Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > A rectangular open channel of 6 m width is ca...
Start Learning for Free
A rectangular open channel of 6 m width is carrying discharge of 20 m3/s . Consider the acceleration due to gravity as 9.81m/s2 and assume water as incompressible and inviscid. The depth of flow in the channel at which the specific energy of the flowing water is minimum for given discharge will then be:
- a)2.56 m
- b)0.82 m
- c)1.04 m
- d)3.18 m
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A rectangular open channel of 6 m width is carrying discharge of 20 m3...
The specific energy of flowing water in an open channel is the sum of its elevation head and velocity head. The elevation head represents the potential energy of the water, while the velocity head represents the kinetic energy of the water.
To find the depth of flow at which the specific energy is minimum, we need to calculate the specific energy for different depths and determine the depth that gives the lowest value.
Given data:
Width of the channel (b) = 6 m
Discharge (Q) = 20 m3/s
Acceleration due to gravity (g) = 9.81 m/s2
The specific energy (E) is given by the equation:
E = (y + V^2 / 2g) + z
Where:
y = depth of flow
V = velocity of flow
z = elevation of the channel bottom
To find the depth of flow at which the specific energy is minimum, we will differentiate the specific energy equation with respect to y and equate it to zero.
Calculations:
1. Velocity of flow (V):
Q = b * y * V
20 = 6 * y * V
V = 20 / (6y)
2. Elevation of the channel bottom (z):
Assuming the channel bottom is at a constant elevation, z can be considered zero.
3. Specific energy equation:
E = (y + V^2 / 2g) + z
Substituting the values of V and z into the equation:
E = (y + (20 / (6y))^2 / 2 * 9.81) + 0
E = (y + 100 / (3y^2)) + 0
E = (3y^3 + 100) / (3y^2)
To find the minimum specific energy, we differentiate E with respect to y and equate it to zero:
dE/dy = (9y^2 - 200) / (3y^3) = 0
Solving the equation:
9y^2 - 200 = 0
y^2 = 200 / 9
y = √(200 / 9)
y ≈ 1.04 m
Therefore, the depth of flow in the channel at which the specific energy of the flowing water is minimum for the given discharge is approximately 1.04 m. Hence, the correct answer is option C.
To find the depth of flow at which the specific energy is minimum, we need to calculate the specific energy for different depths and determine the depth that gives the lowest value.
Given data:
Width of the channel (b) = 6 m
Discharge (Q) = 20 m3/s
Acceleration due to gravity (g) = 9.81 m/s2
The specific energy (E) is given by the equation:
E = (y + V^2 / 2g) + z
Where:
y = depth of flow
V = velocity of flow
z = elevation of the channel bottom
To find the depth of flow at which the specific energy is minimum, we will differentiate the specific energy equation with respect to y and equate it to zero.
Calculations:
1. Velocity of flow (V):
Q = b * y * V
20 = 6 * y * V
V = 20 / (6y)
2. Elevation of the channel bottom (z):
Assuming the channel bottom is at a constant elevation, z can be considered zero.
3. Specific energy equation:
E = (y + V^2 / 2g) + z
Substituting the values of V and z into the equation:
E = (y + (20 / (6y))^2 / 2 * 9.81) + 0
E = (y + 100 / (3y^2)) + 0
E = (3y^3 + 100) / (3y^2)
To find the minimum specific energy, we differentiate E with respect to y and equate it to zero:
dE/dy = (9y^2 - 200) / (3y^3) = 0
Solving the equation:
9y^2 - 200 = 0
y^2 = 200 / 9
y = √(200 / 9)
y ≈ 1.04 m
Therefore, the depth of flow in the channel at which the specific energy of the flowing water is minimum for the given discharge is approximately 1.04 m. Hence, the correct answer is option C.
Free Test
FREE
| Start Free Test |
Community Answer
A rectangular open channel of 6 m width is carrying discharge of 20 m3...
Given :
Width of channel, (B) = 6 m
Discharge of channel, (Q) = 20 m3 /sec
∴ Depth of flow at which SE will be minimum is critical depth and is value 1.04 m.
Hence, the correct option is (C).
Width of channel, (B) = 6 m
Discharge of channel, (Q) = 20 m3 /sec
∴ Depth of flow at which SE will be minimum is critical depth and is value 1.04 m.
Hence, the correct option is (C).
Attention Civil Engineering (CE) Students!
To make sure you are not studying endlessly, EduRev has designed Civil Engineering (CE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Civil Engineering (CE).
|
Explore Courses for Civil Engineering (CE) exam
|
|
Similar Civil Engineering (CE) Doubts
Top Courses for Civil Engineering (CE)View all
A rectangular open channel of 6 m width is carrying discharge of 20 m3/s . Consider the acceleration due to gravity as 9.81m/s2 and assume water as incompressible and inviscid. The depth of flow in the channel at which the specific energy of the flowing water is minimum for given discharge will then be:a)2.56 m b)0.82 mc)1.04 md)3.18 mCorrect answer is option 'C'. Can you explain this answer?
Question Description
A rectangular open channel of 6 m width is carrying discharge of 20 m3/s . Consider the acceleration due to gravity as 9.81m/s2 and assume water as incompressible and inviscid. The depth of flow in the channel at which the specific energy of the flowing water is minimum for given discharge will then be:a)2.56 m b)0.82 mc)1.04 md)3.18 mCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A rectangular open channel of 6 m width is carrying discharge of 20 m3/s . Consider the acceleration due to gravity as 9.81m/s2 and assume water as incompressible and inviscid. The depth of flow in the channel at which the specific energy of the flowing water is minimum for given discharge will then be:a)2.56 m b)0.82 mc)1.04 md)3.18 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular open channel of 6 m width is carrying discharge of 20 m3/s . Consider the acceleration due to gravity as 9.81m/s2 and assume water as incompressible and inviscid. The depth of flow in the channel at which the specific energy of the flowing water is minimum for given discharge will then be:a)2.56 m b)0.82 mc)1.04 md)3.18 mCorrect answer is option 'C'. Can you explain this answer?.
A rectangular open channel of 6 m width is carrying discharge of 20 m3/s . Consider the acceleration due to gravity as 9.81m/s2 and assume water as incompressible and inviscid. The depth of flow in the channel at which the specific energy of the flowing water is minimum for given discharge will then be:a)2.56 m b)0.82 mc)1.04 md)3.18 mCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A rectangular open channel of 6 m width is carrying discharge of 20 m3/s . Consider the acceleration due to gravity as 9.81m/s2 and assume water as incompressible and inviscid. The depth of flow in the channel at which the specific energy of the flowing water is minimum for given discharge will then be:a)2.56 m b)0.82 mc)1.04 md)3.18 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular open channel of 6 m width is carrying discharge of 20 m3/s . Consider the acceleration due to gravity as 9.81m/s2 and assume water as incompressible and inviscid. The depth of flow in the channel at which the specific energy of the flowing water is minimum for given discharge will then be:a)2.56 m b)0.82 mc)1.04 md)3.18 mCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A rectangular open channel of 6 m width is carrying discharge of 20 m3/s . Consider the acceleration due to gravity as 9.81m/s2 and assume water as incompressible and inviscid. The depth of flow in the channel at which the specific energy of the flowing water is minimum for given discharge will then be:a)2.56 m b)0.82 mc)1.04 md)3.18 mCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
Here you can find the meaning of A rectangular open channel of 6 m width is carrying discharge of 20 m3/s . Consider the acceleration due to gravity as 9.81m/s2 and assume water as incompressible and inviscid. The depth of flow in the channel at which the specific energy of the flowing water is minimum for given discharge will then be:a)2.56 m b)0.82 mc)1.04 md)3.18 mCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A rectangular open channel of 6 m width is carrying discharge of 20 m3/s . Consider the acceleration due to gravity as 9.81m/s2 and assume water as incompressible and inviscid. The depth of flow in the channel at which the specific energy of the flowing water is minimum for given discharge will then be:a)2.56 m b)0.82 mc)1.04 md)3.18 mCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A rectangular open channel of 6 m width is carrying discharge of 20 m3/s . Consider the acceleration due to gravity as 9.81m/s2 and assume water as incompressible and inviscid. The depth of flow in the channel at which the specific energy of the flowing water is minimum for given discharge will then be:a)2.56 m b)0.82 mc)1.04 md)3.18 mCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A rectangular open channel of 6 m width is carrying discharge of 20 m3/s . Consider the acceleration due to gravity as 9.81m/s2 and assume water as incompressible and inviscid. The depth of flow in the channel at which the specific energy of the flowing water is minimum for given discharge will then be:a)2.56 m b)0.82 mc)1.04 md)3.18 mCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A rectangular open channel of 6 m width is carrying discharge of 20 m3/s . Consider the acceleration due to gravity as 9.81m/s2 and assume water as incompressible and inviscid. The depth of flow in the channel at which the specific energy of the flowing water is minimum for given discharge will then be:a)2.56 m b)0.82 mc)1.04 md)3.18 mCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
|
|
Explore Courses for Civil Engineering (CE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup