LNS Hydraulic L1-V4
LNS Hydraulic L1-V4
LNS Hydraulic L1-V4
Lecture 1
FUNDAMENTAL CONCEPTS
September 2020
1. PREFACE (1)
4
2. Background (3)
(Source : VT CHOW (1959). Open Channel Hydraulics)
5
2. Background (4)
6
2. Background (5)
7
2. Background (6)
(Source : VT CHOW (1959). Open Channel Hydraulics)
8
2. Background (7)
(Source : VT CHOW (1959). Open Channel Hydraulics)
9
2. Background (8)
(Source : VT CHOW (1959). Open Channel Hydraulics)
10
2. Background (9)
(Source : VT CHOW (1959). Open Channel Hydraulics)
11
2. Background (10)
(Source : VT CHOW (1959). Open Channel Hydraulics)
12
2. Background (11)
(Source : VT CHOW (1959). Open Channel Hydraulics)
13
3. Flow Classifications (1)
Source : ASCE/WEF (1992). Design and Construction of Urban Stormwater Management System
14
3. Flow Classifications (2)
15
3. Flow Classifications (3)
16
3. Flow Classifications (4)
17
3. Flow Classifications (5)
Turbulent Flows
When Re > 2,500*, τ =ρl²(dv/dy)²
where mixing length, l = κy;
von Karman’s constant,κ=0.4
19
3. Flow Classifications (7)
20
3. Flow Classifications (8)
21
3. Flow Classifications (9)
22
3. Flow Classifications (10)
where:
C=
g = acceleration due to gravity = 9.81
Dm = Hydraulic Mean Depth = A/B = y, water depth
(approximately) for wide channel
A = flow cross sectional area
B = top water width
23
3. Flow Classifications (11)
Therefore, Fr = V/c = V/
Fr² = Q² B/(gA³)
To be exact, Fr² = αQ²B/(gA³)
where α = Coriolis Coefficient (Energy
Coefficient to correct for non
uniform velocity distribution over
the flow depth)
24
3. Flow Classifications (12)
25
3. Flow Classifications (13)
Notes:
(a) For simplicity, assume the coefficient, α=1
for most applications.
(b) Froude No. is the most important in Open
Channel Hydraulics and mostly dictates
scale hydraulic modelling
26
3. Flow Classifications (14)
28
3. Flow Classifications (16)
31
4. Conservation Laws (3)
(Source : VT CHOW (1988). Applied Hydrology.)
32
4. Conservation Laws (4)
(Source : VT CHOW (1988). Applied Hydrology.)
33
4. Conservation Laws (5)
(Source : VT CHOW (1988). Applied Hydrology.)
35
4. Conservation Laws (7)
(Source : VT CHOW (1988). Applied Hydrology.)
36
4. Conservation Laws (8)
(Source : VT CHOW (1988). Applied Hydrology.)
37
4. Conservation Laws (9)
(Source : VT CHOW (1988). Applied Hydrology.)
38
4. Conservation Laws (10)
(Source : VT CHOW (1988). Applied Hydrology.)
39
4. Conservation Laws (11)
(Source : VT CHOW (1988). Applied Hydrology.)
40
4. Conservation Laws (12)
(Source : VT CHOW (1988). Applied Hydrology.)
41
4. Conservation Laws (13)
42 m-direction:perpendicular to n, s directions
4. Conservation Laws (14)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
43
4. Conservation Laws (15)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
44
4. Conservation Laws (16)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
45
4. Conservation Laws (17)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
46
4. Conservation Laws (18)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
47
4. Conservation Laws (19)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
48
4. Conservation Laws (20)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
49
4. Conservation Laws (21)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
50
4. Conservation Laws (22)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
51
4. Conservation Laws (23)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
52
4. Conservation Laws (24)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
53
4. Conservation Laws (25)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
54
4. Conservation Laws (26)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
55
4. Conservation Laws (27)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
56
4. Conservation Laws (28)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
57
4. Conservation Laws (29)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
58
4. Conservation Laws (30)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
59
4. Conservation Laws (31)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
60
4. Conservation Laws (32)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
61
4. Conservation Laws (33)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
62
4. Conservation Laws (34)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
63
4. Conservation Laws (35)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
64
4. Conservation Laws (36)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
65
4. Conservation Laws (37)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
66
4. Conservation Laws (38)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
67
4. Conservation Laws (39)
(Source : Bos, Editor (1978). Discharge Measurement Structures.)
68
4. Conservation Laws (40)
F dt = βd (mV)
Where F = Resultant Force (vector quantity) on Control
Volume;
dt = change in time;
d(mV) = change in momentum (vector quantity) across
boundary of Control Volume
β = Boussinesq coefficient (Momentum Correction
Factor)
69
5. Uniform Flow (1)
70
5. Uniform Flow (2)
73
5. Uniform Flow (5)
(Source: VT CHOW (1988); Applied Hydrology)
74
5. Uniform Flow (6)
(Source: VT CHOW (1988); Applied Hydrology)
75
5. Uniform Flow (7)
(Source: VT CHOW (1988); Applied Hydrology)
76
5. Uniform Flow (8)
(Source: VT CHOW (1988); Applied Hydrology)
77
5. Uniform Flow (9)
(Source: VT CHOW (1988); Applied Hydrology)
78
5. Uniform Flow (10)
(Source: VT CHOW (1988); Applied Hydrology)
79
5. Uniform Flow (11)
(Source: VT CHOW (1988); Applied Hydrology)
80
5. Uniform Flow (12)
(Source: VT CHOW (1988); Applied Hydrology)
81
5. Uniform Flow (13)
(Source: VT CHOW (1988); Applied Hydrology)
82
5. Uniform Flow (14)
(Source: VT CHOW (1988); Applied Hydrology)
83
5. Uniform Flow (15)
(Source: VT CHOW (1988); Applied Hydrology)
84
5. Uniform Flow (16)
(Source: Mays (2004). Urban Stormwater Management Tools)
85
5. Uniform Flow (17)
(Source: Mays (2004). Urban Stormwater Management Tools)
86
5. Uniform Flow (18)
(Source: Mays (2004). Urban Stormwater Management Tools)
87
5. Uniform Flow (19)
(Source: Mays (2004). Urban Stormwater Management Tools)
88
5. Uniform Flow (20)
(Source: VT CHOW (1959); Open Channel Hydraulics)
89
5. Uniform Flow (21)
(Source: VT CHOW (1959); Open Channel Hydraulics)
90
5. Uniform Flow (22)
(Source: VT CHOW (1959); Open Channel Hydraulics)
91
5. Uniform Flow (23)
(Source: VT CHOW (1959); Open Channel Hydraulics)
92
5. Uniform Flow (24)
(Source: VT CHOW (1959); Open Channel Hydraulics)
93
5. Uniform Flow (25)
(Source: VT CHOW (1959); Open Channel Hydraulics)
94
5. Uniform Flow (26)
(Source: VT CHOW (1959); Open Channel Hydraulics)
95
5. Uniform Flow (27)
(Source: VT CHOW (1959); Open Channel Hydraulics)
96
5. Uniform Flow (28)
(Source: VT CHOW (1959); Open Channel Hydraulics)
97
5. Uniform Flow (29)
(Source: VT CHOW (1959); Open Channel Hydraulics)
98
5. Uniform Flow (30)
(Source: VT CHOW (1959); Open Channel Hydraulics)
99
5. Uniform Flow (31)
(Source: VT CHOW (1959); Open Channel Hydraulics)
100
5. Uniform Flow (32)
(Source: VT CHOW (1959); Open Channel Hydraulics)
101
5. Uniform Flow (33)
(Source: VT CHOW (1959); Open Channel Hydraulics)
102
5. Uniform Flow (34)
(Source: VT CHOW (1959); Open Channel Hydraulics)
103
5. Uniform Flow (35)
(Source: VT CHOW (1959); Open Channel Hydraulics)
104
6. Critical Flow (1)
(Source: Bos, editor (1978). Discharge Measurement Structures)
105
6. Critical Flow (2)
(Source: Bos, editor (1978). Discharge Measurement Structures)
106
6. Critical Flow (3)
(Source: Bos, editor (1978). Discharge Measurement Structures)
107
6. Critical Flow (4)
(Source: Bos, editor (1978). Discharge Measurement Structures)
108
6. Critical Flow (5)
(Source: Bos, editor (1978). Discharge Measurement Structures)
Direction of flow
Hydraulic Jump - 2
Direction of flow
109
6. Critical Flow (6)
(Source: Bos, editor (1978). Discharge Measurement Structures)
Hydraulic Jump - 4
Direction of flow
110
6. Critical Flow (7)
(Source: Bos, editor (1978). Discharge Measurement Structures)
111
6. Critical Flow (8)
(Source: Bos, editor (1978). Discharge Measurement Structures)
113
6. Critical Flow (10)
(Source: Bos, editor (1978). Discharge Measurement Structures)
114
6. Critical Flow (11)
(Source: Bos, editor (1978). Discharge Measurement Structures)
115
6. Critical Flow (12)
(Source: Bos, editor (1978). Discharge Measurement Structures)
116
6. Critical Flow (13)
(Source: Bos, editor (1978). Discharge Measurement Structures)
117
6. Critical Flow (14)
(Source: Bos, editor (1978). Discharge Measurement Structures)
118
6. Critical Flow (15)
(Source: Bos, editor (1978). Discharge Measurement Structures)
119
6. Critical Flow (16)
(Source: Bos, editor (1978). Discharge Measurement Structures)
120 Flow over a round-noise broad-created weir with rectangular control section
6. Critical Flow (17)
(Source: Bos, editor (1978). Discharge Measurement Structures)
121
6. Critical Flow (18)
(Source: Bos, editor (1978). Discharge Measurement Structures)
122
6. Critical Flow (19)
(Source: Bos, editor (1978). Discharge Measurement Structures)
123
6. Critical Flow (20)
(Source: Bos, editor (1978). Discharge Measurement Structures)
124
6. Critical Flow (21)
(Source: Bos, editor (1978). Discharge Measurement Structures)
125
6. Critical Flow (22)
(Source: Bos, editor (1978). Discharge Measurement Structures)
126
6. Critical Flow (23)
(Source: Bos, editor (1978). Discharge Measurement Structures)
127
6. Critical Flow (24)
(Source: Bos, editor (1978). Discharge Measurement Structures)
128
6. Critical Flow (25)
(Source: Bos, editor (1978). Discharge Measurement Structures)
129
6. Critical Flow (26)
(Source: Bos, editor (1978). Discharge Measurement Structures)
130
6. Critical Flow (27)
(Source: Bos, editor (1978). Discharge Measurement Structures)
131
6. Critical Flow (28)
(Source: Bos, editor (1978). Discharge Measurement Structures)
132
6. Critical Flow (29)
(Source: Bos, editor (1978). Discharge Measurement Structures)
133
6. Critical Flow (30)
(Source: Bos, editor (1978). Discharge Measurement Structures)
134
6. Critical Flow (31)
(Source: Bos, editor (1978). Discharge Measurement Structures)
135
6. Critical Flow (32)
(Source: Bos, editor (1978). Discharge Measurement Structures)
136
6. Critical Flow (33)
(Source: Bos, editor (1978). Discharge Measurement Structures)
137
6. Critical Flow (34)
(Source: Bos, editor (1978). Discharge Measurement Structures)
138
6. Critical Flow (35)
(Source: Bos, editor (1978). Discharge Measurement Structures)
139
6. Critical Flow (36)
(Source: Bos, editor (1978). Discharge Measurement Structures)
140
6. Critical Flow (37)
(Source: Bos, editor (1978). Discharge Measurement Structures)
141
6. Critical Flow (38)
(Source: Bos, editor (1978). Discharge Measurement Structures)
142
6. Critical Flow (39)
(Source: Bos, editor (1978). Discharge Measurement Structures)
143
6. Critical Flow (40)
(Source: Bos, editor (1978). Discharge Measurement Structures)
144
6. Critical Flow (41)
(Source: Bos, editor (1978). Discharge Measurement Structures)
145
6. Critical Flow (42)
(Source: Bos, editor (1978). Discharge Measurement Structures)
146
6. Critical Flow (43)
(Source: Bos, editor (1978). Discharge Measurement Structures)
147
6. Critical Flow (44)
(Source: Bos, editor (1978). Discharge Measurement Structures)
148
6. Critical Flow (45)
(Source: Bos, editor (1978). Discharge Measurement Structures)
149
6. Critical Flow (46)
(Source: Bos, editor (1978). Discharge Measurement Structures)
150
6. Critical Flow (47)
(Source: Bos, editor (1978). Discharge Measurement Structures)
151
6. Critical Flow (48)
(Source: Bos, editor (1978). Discharge Measurement Structures)
152
6. Critical Flow (49)
(Source: Bos, editor (1978). Discharge Measurement Structures)
153
6. Critical Flow (50)
(Source: Bos, editor (1978). Discharge Measurement Structures)
154
6. Critical Flow (51)
(Source: Bos, editor (1978). Discharge Measurement Structures)
155
6. Critical Flow (52)
(Source: Bos, editor (1978). Discharge Measurement Structures)
156
6. Critical Flow (53)
(Source: Bos, editor (1978). Discharge Measurement Structures)
157
6. Critical Flow (54)
(Source: Bos, editor (1978). Discharge Measurement Structures)
158
6. Critical Flow (55)
(Source: Bos, editor (1978). Discharge Measurement Structures)
159
6. Critical Flow (56)
(Source: Bos, editor (1978). Discharge Measurement Structures)
160
6. Critical Flow (57)
(Source: Bos, editor (1978). Discharge Measurement Structures)
161
6. Critical Flow (58)
(Source: VT CHOW (1959); Open Channel Hydraulics)
162
6. Critical Flow (59)
(Source: VT CHOW (1959); Open Channel Hydraulics)
163
6. Critical Flow (60)
(Source: VT CHOW (1959); Open Channel Hydraulics)
164
6. Critical Flow (61)
(Source: VT CHOW (1959); Open Channel Hydraulics)
165
6. Critical Flow (62)
(Source: VT CHOW (1959); Open Channel Hydraulics)
166
6. Critical Flow (63)
(Source: VT CHOW (1959); Open Channel Hydraulics)
167
6. Critical Flow (64)
(Source: VT CHOW (1959); Open Channel Hydraulics)
168
6. Critical Flow (65)
(Source: VT CHOW (1959); Open Channel Hydraulics)
169
6. Critical Flow (66)
(Source: VT CHOW (1959); Open Channel Hydraulics)
170
6. Critical Flow (67)
(Source: VT CHOW (1959); Open Channel Hydraulics)
171
6. Critical Flow (68)
(Source: VT CHOW (1959); Open Channel Hydraulics)
172
6. Critical Flow (69)
(Source: VT CHOW (1959); Open Channel Hydraulics)
173
6. Critical Flow (70)
(Source: VT CHOW (1959); Open Channel Hydraulics)
174
6. Critical Flow (71)
(Source: VT CHOW (1959); Open Channel Hydraulics)
175
6. Critical Flow (72)
(Source: VT CHOW (1959); Open Channel Hydraulics)
176
6. Critical Flow (73)
(Source: VT CHOW (1959); Open Channel Hydraulics)
177
6. Critical Flow (74)
(Source: VT CHOW (1959); Open Channel Hydraulics)
178
6. Critical Flow (75)
(Source: VT CHOW (1959); Open Channel Hydraulics)
179
6. Critical Flow (76)
(Source: VT CHOW (1959); Open Channel Hydraulics)
180
6. Critical Flow (77)
(Source: VT CHOW (1959); Open Channel Hydraulics)
181
6. Critical Flow (78)
(Source: VT CHOW (1959); Open Channel Hydraulics)
182
6. Critical Flow (79)
(Source: VT CHOW (1959); Open Channel Hydraulics)
183
6. Critical Flow (80)
(Source: VT CHOW (1959); Open Channel Hydraulics)
184
7. References (1)
Thank You
pkeungchan@gmail.com
pkchan54@hku.hk
186