Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > State whether the following flow field is ph...
Start Learning for Free
State whether the following flow field is physically possible? u = 3xy2 + 2x + y2 and v = x2 − 2y − y3
- a)Possible for steady incompressible rotational flow
- b)Possible for steady incompressible irrotational flow
- c)Possible for steady compressible rotational flow
- d)Possible for steady compressible irrotational flow
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
State whether the following flow field is physically possible? u = 3x...
Checking for incompressible continuity equation i.e
View all questions of this test
⇒∂u / ∂x + ∂v / ∂y = 3y2 + 2 − 2 − 3y2 = 0 The flow satisfies incompressible continuity equation, so it is incompressible.
Since u and v are not functions of time, flow is steady. Also
∂v / ∂x − ∂u / ∂y = 2x − 6xy − 2y
i.e vorticity is non-zero.
Thus, flow is rotational.
Most Upvoted Answer
State whether the following flow field is physically possible? u = 3x...
Given flow field: u = 3xy^2 + 2x - y^2 and v = x^2 - 2y - y^3
To determine whether the flow field is physically possible, we need to consider certain properties of the flow field such as continuity equation, irrotational flow, and compressibility.
1. Continuity Equation:
The continuity equation for an incompressible flow is given by ∇ · V = 0, where V is the velocity vector field. Let's calculate ∇ · V for the given flow field:
∇ · V = ∂u/∂x + ∂v/∂y
= (3y^2 + 2) + (2x - 2y - 3y^2)
= 2x - 2y
From the continuity equation, it can be observed that the flow field is incompressible only if ∇ · V = 0. In this case, the flow field is incompressible as the equation evaluates to 2x - 2y.
2. Irrotational Flow:
An irrotational flow field has zero vorticity, which means the curl of the velocity vector field (∇ × V) should be zero. Let's calculate ∇ × V for the given flow field:
∇ × V = (∂v/∂x - ∂u/∂y) i + (∂u/∂x + ∂v/∂y) j
= (-2 + 2x - 6y^2) i + (3y^2 + 2 - 2x) j
From the expression for ∇ × V, it can be observed that the flow field is rotational as it has non-zero vorticity.
3. Compressibility:
To determine compressibility, we need to check if the flow field satisfies the compressible flow equations, which are not given in the question. As the equations are not provided, we cannot determine the compressibility of the flow field.
Conclusion:
Based on the analysis above, we can conclude that the given flow field is possible for steady incompressible rotational flow.
To determine whether the flow field is physically possible, we need to consider certain properties of the flow field such as continuity equation, irrotational flow, and compressibility.
1. Continuity Equation:
The continuity equation for an incompressible flow is given by ∇ · V = 0, where V is the velocity vector field. Let's calculate ∇ · V for the given flow field:
∇ · V = ∂u/∂x + ∂v/∂y
= (3y^2 + 2) + (2x - 2y - 3y^2)
= 2x - 2y
From the continuity equation, it can be observed that the flow field is incompressible only if ∇ · V = 0. In this case, the flow field is incompressible as the equation evaluates to 2x - 2y.
2. Irrotational Flow:
An irrotational flow field has zero vorticity, which means the curl of the velocity vector field (∇ × V) should be zero. Let's calculate ∇ × V for the given flow field:
∇ × V = (∂v/∂x - ∂u/∂y) i + (∂u/∂x + ∂v/∂y) j
= (-2 + 2x - 6y^2) i + (3y^2 + 2 - 2x) j
From the expression for ∇ × V, it can be observed that the flow field is rotational as it has non-zero vorticity.
3. Compressibility:
To determine compressibility, we need to check if the flow field satisfies the compressible flow equations, which are not given in the question. As the equations are not provided, we cannot determine the compressibility of the flow field.
Conclusion:
Based on the analysis above, we can conclude that the given flow field is possible for steady incompressible rotational flow.
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
State whether the following flow field is physically possible? u = 3xy2 + 2x + y2 and v = x2 − 2y − y3a) Possible for steady incompressible rotational flowb) Possible for steady incompressible irrotational flowc) Possible for steady compressible rotational flowd) Possible for steady compressible irrotational flowCorrect answer is option 'A'. Can you explain this answer?
Question Description
State whether the following flow field is physically possible? u = 3xy2 + 2x + y2 and v = x2 − 2y − y3a) Possible for steady incompressible rotational flowb) Possible for steady incompressible irrotational flowc) Possible for steady compressible rotational flowd) Possible for steady compressible irrotational flowCorrect answer is option 'A'. 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 State whether the following flow field is physically possible? u = 3xy2 + 2x + y2 and v = x2 − 2y − y3a) Possible for steady incompressible rotational flowb) Possible for steady incompressible irrotational flowc) Possible for steady compressible rotational flowd) Possible for steady compressible irrotational flowCorrect answer is option 'A'. 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 State whether the following flow field is physically possible? u = 3xy2 + 2x + y2 and v = x2 − 2y − y3a) Possible for steady incompressible rotational flowb) Possible for steady incompressible irrotational flowc) Possible for steady compressible rotational flowd) Possible for steady compressible irrotational flowCorrect answer is option 'A'. Can you explain this answer?.
State whether the following flow field is physically possible? u = 3xy2 + 2x + y2 and v = x2 − 2y − y3a) Possible for steady incompressible rotational flowb) Possible for steady incompressible irrotational flowc) Possible for steady compressible rotational flowd) Possible for steady compressible irrotational flowCorrect answer is option 'A'. 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 State whether the following flow field is physically possible? u = 3xy2 + 2x + y2 and v = x2 − 2y − y3a) Possible for steady incompressible rotational flowb) Possible for steady incompressible irrotational flowc) Possible for steady compressible rotational flowd) Possible for steady compressible irrotational flowCorrect answer is option 'A'. 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 State whether the following flow field is physically possible? u = 3xy2 + 2x + y2 and v = x2 − 2y − y3a) Possible for steady incompressible rotational flowb) Possible for steady incompressible irrotational flowc) Possible for steady compressible rotational flowd) Possible for steady compressible irrotational flowCorrect answer is option 'A'. Can you explain this answer?.
Solutions for State whether the following flow field is physically possible? u = 3xy2 + 2x + y2 and v = x2 − 2y − y3a) Possible for steady incompressible rotational flowb) Possible for steady incompressible irrotational flowc) Possible for steady compressible rotational flowd) Possible for steady compressible irrotational flowCorrect answer is option 'A'. 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 State whether the following flow field is physically possible? u = 3xy2 + 2x + y2 and v = x2 − 2y − y3a) Possible for steady incompressible rotational flowb) Possible for steady incompressible irrotational flowc) Possible for steady compressible rotational flowd) Possible for steady compressible irrotational flowCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
State whether the following flow field is physically possible? u = 3xy2 + 2x + y2 and v = x2 − 2y − y3a) Possible for steady incompressible rotational flowb) Possible for steady incompressible irrotational flowc) Possible for steady compressible rotational flowd) Possible for steady compressible irrotational flowCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for State whether the following flow field is physically possible? u = 3xy2 + 2x + y2 and v = x2 − 2y − y3a) Possible for steady incompressible rotational flowb) Possible for steady incompressible irrotational flowc) Possible for steady compressible rotational flowd) Possible for steady compressible irrotational flowCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of State whether the following flow field is physically possible? u = 3xy2 + 2x + y2 and v = x2 − 2y − y3a) Possible for steady incompressible rotational flowb) Possible for steady incompressible irrotational flowc) Possible for steady compressible rotational flowd) Possible for steady compressible irrotational flowCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice State whether the following flow field is physically possible? u = 3xy2 + 2x + y2 and v = x2 − 2y − y3a) Possible for steady incompressible rotational flowb) Possible for steady incompressible irrotational flowc) Possible for steady compressible rotational flowd) Possible for steady compressible irrotational flowCorrect answer is option 'A'. 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