
o
two
p
ar
ts
as
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
e
lef
t
-
h
an
d
s
id
e
is
th
e
f
i
r
s
t
p
ar
t
o
f
th
e
s
y
s
tem
,
wh
er
e
th
e
s
y
s
tem
d
is
p
lay
s
a
p
latf
o
r
m
th
at
allo
ws th
e
u
s
er
to
m
an
u
ally
in
p
u
t t
h
e
v
alu
es o
f
all
d
ata.
T
h
e
r
ad
io
b
u
tto
n
f
u
n
ctio
n
is
to
s
elec
t
th
e
ch
an
n
el
ty
p
e
f
o
r
eith
er
th
e
tr
a
p
ez
o
id
al
ch
a
n
n
el
o
r
V
-
s
h
ap
ed
ch
an
n
el.
T
h
e
ca
lcu
late
b
u
tto
n
will
ca
lcu
late
th
e
v
alu
e
o
f
th
e
p
o
ly
n
o
m
ial
eq
u
atio
n
b
ased
o
n
th
e
in
p
u
t
v
alu
es.
T
h
is
s
tate
o
f
eq
u
atio
n
is
th
e
n
ew
s
im
p
lifie
d
v
er
s
io
n
o
f
th
e
g
en
er
al
eq
u
atio
n
o
f
t
h
e
b
eh
a
v
i
o
r
o
f
wate
r
f
lo
w
at
th
e
co
m
b
in
in
g
ch
an
n
el
ju
n
cti
o
n
.
T
o
s
o
lv
e
t
h
e
g
en
e
r
al
eq
u
a
tio
n
,
th
e
u
s
er
n
ee
d
s
to
p
er
f
o
r
m
New
to
n
’
s
m
eth
o
d
o
n
th
e
eq
u
atio
n
b
y
d
ef
in
i
n
g
t
h
e
to
ler
an
ce
v
alu
e
(
T
o
l
)
a
n
d
m
a
x
i
m
u
m
n
u
m
b
e
r
o
f
i
t
e
r
a
t
i
o
n
s
(
NO
I
)
a
t
t
h
e
p
r
o
v
i
d
e
d
t
e
x
t
e
d
i
t
o
r
s
b
e
f
o
r
e
p
u
s
h
i
n
g
th
e
a
p
p
r
o
x
i
m
a
t
e
b
u
t
t
o
n
.
A
n
o
th
e
r
o
u
t
p
u
t
p
l
a
t
f
o
r
m
d
i
s
p
l
a
y
s
a
l
l
t
h
e
r
o
o
ts
o
f
t
h
e
po
l
y
n
o
m
i
a
l
.
I
t
c
o
n
s
i
s
ts
o
f
f
i
v
e
r
o
o
t
s
i
f
t
h
e
p
o
l
y
n
o
m
i
a
l
i
s
i
n
d
e
g
r
e
e
f
i
v
e
f
o
r
t
h
e
t
r
a
p
e
z
o
i
d
a
l
c
h
a
n
n
e
l
.
T
h
e
v
a
l
u
e
w
i
l
l
b
e
d
is
p
l
a
y
e
d
r
i
g
h
t
a
f
te
r
th
e
a
p
p
r
o
x
i
m
a
t
e
b
u
t
t
o
n
h
as
b
ee
n
c
l
i
c
k
e
d
.
A
ll
t
h
e
v
a
l
u
es
wi
l
l
b
e
d
is
p
l
a
y
e
d
at
t
h
e
s
a
m
e
t
i
m
e
w
it
h
t
h
e
f
i
n
a
l
o
u
t
p
u
t
,
w
h
i
c
h
i
n
c
l
u
d
es
p
r
e
d
i
ct
e
d
f
l
o
w
d
e
p
t
h
r
at
i
o
o
f
c
h
a
n
n
e
l
1
t
o
c
h
a
n
n
e
l
3
(
r
y
),
p
r
ed
icted
d
ep
th
f
o
r
ch
an
n
el
1
(
1
y
)
an
d
th
e
n
u
m
b
er
o
f
iter
atio
n
s
(
NOI
)
in
v
o
lv
ed
in
t
h
e
n
u
m
er
i
ca
l
m
eth
o
d
.
T
h
e
s
ec
o
n
d
p
ar
t
o
f
th
e
s
y
s
tem
lies
at
th
e
r
ig
h
t
-
h
an
d
s
id
e
o
f
th
e
GUI
.
I
t
d
is
p
lay
s
a
p
latf
o
r
m
th
at
s
h
o
ws
a
C
ar
tesi
an
g
r
ap
h
r
ep
r
esen
tin
g
th
e
p
atter
n
b
eh
av
io
r
o
f
wate
r
f
l
o
w
at
th
e
co
m
b
in
in
g
ch
an
n
el
ju
n
ctio
n
.
T
h
e
g
r
ap
h
is
m
ain
ly
ab
o
u
t
t
h
e
r
elatio
n
s
h
ip
b
etwe
en
s
o
m
e
v
ar
iab
les
in
clu
d
in
g
3
F
,
f
l
o
w
r
ate
r
atio
o
f
ch
an
n
el
2
an
d
ch
an
n
el
3
(
q
r
)
,
an
g
le
o
f
c
h
an
n
el
1
f
r
o
m
th
e
c
h
an
n
el
3
a
x
is
(
1
)
a
n
d
t
h
e
f
l
o
w
d
ep
th
o
f
ch
a
n
n
el
3
(
3
y
)
,
wh
ich
is
r
ep
r
esen
ted
b
y
th
e
x
-
ax
is
an
d
its
ef
f
ec
t o
n
r
y
,
wh
ich
is
r
ep
r
esen
ted
b
y
t
h
e
y
-
ax
is
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
N
u
merica
l in
ve
s
tig
a
tio
n
o
n
th
e
b
eh
a
vio
r
o
f c
o
mb
in
in
g
o
p
e
n
-
ch
a
n
n
el
flo
w
(
N
o
r
A
z
n
i S
h
a
h
a
r
i
)
1115
Fig
u
r
e
2
.
Gr
a
p
h
ical
u
s
er
in
ter
f
ac
e
f
o
r
c
o
m
b
in
in
g
f
lo
w
3.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
T
ab
le
2
s
h
o
ws
th
e
g
e
o
m
etr
ica
l
d
etails
an
d
T
a
b
le
3
s
h
o
ws
th
e
ex
p
er
im
e
n
tal
an
d
m
ea
s
u
r
e
d
h
y
d
r
a
u
lic
d
etails
o
f
th
e
tr
a
p
ez
o
id
al
c
h
an
n
el
u
s
ed
b
y
[
2
2
]
.
I
t
ca
n
b
e
s
ee
n
f
r
o
m
T
ab
le
2
f
o
r
th
e
tr
a
p
e
zo
id
al
ch
an
n
el,
th
at
th
e
b
o
tto
m
wid
th
,
b
o
f
all
ch
an
n
els
h
as
b
ee
n
k
ep
t
d
if
f
er
e
n
t.
Fu
r
th
er
,
th
e
b
r
an
c
h
in
g
a
n
g
le
o
f
th
e
b
r
an
ch
ch
an
n
el
1
an
d
b
r
an
c
h
ch
an
n
el
2
h
as
b
ee
n
k
ep
t
at
3
0
°
an
d
9
0
º
r
esp
ec
tiv
ely
to
th
e
ax
is
o
f
ch
an
n
el
3
.
T
a
b
le
3
s
h
o
ws
th
at
th
er
e
ar
e
f
o
u
r
p
ar
a
m
eter
s
in
v
o
lv
ed
,
wh
ich
in
clu
d
e
th
e
3
F
,
r
q
an
d
m
ea
s
u
r
e
d
d
e
p
th
(
1
y
an
d
3
y
)
.
T
h
e
s
id
e
s
lo
p
e
tim
es
f
lo
w
d
ep
th
to
b
o
tto
m
wid
th
r
atio
i
s
also
a
p
ar
t
o
f
th
e
e
x
p
er
im
en
tal
an
d
m
ea
s
u
r
ed
h
y
d
r
a
u
lic
d
etails.
T
ab
le
2
.
Geo
m
et
r
ical
ch
ar
ac
te
r
is
tics
o
f
th
e
ch
an
n
el
s
C
h
a
n
n
e
l
Tr
a
p
e
z
o
i
d
a
l
V
-
S
h
a
p
e
d
1
2
3
1
2
3
B
o
t
t
o
m w
i
d
t
h
(
m)
,
b
0
.
1
7
2
0
.
0
7
2
0
.
2
7
2
NA
NA
NA
Th
e
c
o
mb
i
n
i
n
g
a
n
g
l
e
f
r
o
m
t
h
e
d
i
r
e
c
t
i
o
n
o
f
f
l
o
w
i
n
ma
i
n
c
h
a
n
n
e
l
,
30
r
ad
6
=
90
r
ad
2
=
NA
30
r
ad
6
=
90
r
ad
2
=
NA
T
ab
le
3
.
E
x
p
er
im
en
tal
a
n
d
m
e
asu
r
ed
ch
ar
ac
ter
is
tics
o
f
th
e
c
h
an
n
els
Ex
p
e
r
i
m
e
n
t
s (E)
H
y
d
r
a
u
l
i
c
s
Tr
a
p
e
z
o
i
d
a
l
[
2
2
]
V
-
sh
a
p
e
d
E1
E2
E3
E1
E2
E3
Th
e
si
d
e
sl
o
p
e
x
f
l
o
w
d
e
p
t
h
t
o
b
o
t
t
o
m
w
i
d
t
h
r
a
t
i
o
o
f
c
h
a
n
n
e
l
3
,
3
k
0
.
1
9
3
0
.
1
7
0
0
.
1
9
7
NA
NA
NA
F
r
o
u
d
e
n
u
m
b
e
r
o
f
c
h
a
n
n
e
l
3
,
3
F
0
.
2
0
2
0
.
2
7
8
0
.
3
6
5
0
.
2
0
2
0
.
2
7
8
0
.
3
6
5
F
l
o
w
r
a
t
e
r
a
t
i
o
o
f
c
h
a
n
n
e
l
2
t
o
c
h
a
n
n
e
l
3
,
r
q
0
.
4
3
9
0
.
5
0
0
0
.
8
7
5
0
.
4
3
9
0
.
5
0
0
0
.
8
7
5
M
e
a
su
r
e
d
f
l
o
w
d
e
p
t
h
o
f
c
h
a
n
n
e
l
3
,
3
y
0
.
0
9
1
1
0
.
8
0
1
0
.
0
9
2
6
0
.
0
9
1
1
0
.
8
0
1
0
.
0
9
2
6
M
e
a
su
r
e
d
f
l
o
w
d
e
p
t
h
o
f
c
h
a
n
n
e
l
1
,
1
y
0
.
0
9
4
5
0
.
0
8
3
8
0
.
1
0
5
3
-
-
-
3
.
1
.
E
x
perim
ent
v
a
lid
a
t
io
n
T
h
r
ee
s
ets
o
f
ex
p
er
im
en
tal
d
a
ta
(
E
1
,
E
2
an
d
E
3
)
a
r
e
ta
k
en
f
r
o
m
[
2
2
]
t
o
v
ali
d
ate
th
e
p
r
e
d
icted
f
lo
w
ch
ar
ac
ter
is
tic
o
f
tr
a
p
ez
o
id
al
c
h
an
n
els
o
b
tain
e
d
f
r
o
m
(
1
4
)
.
I
n
T
ab
le
4
,
th
e
r
esu
lts
s
h
o
w
a
v
e
r
y
g
o
o
d
ag
r
ee
m
e
n
t
b
etwe
en
ex
p
e
r
im
en
t
an
d
p
r
e
d
icted
1
y
with
esti
m
ated
er
r
o
r
1
.
5
4
%,
0
.
0
0
9
%
an
d
2
.
5
7
%.
I
t
s
h
o
ws
th
at
th
e
p
r
ed
icted
1
y
p
r
o
d
u
ce
d
b
y
th
e
p
r
o
p
o
s
ed
eq
u
atio
n
m
atch
es v
e
r
y
well
with
th
e
ex
p
er
im
en
tal
d
ata.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
23
,
No
.
2
,
Au
g
u
s
t 2
0
2
1
:
1
1
1
0
-
1
1
1
9
1116
T
ab
le
4
.
C
o
m
p
a
r
is
o
n
o
f
f
lo
w
d
ep
th
b
etwe
en
ex
p
er
im
e
n
t a
n
d
n
u
m
er
ical
m
eth
o
d
Ex
p
e
r
i
m
e
n
t
s (E)
H
y
d
r
a
u
l
i
c
s
Tr
a
p
e
z
o
i
d
a
l
[
2
2
]
V
-
sh
a
p
e
d
E1
E2
E3
E1
E2
E3
F
l
o
w
d
e
p
t
h
o
f
c
h
a
n
n
e
l
1
,
1
y
(
Ex
p
e
r
i
me
n
t
)
0
.
0
9
4
5
0
.
0
8
3
8
0
.
1
0
5
3
NA
NA
NA
D
e
p
t
h
r
a
t
i
o
,
r
y
(
P
r
e
d
i
c
t
e
d
)
1
.
0
2
1
4
1
.
0
4
6
1
1
.
1
0
5
8
1
.
0
1
4
8
1
.
0
2
9
9
1
.
0
6
1
9
F
l
o
w
d
e
p
t
h
o
f
c
h
a
n
n
e
l
1
,
1
y
(
P
r
e
d
i
c
t
e
d
)
0
.
0
9
3
0
4
7
0
.
0
8
3
7
9
2
0
.
1
0
2
4
0
.
0
9
2
4
4
7
0
.
0
8
2
4
9
1
0
.
0
9
8
3
3
2
R
e
l
a
t
i
v
e
e
r
r
o
r
(
%)
1
.
5
4
%
0
.
0
0
9
%
2
.
5
7
%
-
-
-
3
.
2
.
Sens
it
iv
it
y
a
na
l
y
s
is
o
f
f
l
o
w
depth
ra
t
io
(
r
y
)
o
n
t
ra
pezo
i
da
l a
nd
V
-
s
ha
pe
cha
nn
e
l
T
h
e
s
en
s
itiv
ity
to
f
lo
w
d
ep
th
r
ef
lects
th
e
d
eg
r
ee
to
wh
ich
th
e
ch
an
g
es
in
Fro
u
d
e
n
u
m
b
er
an
d
f
lo
w
r
ate
ca
n
af
f
ec
t
th
e
f
lo
w
d
ep
th
.
Fo
r
ea
ch
p
ar
am
eter
,
th
e
E
3
d
ata
in
T
ab
le
3
ar
e
ad
d
ed
an
d
r
ed
u
ce
d
b
y
0
.
2
5
.
Fig
u
r
es
3
a
n
d
Fig
u
r
e
4
d
ep
i
ct
th
e
g
r
ap
h
ical
r
ep
r
esen
tati
o
n
o
f
3
an
d
to
th
e
p
o
l
y
n
o
m
ia
l
r
o
o
t,
r
y
f
o
r
tr
ap
ez
o
id
al
ch
a
n
n
els,
r
esp
ec
ti
v
ely
.
I
n
Fig
u
r
e
3
,
it
is
u
n
d
en
ia
b
le
th
at
ch
an
g
es
i
n
3
s
h
o
ws
th
e
b
ig
g
e
s
t
g
ap
with
t
h
e
r
e
q
u
ir
e
d
r
o
o
t,
wh
ile
in
Fig
u
r
e
4
,
it
is
o
b
v
io
u
s
th
at
r
q
s
h
o
ws
a
lar
g
er
g
a
p
with
th
e
v
alu
e
o
f
r
o
o
t,
b
u
t
s
lig
h
tly
s
m
aller
co
m
p
ar
ed
to
th
e
g
ap
m
a
d
e
b
y
3
.
Su
b
s
eq
u
en
tl
y
,
t
h
e
ef
f
e
cts
o
f
3
an
d
to
th
e
p
o
ly
n
o
m
ial
r
o
o
t,
r
y
f
o
r
V
-
s
h
ap
ed
ch
an
n
els
ar
e
illu
s
tr
ated
in
Fig
u
r
es 5
an
d
Fig
u
r
e
6
.
I
t
ca
n
b
e
s
ee
n
clea
r
ly
th
at
th
e
p
atter
n
o
f
th
e
r
esu
lts
(
Fig
u
r
es 3
-
6
)
is
s
im
ilar
to
th
at
o
f
[
1
0
]
a
n
d
[
2
2
]
,
in
wh
ich
th
e
m
ai
n
f
ac
t
o
r
s
to
h
av
e
an
ef
f
ec
t
o
n
th
e
wate
r
d
e
p
th
in
th
e
b
r
a
n
ch
ch
an
n
el
s
y
s
tem
ar
e
th
e
f
lo
w
r
ate
r
atio
an
d
Fro
u
d
e
n
u
m
b
e
r
.
Fu
r
t
h
er
m
o
r
e
,
th
e
s
id
e
s
lo
p
e
tim
es f
lo
w
d
ep
th
to
th
e
b
o
tto
m
wid
t
h
r
atio
o
f
ch
an
n
el
3
(
3
k
)
,
th
e
b
o
tto
m
wid
th
r
atio
o
f
c
h
an
n
el
1
to
ch
a
n
n
el
3
(
1
r
b
)
a
n
d
t
h
e
v
alu
e
o
f
th
e
an
g
le
o
f
ch
a
n
n
el
1
(
1
)
ar
e
s
lig
h
tly
af
f
ec
ted
an
d
d
if
f
ic
u
lt to
id
en
tify
.
Fig
u
r
e
3
.
T
h
e
ef
f
ec
t
o
f
3
F
to
th
e
p
o
ly
n
o
m
ial
r
o
o
t,
r
y
f
o
r
tr
ap
ez
o
id
al
ch
an
n
el
Fig
u
r
e
4
.
T
h
e
ef
f
ec
t
o
f
r
q
to
th
e
p
o
ly
n
o
m
ial
r
o
o
t,
r
y
f
o
r
tr
ap
ez
o
id
al
ch
an
n
el
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
N
u
merica
l in
ve
s
tig
a
tio
n
o
n
th
e
b
eh
a
vio
r
o
f c
o
mb
in
in
g
o
p
e
n
-
ch
a
n
n
el
flo
w
(
N
o
r
A
z
n
i S
h
a
h
a
r
i
)
1117
Fig
u
r
e
5
.
T
h
e
ef
f
ec
t
o
f
3
F
to
th
e
p
o
ly
n
o
m
ial
r
o
o
t,
r
y
f
o
r
V
-
s
h
ap
e
d
ch
an
n
el
Fig
u
r
e
6.
T
h
e
ef
f
ec
t
o
f
r
q
to
th
e
p
o
ly
n
o
m
ial
r
o
o
t,
r
y
f
o
r
V
-
s
h
ap
e
d
ch
an
n
el
I
n
c
o
n
clu
s
io
n
,
3
F
p
lay
s
th
e
m
aj
o
r
r
o
le
in
d
ete
r
m
in
in
g
th
e
m
a
x
im
u
m
1
y
to
av
o
id
t
h
e
o
v
er
f
l
o
w
o
f
wate
r
in
b
o
th
T
r
ap
ez
o
id
al
an
d
V
-
s
h
ap
e
ch
an
n
els.
T
h
is
s
u
p
p
o
r
ts
th
e
r
esu
lt
b
y
[
1
2
]
th
at
s
tates
th
e
n
o
n
lin
ea
r
m
o
d
els
ar
e
m
o
r
e
s
en
s
itiv
e
to
3
F
.
T
h
is
is
r
atio
n
al
b
ec
au
s
e
th
e
in
f
lo
w
wate
r
o
b
v
io
u
s
ly
d
ep
en
d
s
o
n
th
e
co
n
d
itio
n
o
f
th
e
wate
r
f
l
o
w
at
th
e
o
u
tf
lo
w
wate
r
.
I
t
r
ea
cts
d
if
f
er
en
tly
,
d
e
p
en
d
i
n
g
o
n
th
e
b
e
h
av
io
r
o
f
th
e
wate
r
f
lo
w,
wh
er
e
th
e
f
l
o
w
m
ay
b
e
s
u
b
cr
itical
(
1
F
)
,
cr
itical
(
1
=
F
)
,
o
r
s
u
p
er
cr
itical
(
1
F
)
.
B
esid
es,
r
q
p
lay
s
th
e
s
ec
o
n
d
m
o
s
t
im
p
o
r
tan
t
p
a
r
t
in
d
eter
m
in
in
g
th
e
v
alu
e
o
f
1
y
.
T
h
is
h
ap
p
en
s
b
ec
a
u
s
e
th
e
r
q
h
ig
h
ly
d
e
p
en
d
s
o
n
th
e
h
y
d
r
au
lic
v
elo
city
o
f
t
h
e
wate
r
f
lo
w,
V
an
d
th
e
cr
o
s
s
-
s
ec
tio
n
al
ar
ea
o
f
th
e
wate
r
f
lo
w,
A
.
T
h
u
s
,
th
e
ch
an
g
e
in
r
q
af
f
ec
ts
th
e
m
ax
i
m
u
m
1
y
.
L
astl
y
,
it
is
o
b
v
io
u
s
th
at
1
h
as
a
m
in
im
al
ef
f
ec
t
o
n
th
e
b
eh
av
io
r
o
f
wate
r
f
lo
w
in
th
e
wate
r
f
lo
w
s
y
s
tem
.
3
.
3
.
Co
m
pa
riso
n bet
wee
n T
ra
pezo
ida
l a
nd
V
-
s
ha
ped c
h
a
nn
el
j
un
ct
io
n
t
o
t
he
depth
ra
t
io
r
y
T
h
e
p
ar
am
etr
ic
in
v
esti
g
atio
n
o
f
two
p
ar
am
eter
s
,
3
F
an
d
r
q
is
m
a
d
e
in
o
r
d
er
to
an
aly
s
e
th
e
ef
f
e
ct
o
f
p
ar
am
eter
s
o
n
r
y
in
b
o
th
tr
a
p
ez
o
id
al
an
d
V
-
s
h
ap
ed
ch
an
n
els.
T
h
e
E
3
d
ata
in
T
ab
les 2
an
d
3
a
r
e
u
s
ed
as f
ix
ed
v
ar
iab
les.
T
h
e
p
r
o
p
er
ty
v
alu
e
s
o
f
o
th
er
ca
s
es
ar
e
o
b
tain
ed
b
y
v
ar
y
i
n
g
ea
ch
p
a
r
am
eter
,
wh
ils
t
k
ee
p
in
g
th
e
o
th
er
v
alu
e
co
n
s
tan
t.
Fig
u
r
es 7
an
d
8
illu
s
tr
ate
th
e
ef
f
ec
t
o
f
3
F
an
d
r
q
on
r
y
r
esp
ec
tiv
ely
.
Fig
u
r
e
7
s
h
o
ws
th
at
th
e
tr
ap
ez
o
id
al
ch
an
n
el
h
as
th
e
h
ig
h
est
v
alu
e
o
f
r
y
with
a
v
alu
e
o
f
1
.
6
co
m
p
ar
ed
to
1
.
3
5
f
o
r
th
e
V
-
s
h
ap
ed
ch
an
n
el
as
3
F
in
cr
ea
s
es.
I
n
Fig
u
r
e
8
,
th
e
h
ig
h
est
v
alu
e
o
f
r
y
is
1
.
1
2
f
o
r
th
e
tr
ap
ez
o
id
al
c
h
an
n
el
a
n
d
1
.
0
6
f
o
r
th
e
V
-
s
h
ap
ed
c
h
an
n
el
with
th
e
in
cr
ea
s
e
o
f
r
q
.
Ov
er
all,
as
b
o
th
p
ar
am
eter
in
cr
ea
s
e,
th
e
r
ate
o
f
in
cr
ea
s
e
in
r
y
is
h
ig
h
er
f
o
r
th
e
t
r
ap
ez
o
id
al
ch
a
n
n
el
co
m
p
ar
ed
to
th
e
V
-
s
h
ap
ed
ch
an
n
el.
T
h
e
in
cr
ea
s
e
o
f
r
y
with
th
e
o
b
s
er
v
atio
n
o
f
eq
u
al
u
p
s
tr
ea
m
d
ep
th
,
12
=
yy
is
co
n
s
i
s
ten
t
as
s
h
o
wn
in
th
e
p
r
ev
io
u
s
s
tu
d
i
es
[
1
2
]
,
[
1
7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
23
,
No
.
2
,
Au
g
u
s
t 2
0
2
1
:
1
1
1
0
-
1
1
1
9
1118
Fig
u
r
e
7
.
T
h
e
ef
f
ec
t
o
f
3
F
on
r
y
Fig
u
r
e
8
.
T
h
e
ef
f
ec
t
o
f
r
q
on
r
y
4.
CO
NCLU
SI
O
N
T
h
e
g
en
er
al
eq
u
atio
n
s
o
f
o
p
en
-
ch
an
n
el
f
lo
w
f
o
r
th
e
ty
p
es
o
f
tr
ap
ez
o
id
al
an
d
V
-
s
h
a
p
ed
cr
o
s
s
-
s
ec
tio
n
al
ch
an
n
els
h
av
e
b
ee
n
d
ev
elo
p
e
d
in
th
e
f
o
r
m
o
f
p
o
l
y
n
o
m
ial
eq
u
atio
n
s
with
d
eg
r
ee
f
iv
e
b
y
tak
i
n
g
in
to
ac
co
u
n
t
two
b
r
an
c
h
ch
a
n
n
els
th
at
u
n
ite,
f
o
r
m
in
g
a
s
in
g
le
m
ain
ch
an
n
el.
T
h
e
m
o
d
if
ied
eq
u
atio
n
s
co
n
s
is
t
o
f
f
iv
e
p
ar
am
eter
s
,
wh
ich
r
ep
r
es
en
t
b
o
th
p
h
y
s
ical
an
d
f
lo
w
ch
ar
ac
ter
is
tics
o
f
th
e
wate
r
.
T
h
e
p
ar
a
m
etr
ic
in
v
esti
g
atio
n
h
as
b
ee
n
ca
r
r
ied
o
u
t
to
u
n
d
er
s
tan
d
th
e
in
ter
d
ep
en
d
e
n
ce
o
f
s
o
m
e
o
f
th
e
r
esp
o
n
d
in
g
v
a
r
iab
les,
wh
er
e
th
e
Fr
o
u
d
e
n
u
m
b
er
g
iv
es
th
e
g
r
ea
test
im
p
ac
t
o
n
th
e
wate
r
f
lo
w
d
e
p
th
.
Fu
r
th
er
m
o
r
e,
th
e
r
ate
o
f
in
cr
ea
s
e
o
f
d
ep
th
f
l
o
w
f
o
r
th
e
tr
ap
ez
o
id
al
ch
an
n
el
is
h
ig
h
er
th
an
th
e
V
-
s
h
ap
ed
ch
an
n
el
as
th
e
Fro
u
d
e
n
u
m
b
e
r
an
d
f
lo
w
r
ate
r
atio
in
cr
ea
s
e.
T
h
er
ef
o
r
e,
th
e
tr
ap
ez
o
id
al
ch
a
n
n
el
is
r
ec
o
m
m
en
d
e
d
to
av
o
id
wat
er
o
v
er
f
lo
w
in
th
e
co
m
b
in
in
g
o
p
e
n
-
ch
a
n
n
el
f
lo
w
.
Nev
er
th
eless
,
th
is
s
tu
d
y
r
ela
tes
o
n
ly
to
co
m
b
in
in
g
o
p
e
n
-
c
h
an
n
el
f
lo
w.
T
h
u
s
,
th
e
m
o
d
if
ied
eq
u
atio
n
o
f
d
iv
i
d
in
g
f
lo
w
f
o
r
tr
ap
ez
o
id
al
an
d
V
-
s
h
ap
ed
ch
an
n
els
m
ay
b
e
co
n
s
id
er
ed
f
o
r
f
u
t
u
r
e
r
esear
ch
.
RE
F
E
R
E
NC
E
S
[1
]
G
.
K
e
ss
e
rw
a
n
i,
J.
Va
z
q
u
e
z
,
N.
Riv
iere
,
Q.
Li
a
n
g
,
G
.
Trav
in
,
a
n
d
R.
M
o
se
,
"
Ne
w
Ap
p
r
o
a
c
h
fo
r
P
re
d
ictin
g
F
lo
w
Bifu
rc
a
ti
o
n
a
t
Ri
g
h
t
-
A
n
g
led
O
p
e
n
-
Ch
a
n
n
e
l
Ju
n
c
ti
o
n
,
"
J
o
u
rn
a
l
o
f
Hy
d
ra
u
li
c
E
n
g
i
n
e
e
ri
n
g
,
v
o
l
.
1
3
6
,
n
o
.
9
,
p
p
.
6
6
2
-
6
6
8
,
2
0
1
0
,
d
o
i:
1
0
.
1
0
6
1
/(
ASCE
)HY
.
1
9
4
3
-
7
9
0
0
.
0
0
0
0
2
2
2
.
[2
]
A.
S
.
Ra
m
a
m
u
rth
y
,
L.
B.
Ca
rb
a
ll
a
d
a
,
a
n
d
D.
M
.
Tran
,
"
C
o
m
b
in
in
g
Op
e
n
Ch
a
n
n
e
l
F
l
o
w
a
t
Ri
g
h
t
An
g
led
Ju
n
c
ti
o
n
s,
"
J
o
u
rn
a
l
o
f
Hy
d
ra
u
li
c
E
n
g
i
n
e
e
rin
g
,
v
o
l.
1
1
4
,
n
o
.
1
2
,
p
p
.
1
4
4
9
-
1
4
6
0
,
1
9
8
8
,
d
o
i
:
1
0
.
1
0
6
1
/(AS
CE)0
7
3
3
-
9
4
2
9
(
1
9
8
8
)
1
1
4
:1
2
(1
4
4
9
).
[3
]
A.
K.
P
a
n
d
e
y
a
n
d
P
.
K.
M
o
h
a
p
a
tra,
"
3
D
sim
u
lati
o
n
o
f
f
lo
w
I
n
a
ri
g
h
t
a
n
g
led
c
h
a
n
n
e
l
ju
n
c
ti
o
n
wit
h
a
p
it
,
"
in
W
o
rl
d
En
v
iro
n
me
n
ta
l
a
n
d
W
a
ter
Res
o
u
rc
e
s
Co
n
g
re
ss
2
0
1
9
:
Hy
d
ra
u
li
c
s,
W
a
ter
wa
y
s,
a
n
d
W
a
ter
Distrib
u
ti
o
n
S
y
ste
ms
An
a
lys
is
,
P
it
tsb
u
rg
h
,
P
e
n
n
s
y
lv
a
n
i
a
,
2
0
1
9
,
p
p
.
1
4
4
-
1
5
8
,
d
o
i:
1
0
.
1
0
6
1
/9
7
8
0
7
8
4
4
8
2
3
5
3
.
0
1
4
.
[4
]
S
.
K.
Biswa
l,
P
.
M
o
h
a
p
a
tra,
a
n
d
K.
M
u
ra
li
d
h
a
r,
"
Hy
d
ra
u
li
c
s
o
f
c
o
m
b
in
in
g
fl
o
w
in
a
rig
h
t
-
a
n
g
led
c
o
m
p
o
u
n
d
o
p
e
n
c
h
a
n
n
e
l
j
u
n
c
ti
o
n
,
"
S
a
d
h
a
n
a
,
v
o
l.
4
1
,
n
o
.
1
,
p
p
.
9
7
-
1
1
0
,
2
0
1
6
,
d
o
i:
1
0
.
1
0
0
7
/s1
2
0
4
6
-
0
1
5
-
0
4
4
2
-
y
.
[5
]
L.
S
c
h
in
d
fe
ss
e
l,
S
.
Cre
e
ll
e
,
a
n
d
T.
De
M
u
ld
e
r,
"
F
lo
w
P
a
tt
e
rn
s
i
n
a
n
Op
e
n
C
h
a
n
n
e
l
Co
n
flu
e
n
c
e
with
I
n
c
re
a
sin
g
l
y
Do
m
in
a
n
t
Tr
ib
u
tary
I
n
flo
w
,
"
W
a
t
e
r,
v
o
l.
7
,
p
p
.
4
7
2
4
-
4
7
5
1
,
2
0
1
5
,
d
o
i:
1
0
.
3
3
9
0
/w
7
0
9
4
7
2
4
.
[6
]
S
.
I.
S
h
a
k
il
,
M
.
J.
U
d
d
i
n
,
a
n
d
C.
M
o
n
d
o
l,
"
N
u
m
e
rica
l
m
o
d
e
ll
i
n
g
o
f
flo
w
i
n
a
9
0
°
c
h
a
n
n
e
l
c
o
n
flu
e
n
c
e
,
"
in
t
h
e
In
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
n
Ci
v
il
En
g
in
e
e
rin
g
fo
r
S
u
st
a
in
a
b
le
De
v
e
lo
p
me
n
t(ICCE
S
D
2
0
2
0
)
,
KU
ET
,
Kh
u
l
n
a
,
Ba
n
g
lad
e
sh
,
2
0
2
0
,
p
p
.
1
-
8
.
[
7]
V.
S
.
Ne
a
ry
a
n
d
A.
J.
O
d
g
a
a
r
d
,
"
Th
re
e
-
d
ime
n
sio
n
a
l
fl
o
w
stru
c
tu
re
a
t
o
p
e
n
-
c
h
a
n
n
e
l
d
i
v
e
rsio
n
s,"
J
o
u
r
n
a
l
o
f
Hy
d
ra
u
li
c
E
n
g
i
n
e
e
rin
g
,
v
o
l.
1
1
9
,
n
o
.
1
1
,
p
p
.
1
2
2
3
-
1
2
3
0
,
1
9
9
3
,
d
o
i:
1
0
.
1
0
6
1
/(A
S
CE)0
7
3
3
-
9
4
2
9
(1
9
9
3
)1
1
9
:1
1
(1
2
2
3
.
[8
]
A.
S
.
Ra
m
a
m
u
rth
y
,
J.
Q
u
,
a
n
d
D.
Vo
,
"
Nu
m
e
rica
l
a
n
d
Ex
p
e
rime
n
tal
S
t
u
d
y
o
f
Di
v
id
in
g
O
p
e
n
-
C
h
a
n
n
e
l
F
l
o
ws
,
"
J
o
u
rn
a
l
o
f
Hy
d
ra
u
li
c
E
n
g
i
n
e
e
rin
g
,
v
o
l.
1
3
3
,
n
o
.
1
0
,
p
p
.
1
1
3
5
-
1
1
4
4
,
2
0
0
7
,
d
o
i
:
1
0
.
1
0
6
1
/(AS
CE)0
7
3
3
-
9
4
2
9
(
2
0
0
7
)
1
3
3
:1
0
(1
1
3
5
).
[9
]
I.
M
.
H.
Ra
sh
wa
n
,
"
D
y
n
a
m
ic
M
o
d
e
l
fo
r
S
u
b
c
rit
ica
l
Di
v
id
i
n
g
F
lo
ws
in
o
p
e
n
C
h
a
n
n
e
l
Ju
n
c
ti
o
n
,
"
in
Ei
g
h
t
h
In
ter
n
a
t
io
n
a
l
W
a
ter
T
e
c
h
n
o
lo
g
y
Co
n
fer
e
n
c
e
,
IW
T
C8
2
0
0
4
,
Ale
x
a
n
d
ria,
E
g
y
p
t,
2
0
0
4
,
p
p
.
5
1
1
-
5
2
0
.
[1
0
]
C.
-
C.
Hs
u
,
C.
-
J.
Tan
g
,
W.
-
J.
Lee
,
a
n
d
M
.
-
Y.
S
h
ieh
,
"
S
u
b
c
rit
ica
l
9
0
°
Eq
u
a
l
-
Wi
d
th
Op
e
n
-
C
h
a
n
n
e
l
Div
id
i
n
g
F
lo
w,
"
J
o
u
rn
a
l
o
f
Hy
d
r
a
u
li
c
En
g
i
n
e
e
rin
g
,
v
o
l
.
1
2
8
,
n
o
.
7
,
p
p
.
7
1
6
-
7
2
0
,
2
0
0
2
,
d
o
i:
1
0
.
1
0
6
1
/(AS
CE)0
7
3
3
-
9
4
2
9
(
2
0
0
2
)
1
2
8
:7
(
7
1
6
).
[1
1
]
Ba
rk
d
o
l
l,
Brian
D.
,
B.
L.
Ha
g
e
n
,
a
n
d
A.
J.
Od
g
a
a
rd
,
"
E
x
p
e
ri
m
e
n
tal
Co
m
p
a
riso
n
Of
D
iv
i
d
in
g
Op
e
n
-
Ch
a
n
n
e
l
Wi
th
d
u
c
t
F
lo
w
In
T
-
Ju
n
c
ti
o
n
,
"
J
o
u
rn
a
l
o
f
Hy
d
r
a
u
li
c
En
g
i
n
e
e
rin
g
,
v
o
l.
1
2
4
,
n
o
.
1
,
p
p
.
9
2
-
9
5
,
1
9
9
8
,
d
o
i:
1
0
.
1
0
6
1
/(AS
CE)
0
7
3
3
-
9
4
2
9
(
1
9
9
8
)
1
2
4
:1
(
9
2
).
[1
2
]
G
.
K
e
s
s
e
r
w
a
n
i
,
R
.
G
h
o
s
t
i
n
e
,
J
.
V
a
z
q
u
e
z
,
R
.
M
o
s
é
,
M
.
A
b
d
a
l
l
a
h
,
a
n
d
A
.
G
h
e
n
a
i
m
,
"
S
i
m
u
l
a
t
i
o
n
o
f
s
u
b
c
r
i
t
i
c
a
l
f
l
o
w
a
t
o
p
e
n
-
c
h
a
n
n
e
l
j
u
n
c
t
i
o
n
,
"
A
d
v
a
n
c
e
s
i
n
W
a
t
e
r
R
e
s
o
u
r
c
e
s
,
vo
l
.
3
1
,
n
o
.
2
,
p
p
.
2
8
7
-
2
9
7
,
2
0
0
8
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
a
d
v
w
a
t
r
e
s
.
2
0
0
7
.
0
8
.
0
0
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
N
u
merica
l in
ve
s
tig
a
tio
n
o
n
th
e
b
eh
a
vio
r
o
f c
o
mb
in
in
g
o
p
e
n
-
ch
a
n
n
el
flo
w
(
N
o
r
A
z
n
i S
h
a
h
a
r
i
)
1119
[1
3
]
R.
G
h
o
stin
e
,
J.
Va
z
q
u
e
z
,
A.
T
e
rfo
u
s,
R
.
M
o
se
,
a
n
d
A
.
G
h
e
n
a
im,
"
Co
m
p
a
ra
ti
v
e
stu
d
y
o
f
1
D
a
n
d
2
D
fl
o
w
sim
u
latio
n
s
a
t
o
p
e
n
-
c
h
a
n
n
e
l
j
u
n
c
ti
o
n
s,"
J
o
u
r
n
a
l
o
f
Hy
d
ra
u
li
c
Res
e
a
rc
h
,
vo
l
.
5
0
,
n
o
.
2
,
p
p
.
1
6
4
-
1
7
0
,
2
0
1
2
,
d
o
i:
1
0
.
1
0
8
0
/0
0
2
2
1
6
8
6
.
2
0
1
2
.
6
6
1
5
6
3
.
[1
4
]
K.
El
Ka
d
i
Ab
d
e
rre
z
z
a
k
,
L.
Le
wic
k
i,
A.
P
a
q
u
ier,
N.
Riv
ière
,
a
n
d
G
.
Trav
i
n
,
"
Div
isio
n
o
f
c
rit
ica
l
flo
w
a
t
th
re
e
-
b
ra
n
c
h
o
p
e
n
-
c
h
a
n
n
e
l
i
n
ters
e
c
ti
o
n
,
"
J
o
u
rn
a
l
o
f
Hy
d
ra
u
li
c
Res
e
a
rc
h
,
vo
l.
4
9
,
n
o
.
2
,
p
p
.
2
3
1
-
2
3
8
,
2
0
1
1
,
d
o
i:
1
0
.
1
0
8
0
/0
0
2
2
1
6
8
6
.
2
0
1
1
.
5
5
8
1
7
4
.
[1
5
]
C.
-
C.
Hs
u
,
F
.
-
S
.
Wu
,
a
n
d
W.
-
J.
Lee
,
"
F
lo
w
a
t
9
0
°
Eq
u
a
l
-
wid
t
h
Op
e
n
Ch
a
n
n
e
l
Ju
n
c
ti
o
n
,
"
J
o
u
rn
a
l
o
f
Hy
d
r
a
u
li
c
En
g
i
n
e
e
rin
g
,
v
o
l.
1
2
4
,
n
o
.
2
,
p
p
.
1
8
6
-
1
9
1
,
1
9
9
8
,
d
o
i:
1
0
.
1
0
6
1
/(AS
CE)0
7
3
3
-
9
4
2
9
(
1
9
9
8
)
1
2
4
:2
(
1
8
6
).
[1
6
]
S
.
K.
G
u
rra
m
,
K.
S
.
Ka
r
k
i,
a
n
d
W.
H.
Ha
g
e
r,
"
S
u
b
c
rit
ica
l
J
u
n
c
ti
o
n
F
l
o
w,"
J
o
u
r
n
a
l
o
f
Hy
d
ra
u
li
c
En
g
in
e
e
rin
g
,
vol
.
1
2
3
,
n
o
.
5
,
p
p
.
4
4
7
-
4
5
5
,
1
9
9
7
,
d
o
i:
1
0
.
1
0
6
1
/(A
S
CE)0
7
3
3
-
9
4
2
9
(1
9
9
7
)
1
2
3
:5
(
4
4
7
).
[1
7
]
S
.
A.
S
h
a
b
a
y
e
k
,
P
.
S
teffle
r,
a
n
d
F
.
Hic
k
s,
"
Dy
n
a
m
ic
M
o
d
e
l
fo
r
S
u
b
c
rit
ica
l
Co
m
b
i
n
in
g
F
l
o
ws
in
Ch
a
n
n
e
l
Ju
n
c
ti
o
n
s,"
J
o
u
r
n
a
l
o
f
Hy
d
r
a
u
li
c
En
g
in
e
e
rin
g
,
v
o
l.
1
2
8
,
p
p
.
8
2
1
-
8
2
8
,
2
0
0
2
,
d
o
i
:
1
0
.
1
0
6
1
/(AS
CE)0
7
3
3
-
9
4
2
9
(
2
0
0
2
)
1
2
8
:9
(
8
2
1
).
[1
8
]
R.
G
h
o
stin
e
,
J.
Va
z
q
u
e
z
,
A.
Terfo
u
s,
N.
Ri
v
ière
,
A.
G
h
e
n
a
im,
a
n
d
R.
M
o
sé
,
"
A
c
o
m
p
a
ra
ti
v
e
stu
d
y
o
f
1
D
a
n
d
2
D
a
p
p
ro
a
c
h
e
s
f
o
r
sim
u
lati
n
g
fl
o
ws
a
t
rig
h
t
a
n
g
led
d
iv
i
d
in
g
ju
n
c
ti
o
n
s,
"
A
p
p
l
ied
M
a
t
h
e
ma
ti
c
s
a
n
d
Co
mp
u
ta
ti
o
n
,
v
o
l.
2
1
9
,
n
o
.
1
0
,
p
p
.
5
0
7
0
-
5
0
8
2
,
2
0
1
3
,
d
o
i:
1
0
.
1
0
1
6
/j
.
a
m
c
.
2
0
1
2
.
1
1
.
0
4
8
.
[1
9
]
H.
Lu
o
,
D.
K.
F
y
tan
id
is,
A.
R.
S
c
h
m
id
t,
a
n
d
M
.
H.
G
a
rc
ía,
"
Co
m
p
a
ra
ti
v
e
1
D
a
n
d
3
D
n
u
m
e
rica
l
in
v
e
stig
a
t
io
n
o
f
o
p
e
n
-
c
h
a
n
n
e
l
ju
n
c
ti
o
n
flo
ws
a
n
d
e
n
e
r
g
y
l
o
ss
e
s,"
A
d
v
a
n
c
e
s
in
W
a
ter
Res
o
u
rc
e
s,
v
o
l
.
1
1
7
,
p
p
.
1
2
0
-
1
3
9
,
2
0
1
8
,
d
o
i:
1
0
.
1
0
1
6
/j
.
a
d
v
wa
tres
.
2
0
1
8
.
0
5
.
0
1
2
.
[2
0
]
B.
C.
Ye
n
,
"
Op
e
n
C
h
a
n
n
e
l
F
l
o
w
Re
sista
n
c
e
,
"
J
o
u
rn
a
l
o
f
h
y
d
r
a
u
li
c
e
n
g
in
e
e
rin
g
,
v
o
l.
1
2
8
,
n
o
.
1
,
p
p
.
20
-
3
9
,
2
0
0
2
,
d
o
i:
1
0
.
1
0
6
1
/(AS
CE)
0
7
3
3
-
9
4
2
9
(
2
0
0
2
)
1
2
8
:1
(
2
0
).
[2
1
]
L.
S
c
h
i
n
d
fe
ss
e
l,
S
.
Cre
ë
ll
e
,
a
n
d
T.
De
M
u
ld
e
r,
"
Ho
w
Diffe
re
n
t
Cro
ss
-
S
e
c
ti
o
n
a
l
S
h
a
p
e
s
In
fl
u
e
n
c
e
th
e
S
e
p
a
ra
ti
o
n
Zo
n
e
o
f
a
n
Op
e
n
-
Ch
a
n
n
e
l
Co
n
fl
u
e
n
c
e
,
"
J
o
u
rn
a
l
o
f
Hy
d
r
a
u
l
ic
E
n
g
i
n
e
e
rin
g
,
vo
l.
1
4
3
,
n
o
.
9
,
p
.
0
4
0
1
7
0
3
6
2
0
1
7
,
d
o
i:
1
0
.
1
0
6
1
/(AS
CE)HY.
1
9
4
3
-
7
9
0
0
.
0
0
0
1
3
3
6
.
[2
2
]
A.
K.
P
a
n
d
e
y
a
n
d
R
.
M
ish
ra
,
"
Co
m
p
a
riso
n
o
f
F
lo
w
C
h
a
ra
c
teristics
a
t
Re
c
tan
g
u
lar
a
n
d
Trap
e
z
o
id
a
l
Ch
a
n
n
e
l
Ju
n
c
ti
o
n
s,"
J
o
u
rn
a
l
o
f
Ph
y
sic
s:
Co
n
fer
e
n
c
e
S
e
rie
s,
v
o
l.
3
6
4
,
n
o
.
1
,
p
p
.
1
-
1
1
,
2
0
1
2
,
d
o
i:
1
0
.
1
0
8
8
/
1
7
4
2
-
6
5
9
6
/
3
6
4
/1
/
0
1
2
1
4
1
.
[2
3
]
I.
S
.
M
o
h
d
Zaw
a
wi,
N.
L.
A
b
d
u
ll
a
h
,
H.
Aris
,
B.
A.
Ja
a
fa
r,
N.
A.
H.
No
rwa
z
a
,
a
n
d
M
.
H.
F
.
M
o
h
d
Yu
n
o
s,
"
M
a
th
e
m
a
ti
c
a
l
M
o
d
e
li
n
g
fo
r
F
lo
o
d
M
it
i
g
a
ti
o
n
:
Eff
e
c
t
o
f
Bifu
rc
a
ti
o
n
An
g
les
in
Ri
v
e
r
F
lo
wra
tes
,
"
Ci
v
il
En
g
i
n
e
e
r
in
g
a
n
d
Arc
h
it
e
c
tu
re
v
o
l
.
7
,
n
o
.
6
A,
p
p
.
5
0
-
5
7
,
2
0
1
9
,
d
o
i:
1
0
.
1
3
1
8
9
/ce
a
.
2
0
1
9
.
0
7
1
4
0
6
.
[2
4
]
A.
G
o
li
k
o
v
,
Y
.
G
.
Ev
t
u
sh
e
n
k
o
,
a
n
d
N.
M
o
ll
a
v
e
rd
i
,
"
Ap
p
li
c
a
ti
o
n
o
f
Ne
wt
o
n
'
s
M
e
th
o
d
fo
r
S
o
lv
in
g
Larg
e
Li
n
e
a
r
P
ro
g
ra
m
m
in
g
P
r
o
b
lem
s,"
Co
m
p
u
ta
ti
o
n
a
l
M
a
t
h
e
ma
ti
c
s
a
n
d
M
a
th
e
m
a
ti
c
a
l
Ph
y
sic
s,
v
o
l
.
4
4
,
n
o
.
9
,
p
p
.
1
4
8
4
-
1
4
9
3
,
2
0
0
4
.
[2
5
]
R.
G
u
p
ta,
V.
S
a
wa
rk
a
r,
a
n
d
P
.
Bh
a
v
e
,
"
A
p
p
li
c
a
ti
o
n
o
f
Ne
wto
n
-
Ra
p
h
so
n
M
e
th
o
d
in
O
p
ti
m
a
l
De
sig
n
o
f
Wate
r
Distrib
u
ti
o
n
Ne
two
rk
s,
"
J
o
u
rn
a
l
I
n
d
i
a
n
W
a
ter
wo
rk
s A
ss
o
c
ia
ti
o
n
,
v
o
l.
3
5
,
n
o
.
1
,
p
p
.
3
1
-
3
1
,
2
0
0
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.