Problem 7 Water is flowing in a channel with a rectangular cross-section. The channel has a uniform width of b 10 m, and it is equipped with a broad-crested weir. The height of flow in a channel far upstream of the weir is h₁ 2 m, while the weir is == hweir = 0.8 m above the bed of the channel. = 1. Assuming the flow over the weir is critical, calculate the flow rate in the channel by iteratively solving for the critical depth he. Perform at least 3 iterations. Did the flow rate converge? 2. Given the water depth immediately downstream of the weir is 90% of the critical depth hc, what is the water depth after the flow experiences a hydraulic jump further downstream? 3. How much energy is dissipated by the hydraulic jump? h₁ hweir Figure 7: A subcritical flow goes over a broad-crested weir, and it experiences a hydraulic jump downstream of the weir. Figure not to scale. Open Channel Flow - Rectangular Cross-section իշ h₁ = 12 u² h₁+1 + 2g h₂+22 ལ།དྲ་ 2g Fr (Conservation of energy) U √gh (Froude number) gh h₁ Q=b21 r = (Venturi flume) h₂ 2 = b√gh23 (Broad-crested weir) h1 ≈ 0.61; Q = bCchgate 2ght h₁ + Cchgate h2 Cc = hgate 1 h₁ h₁ H2 h2 (2+ Fr = 1+8Fr - Fr 1+ 2 h₂ h2 H₁ h₁ 2+ Fr (Sluice gate) (Hydraulic jump) Generalized Poiseuille's law for flow in a tube R² (dp Uavg 8μ ( + pgsina ds
Problem 7 Water is flowing in a channel with a rectangular cross-section. The channel has a uniform width of b 10 m, and it is equipped with a broad-crested weir. The height of flow in a channel far upstream of the weir is h₁ 2 m, while the weir is == hweir = 0.8 m above the bed of the channel. = 1. Assuming the flow over the weir is critical, calculate the flow rate in the channel by iteratively solving for the critical depth he. Perform at least 3 iterations. Did the flow rate converge? 2. Given the water depth immediately downstream of the weir is 90% of the critical depth hc, what is the water depth after the flow experiences a hydraulic jump further downstream? 3. How much energy is dissipated by the hydraulic jump? h₁ hweir Figure 7: A subcritical flow goes over a broad-crested weir, and it experiences a hydraulic jump downstream of the weir. Figure not to scale. Open Channel Flow - Rectangular Cross-section իշ h₁ = 12 u² h₁+1 + 2g h₂+22 ལ།དྲ་ 2g Fr (Conservation of energy) U √gh (Froude number) gh h₁ Q=b21 r = (Venturi flume) h₂ 2 = b√gh23 (Broad-crested weir) h1 ≈ 0.61; Q = bCchgate 2ght h₁ + Cchgate h2 Cc = hgate 1 h₁ h₁ H2 h2 (2+ Fr = 1+8Fr - Fr 1+ 2 h₂ h2 H₁ h₁ 2+ Fr (Sluice gate) (Hydraulic jump) Generalized Poiseuille's law for flow in a tube R² (dp Uavg 8μ ( + pgsina ds
Fundamentals of Geotechnical Engineering (MindTap Course List)
5th Edition
ISBN:9781305635180
Author:Braja M. Das, Nagaratnam Sivakugan
Publisher:Braja M. Das, Nagaratnam Sivakugan
Chapter7: Seepage
Section: Chapter Questions
Problem 7.6P
Related questions
Question
Transcribed Image Text:Problem 7
Water is flowing in a channel with a rectangular cross-section. The
channel has a uniform width of b 10 m, and it is equipped with a broad-crested weir.
The height of flow in a channel far upstream of the weir is h₁ 2 m, while the weir is
==
hweir
=
0.8 m above the bed of the channel.
=
1. Assuming the flow over the weir is critical, calculate the flow rate in the channel by
iteratively solving for the critical depth he. Perform at least 3 iterations. Did the flow
rate converge?
2. Given the water depth immediately downstream of the weir is 90% of the critical
depth hc, what is the water depth after the flow experiences a hydraulic jump further
downstream?
3. How much energy is dissipated by the hydraulic jump?
h₁
hweir
Figure 7: A subcritical flow goes over a broad-crested weir, and it experiences a hydraulic jump
downstream of the weir. Figure not to scale.
Transcribed Image Text:Open Channel Flow - Rectangular Cross-section
իշ
h₁
=
12
u²
h₁+1 +
2g
h₂+22
ལ།དྲ་
2g
Fr
(Conservation of energy)
U
√gh
(Froude number)
gh
h₁
Q=b21
r =
(Venturi flume)
h₂
2 = b√gh23 (Broad-crested weir)
h1
≈ 0.61; Q = bCchgate 2ght h₁ + Cchgate
h2
Cc =
hgate
1 h₁
h₁
H2
h2 (2+ Fr
=
1+8Fr
-
Fr
1+
2 h₂
h2
H₁
h₁ 2+ Fr
(Sluice gate)
(Hydraulic jump)
Generalized Poiseuille's law for flow in a tube
R² (dp
Uavg
8μ
(
+ pgsina
ds
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 3 images
Recommended textbooks for you
Fundamentals of Geotechnical Engineering (MindTap…
Civil Engineering
ISBN:
9781305635180
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
Principles of Geotechnical Engineering (MindTap C…
Civil Engineering
ISBN:
9781305970939
Author:
Braja M. Das, Khaled Sobhan
Publisher:
Cengage Learning
Traffic and Highway Engineering
Civil Engineering
ISBN:
9781305156241
Author:
Garber, Nicholas J.
Publisher:
Cengage Learning
Fundamentals of Geotechnical Engineering (MindTap…
Civil Engineering
ISBN:
9781305635180
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
Principles of Geotechnical Engineering (MindTap C…
Civil Engineering
ISBN:
9781305970939
Author:
Braja M. Das, Khaled Sobhan
Publisher:
Cengage Learning
Traffic and Highway Engineering
Civil Engineering
ISBN:
9781305156241
Author:
Garber, Nicholas J.
Publisher:
Cengage Learning
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781305081550
Author:
Braja M. Das
Publisher:
Cengage Learning