➨❶ タ ィ ὥỈࡢタィ ὥỈ ࠊࡣタィὥỈὶ㔞௨ୗࡢὶỈᏳὶୗ ࠊࡏࡉ㈓Ỉ␗ࡢᖖ࡞㜵Ṇࡍᵓ㐀ࡍ ࠋࠊࡓὥỈὶୗࡍὶỈࡢỈໃ⦆ࡍᚲせ࠶ࡀሙࠊࡣ㐺ᙜ࡞ῶໃᕤタࡅࡢ ࡍ㹿 ࠊ࠾࡞ὥỈࡓࠊࡣụࡢሐయཬࡧᇶ♏ᆅ┙୪ࡧ㈓Ỉụᨭ㞀ཬ࠸࡞ࡉᵓ㐀ࡍࠋ ὥỈࡢᵓᡂ ὥỈࠊࡣὶධ㒊ࠊᑟὶ㒊ཬࡧῶໃ㒊ࡗᵓᡂࡉ㹿 ὥỈࡢᵓᡂ ࠊࡣᅗ ♧ࡍ࠺ ࠊὶධ㒊㸦᥋㏆Ỉ㊰ ࠊㄪ㒊⾜⛣ࠊ㒊㸧 ࠊᑟὶ㒊㸦ᨺỈ㊰㸧 ࠊῶໃ 㒊㸦ῶໃᕤ㸧ࡗ࡞࠾ࠊタィὥỈὶ㔞௨ୗࡢὶỈࡀᏳὶୗࡁ࠺タィࡍࠋ ὥỈࠊࡣⰋ㉁࡞ᆅ┙タ⨨ࠊࡋỿୗࠊᾐ㏱ὶ࠸࡞ࡌ⏕ࡀ࠺༑ศ࡞ฎ⌮ࠋࡍ ࡓụ ὥỈ 㒊 ὶἣ ᥋ ㏆ Ỉ ㊰ ᖖ ὶ ⛣⾜㒊 㝈⏺ὶ ㄪ 㒊 ᨺỈ㊰ ᑕὶ ῶໃᕤ ㊴ Ỉ ฟỈ㊰ ᖖ ὶ FWL HWL ࠊ㉺ὶሖ ᨺỈ㊰ ࠊ㟼Ỉụ ᆅ ᒣ ሐయୗὶ㠃 ሐ㡬 ሐ㍈ᅗ ὥỈࡢᵓᡂ 63
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FWL HWL
63
HWL
HWL
HWL
1.5
1.5
64
a b c
d e f
g
65
m s
V P
Hd
d
hv
HP
V m s
d
V
AdQ m s
A d L
d Hd Pg
V
V m sA md mQd m sL mHd mP mg m s
66
m
mm
B=d
d
HC
Q
B mQd m sC
° Hd B
Hd B
B
Hd m
Bdd
d
HCQ
B mQd m sCd m s
Cd
Hd m
67
Hd Hd
B
hv
HdHd
hv
B
68
YdH
X
Y mX mHd m
p
Xp Hd n
np n
Xp p X m
a Hd mb Hd mc Hd m
d Hd mr Hd mr Hd m
Hd m
hv
d
a
rr
b
n
p
Y
X
Hd
Yp
Xp
c
········································································································· (3.4.6)
69
Hd
d
d
Hdh
d
d
Hh
Hd m
hv
hd
P
Hd
d
Qd Cd B HdQd m s Cd m s B m Hd m P m
Cd
P Hd
Hd
P
HP d
70
Hd P
Cd PHd
C
d
d
HHa
HHa
H mHd mP mCCd H Hd
a a H Hd C Cd
Cd
Hd Hd
P
HWL HWL
T
P RT P
T
Hd Hd
R RR Hd HdR Hd
HWL Hd
71
B
A
R
T
R
T
R
T
A
Bt
Bc Bc
R
T
Hd
A
A A
A
B
A A
72
B B Ka Hd
Bt B Bc
B m B mKa
Hd mBt mBc m
d
d
Hdh
d
d
Hh
d
d
Hh
hd d Hd P
P Hd
C
P Hd R1
P/Hd 0.2 0.5 1 2 5
1.8 1.8 2 R1 Hd 0.5Hd 1.8 2
1/4 2.1 2.1 1.84 2.1 2 1.83
( ) 2.0 2.1 2.15 2.16 2.18
······································································································· (3.4.10)
73
b b
74
b b
Hd
P Levelh Vhv h
V
l l
hVA B C
V g
V g
V VgK hm
h V
P Hd h hv Z hg
V Z hhbg
dQ Z
P m Hd m h m hv m
Z m
V m sg m sQd m sb m
h l V l
rFhg
V
hh
rF
l h
Vhb
dQ
·········································································· (3.4.15)
75
Fr
h B ml mV B m s
BC
B hg
V hg
Vg
VVKhm
h C m
hbg
dQ
b C mV C m s
Vhb
dQ
Khm m
hm lII
IR
Vn IR
Vn
n I I R B mR C m
B CA B
C
76
b
VV g
V VgK hm
V g
A B
h V
b
h
L
B
dy
Hd
Hd
d
B
l
i i
X
y
B
d
77
m
s
iB d d B
Fr
DgVFr
m sg m s
D A T mA mT m
1/2.5
m q
m 0 q
Fr
dgV
Bdm
BdmBd
rFgQ ···························································································· (3.4.17)
m 0.7 m d / B 0.5
78
d 0.463rF
Q ( m s ) ··········································································································· (3.4.18)
0.44 0.5 d (0.643 0.61) Q2/5 (m s ) ································································································· (3.4.19)
A
A (B dm ) d (3.4.20)
X Bx (m) Zx (m)
Bx
LXB 11 ················································································································· (3.4.21)
Zx i1 X B (m)
B /B B /B 0.5 B X (m) L (m) B i1 1/13
l (m) l 4 d ························································································································· (3.4.22)
d (m) i2
i2 g n2 Fr 2d
Bd
···································································································· (3.4.23)
n
Bx B
a
Wt
b
Hd
Bx
B
d
R s
m
qd Qd Wt
qd Qd Wt
a b a a
b b
79
p
i
hQQQ
Q XVqVg
VV
h X mQ a m sQ a m sV a m sV a m sq m s m
V V V m sg m s
a a
d d
QQVV
X
h
80
hp
B L i
l
V g
V g
hm
A
B
d
d
V
Vhs
l
81
ms hg
Vdhg
Vd
d A mV m sd B mV m shs mhm m
m
mm R
lVnh
VVVm
RRRm
n R mR m l m
82
USBR III
m s mm s
USBR IV
d
Fdd
1
F
C
g
FF
FFF
dW
d md m
Fdg
V
V m s
83
W mC m s Cg m s
d
d
d L d
W
USBR III
m s m m s
dd1 F1
LIII 3 d2
84
d
d
d Lm
Lm
h
d
d hW h
S hS dh d
h h
W d
III
h h
h
F Vgd
d h
d h
III IV
85
USBR IVF
III d
LIV
W d
h d
Wd min
LIV IV
d LIV
F IV
m s m s
86
A
A
V
W tw
b
tw
tw cmtw
cm
a
cm
W
W
t p W
W
W
cm
A A
W W
W
b
t w
W
c
cm
W tb W
cm
cm
b
cmQ
m /s a b c tw tf tb tp
W Q
Q m sW
m
W
Yq q Q
H
Y
V
d
TW
q
b b
87
I III or IV
He
P
Y
Ld
df dd
VTW
hd
LI III or IVX
Ld
USBR III USBR IVLd D hd He Y
d d F D Yq
YdF
Yd
YgqD c
q m s mg m sY m
dcg
qm
Fdg
V
dVq
m
V m sd d F
USBR III IV F
FUSBR I
88
F USBR IVF USBR III
USBR I
F
D
hd
Lp
LB Lp dc
dc dc
dc
TW dc
He
P
He
P
Y
Ld LI III or IV
df dd TW
hd
Lp Y hd He
Lp Y hd HeLp Y hd He
Lp Y hd He
Lp Y hd He
F V g d
Ld Y hd He
Ld Y hd He
Ld Y hd He
Ld Y hd He
Ld Y hd He
dc Y
df Yd Y
d Y
V d F Xdc df
Y
V
X
89
m dc dc
q q gY hd
dc Lp Lp Dhd He Y
dc
He
P
Y
Lp
LB Lp+ dc
hd
dc
dc
dcTW dc
90
LGW
He
LB
TW He
eG
HgNWL Q m
Q m sW mN g m s
mm W
m He
m LG
USBR IVd d Q d Y Q
q
91
Fb dg
V
Fb m g m sV m s d m
Fb C V dFb mC V m s d m
m
Fb V dFb m V m sd m
m
m
HWL HWL
92
E N D
START
No
Yes
No
Yes
93
1) L L (3 5)H 2)
H
L
94
Westergaard
hbKP whew
hhew
Pew kNKh
w kN mh mb mhew m
hew
Pe wh
Westergaard V
·················································································· (3.4.33)
95
1) 2)
96
1) 2)
97
END
T
START
END
OK
NO
98
1) 2)
99
1) 2)
100
(N/mm2)
SD295 176 264
157 264
SD345 196 294
176 294
( ck 21N/mm2)
8 12
0.42 0.63
1.5 2.25
( ck 24N/mm2)
9 13.5
0.45 0.67
1.6 2.4
101
h m h m
h h
m m m
m
A
RHWLFWL
102
mmm m mm m
(mm) (mm)
200 150 230
200 300 200 250
300 400 230 300
400 300
cm
TT/2
T/2
T/2 T
T/2
103
(VP)
D13mm 16mm D16mm 20mm L 500mm
D16 19mm 19mm D19mm 25mm L 500mm
D22mm 25mm D25mm 30mm L 500mm
1) U.S.Bureau of Reclamation Design of Small Dams
D.R.Waldron Design of Labyrinth Weirs, MSc thesis, Utah State Univ.
D.S.Miller Discharge Characteristics, Balkena PublishersN.Hay,G.Taylor Performance and Design of Labyrinth Weirs, Jour. of HY,ASCE
T/2
T/2
T VP
500 m 500 m
104
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