Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > The velocity potential function of a flow fi...
Start Learning for Free
The velocity potential function of a flow field is given by x2 − y2 + constant. Its stream function will be given by
- a)− 2xy + constant
- b)+ 2xy + constant
- c)− 2xy + f(x)
- d)− 2xy + f(y)
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The velocity potential function of a flow field is given by x2 − y2 +...
Φ = x2 − y2 + C
View all questions of this test
∂ϕ / ∂x = −u and ∂ϕ / ∂y = −v
hence u = −2x and v = +2y
Also
∂ψ / ∂y = u ⟹ ∂ψ / ∂y = −2x ⋯ ①
and
∂ψ / ∂x = −v ⟹ ∂ψ / ∂x = −2y ⋯ ②
Partially integrating both the equations ① and ② we get
ψ = −2xy + f(x) + C1 ⋯ ③ and
ψ = −2xy + g(y) + C2 ⋯ ④
respectively.
Since both the equations ③ and ④ are same hence f(x) and g(y) will be zero and C1 = C2
∴ ψ = −2xy + constant.
Most Upvoted Answer
The velocity potential function of a flow field is given by x2 − y2 +...
Φ = x2 − y2 + C
∂ϕ / ∂x = −u and ∂ϕ / ∂y = −v
hence u = −2x and v = +2y
Also
∂ψ / ∂y = u ⟹ ∂ψ / ∂y = −2x ⋯ ①
and
∂ψ / ∂x = −v ⟹ ∂ψ / ∂x = −2y ⋯ ②
Partially integrating both the equations ① and ② we get
ψ = −2xy + f(x) + C1 ⋯ ③ and
ψ = −2xy + g(y) + C2 ⋯ ④
respectively.
Since both the equations ③ and ④ are same hence f(x) and g(y) will be zero and C1 = C2
∴ ψ = −2xy + constant.
Free Test
FREE
| Start Free Test |
Community Answer
The velocity potential function of a flow field is given by x2 − y2 +...
Explanation:
Given: Velocity potential function φ = x^2 - y^2 + constant
Stream function ψ:
The stream function ψ is related to the velocity components u and v of a 2D flow field by the equations:
u = ∂ψ/∂y
v = -∂ψ/∂x
Relation between velocity potential and stream function:
For an incompressible and irrotational flow, the velocity potential φ and the stream function ψ are related by the Laplace equation:
∇^2φ = -∇^2ψ
Find the stream function ψ:
Given φ = x^2 - y^2 + constant
Taking derivatives with respect to x and y:
∂φ/∂x = 2x
∂φ/∂y = -2y
Comparing these derivatives with the definitions of u and v:
u = 2x
v = -2y
Expressing u and v in terms of ψ:
From u = ∂ψ/∂y:
∂ψ/∂y = 2x
Integrating with respect to y:
ψ = 2xy + f(x)
Comparing this with the given options, the correct stream function is:
ψ = -2xy + constant (option A)
Given: Velocity potential function φ = x^2 - y^2 + constant
Stream function ψ:
The stream function ψ is related to the velocity components u and v of a 2D flow field by the equations:
u = ∂ψ/∂y
v = -∂ψ/∂x
Relation between velocity potential and stream function:
For an incompressible and irrotational flow, the velocity potential φ and the stream function ψ are related by the Laplace equation:
∇^2φ = -∇^2ψ
Find the stream function ψ:
Given φ = x^2 - y^2 + constant
Taking derivatives with respect to x and y:
∂φ/∂x = 2x
∂φ/∂y = -2y
Comparing these derivatives with the definitions of u and v:
u = 2x
v = -2y
Expressing u and v in terms of ψ:
From u = ∂ψ/∂y:
∂ψ/∂y = 2x
Integrating with respect to y:
ψ = 2xy + f(x)
Comparing this with the given options, the correct stream function is:
ψ = -2xy + constant (option A)
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
The velocity potential function of a flow field is given by x2 − y2 + constant. Its stream function will be given bya) − 2xy + constantb) + 2xy + constantc) − 2xy + f(x)d) − 2xy + f(y)Correct answer is option 'A'. Can you explain this answer?
Question Description
The velocity potential function of a flow field is given by x2 − y2 + constant. Its stream function will be given bya) − 2xy + constantb) + 2xy + constantc) − 2xy + f(x)d) − 2xy + f(y)Correct 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 The velocity potential function of a flow field is given by x2 − y2 + constant. Its stream function will be given bya) − 2xy + constantb) + 2xy + constantc) − 2xy + f(x)d) − 2xy + f(y)Correct 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 The velocity potential function of a flow field is given by x2 − y2 + constant. Its stream function will be given bya) − 2xy + constantb) + 2xy + constantc) − 2xy + f(x)d) − 2xy + f(y)Correct answer is option 'A'. Can you explain this answer?.
The velocity potential function of a flow field is given by x2 − y2 + constant. Its stream function will be given bya) − 2xy + constantb) + 2xy + constantc) − 2xy + f(x)d) − 2xy + f(y)Correct 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 The velocity potential function of a flow field is given by x2 − y2 + constant. Its stream function will be given bya) − 2xy + constantb) + 2xy + constantc) − 2xy + f(x)d) − 2xy + f(y)Correct 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 The velocity potential function of a flow field is given by x2 − y2 + constant. Its stream function will be given bya) − 2xy + constantb) + 2xy + constantc) − 2xy + f(x)d) − 2xy + f(y)Correct answer is option 'A'. Can you explain this answer?.
Solutions for The velocity potential function of a flow field is given by x2 − y2 + constant. Its stream function will be given bya) − 2xy + constantb) + 2xy + constantc) − 2xy + f(x)d) − 2xy + f(y)Correct 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 The velocity potential function of a flow field is given by x2 − y2 + constant. Its stream function will be given bya) − 2xy + constantb) + 2xy + constantc) − 2xy + f(x)d) − 2xy + f(y)Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The velocity potential function of a flow field is given by x2 − y2 + constant. Its stream function will be given bya) − 2xy + constantb) + 2xy + constantc) − 2xy + f(x)d) − 2xy + f(y)Correct answer is option 'A'. Can you explain this answer?, a detailed solution for The velocity potential function of a flow field is given by x2 − y2 + constant. Its stream function will be given bya) − 2xy + constantb) + 2xy + constantc) − 2xy + f(x)d) − 2xy + f(y)Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of The velocity potential function of a flow field is given by x2 − y2 + constant. Its stream function will be given bya) − 2xy + constantb) + 2xy + constantc) − 2xy + f(x)d) − 2xy + f(y)Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The velocity potential function of a flow field is given by x2 − y2 + constant. Its stream function will be given bya) − 2xy + constantb) + 2xy + constantc) − 2xy + f(x)d) − 2xy + f(y)Correct 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