The ratio of the upstream depth to downstream depth in a hydraulic jump for a rectangular, horizontal channel is given by: Y2 Y₁ = 1 [√ 1+8F 1] - This was derived using the steady, momentum equation which is written as: 0² Z₁ A₁ + ₁ = Z₂ A₂ gA₂ Note that the momentum equation above assumes that the bottom shearing force is negligible in a horizontal channel (i.e., zero bottom slope). a) Derive the hydraulic equation above (i.e., y2/yı).
The ratio of the upstream depth to downstream depth in a hydraulic jump for a rectangular, horizontal channel is given by: Y2 Y₁ = 1 [√ 1+8F 1] - This was derived using the steady, momentum equation which is written as: 0² Z₁ A₁ + ₁ = Z₂ A₂ gA₂ Note that the momentum equation above assumes that the bottom shearing force is negligible in a horizontal channel (i.e., zero bottom slope). a) Derive the hydraulic equation above (i.e., y2/yı).
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
Please answer item a and b.
![The ratio of the upstream depth to downstream depth in a hydraulic jump for a
rectangular, horizontal channel is given by:
Y2
12/21 - 12/2√₁ +8F² 1]
1
Y₁
This was derived using the steady, momentum equation which is written as:
Z₁ A₁ +
-
=
gA₁ Z₂ A₂+
gA₂
Note that the momentum equation above assumes that the bottom shearing force
is negligible in a horizontal channel (i.e., zero bottom slope).
a)
Derive the hydraulic equation above (i.e., y2/yı).
b)
For the case where the channel slope is significant and that the bed friction
force is not negligible, derive the equation of y2/y1 for a rectangular channel.
If needed, use Manning's equation to express the friction force.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F127c2ae9-d4df-4711-a4a7-28776b6c0062%2F8ad9ac02-c183-4c75-b17f-c05c1aa45d2b%2Fp95avw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The ratio of the upstream depth to downstream depth in a hydraulic jump for a
rectangular, horizontal channel is given by:
Y2
12/21 - 12/2√₁ +8F² 1]
1
Y₁
This was derived using the steady, momentum equation which is written as:
Z₁ A₁ +
-
=
gA₁ Z₂ A₂+
gA₂
Note that the momentum equation above assumes that the bottom shearing force
is negligible in a horizontal channel (i.e., zero bottom slope).
a)
Derive the hydraulic equation above (i.e., y2/yı).
b)
For the case where the channel slope is significant and that the bed friction
force is not negligible, derive the equation of y2/y1 for a rectangular channel.
If needed, use Manning's equation to express the friction force.
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 4 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
Fundamentals of Structural Analysis
Civil Engineering
ISBN:
9780073398006
Author:
Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:
McGraw-Hill Education
Traffic and Highway Engineering
Civil Engineering
ISBN:
9781305156241
Author:
Garber, Nicholas J.
Publisher:
Cengage Learning