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Consider the following statements:
For a two-dimensional potential flow
1. Laplace equation for stream function must be satisfied.
2. Laplace equation for velocity potential must be satisfied.
3. Streamlines and equipotential lines are mutually perpendicular.
4. Stream function and potential function are not interchangeable.
For a two-dimensional potential flow
1. Laplace equation for stream function must be satisfied.
2. Laplace equation for velocity potential must be satisfied.
3. Streamlines and equipotential lines are mutually perpendicular.
4. Stream function and potential function are not interchangeable.
- a)1 and 4 are correct
- b)2 and 4 are correct
- c)1, 2 and 3 are correct
- d)2, 3 and 4 are correct
Correct answer is option 'C'. Can you explain this answer?
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Consider the following statements:For a two-dimensional potential flow...
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Consider the following statements:For a two-dimensional potential flow...
Laplace Equation for Stream Function
The stream function is a mathematical function used to describe the motion of a fluid in two-dimensional potential flow. The Laplace equation for the stream function is given by:
∇²ψ = 0
where ∇² is the Laplacian operator and ψ is the stream function.
Laplace Equation for Velocity Potential
The velocity potential is another mathematical function used to describe the motion of a fluid in two-dimensional potential flow. The Laplace equation for the velocity potential is given by:
∇²φ = 0
where ∇² is the Laplacian operator and φ is the velocity potential.
Streamlines and Equipotential Lines
Streamlines are imaginary lines that represent the path of fluid particles in a flow field. They are always tangent to the velocity vector at any point in the flow field. Equipotential lines, on the other hand, represent regions of constant velocity potential.
It can be shown that streamlines and equipotential lines are always mutually perpendicular to each other in two-dimensional potential flow. This is a consequence of the fact that the velocity vector is always tangent to the streamline, and the gradient of the velocity potential is always perpendicular to the equipotential line.
Interchangeability of Stream Function and Potential Function
In two-dimensional potential flow, the stream function and the velocity potential are related to each other through the following equations:
u = ∂ψ/∂y v = -∂ψ/∂x φ = ∂ψ/∂x φ = -∂ψ/∂y
where u and v are the x and y components of the velocity vector, and x and y are the coordinates in the flow field.
From these equations, it can be seen that the stream function determines the velocity components, while the velocity potential determines the streamlines. Therefore, the stream function and the velocity potential are not interchangeable.
Correct Statements
From the above explanations, we can conclude that the correct statements are:
1. Laplace equation for stream function must be satisfied.
2. Laplace equation for velocity potential must be satisfied.
3. Streamlines and equipotential lines are mutually perpendicular.
Therefore, the correct answer is option 'C' - 1, 2, and 3 are correct.
The stream function is a mathematical function used to describe the motion of a fluid in two-dimensional potential flow. The Laplace equation for the stream function is given by:
∇²ψ = 0
where ∇² is the Laplacian operator and ψ is the stream function.
Laplace Equation for Velocity Potential
The velocity potential is another mathematical function used to describe the motion of a fluid in two-dimensional potential flow. The Laplace equation for the velocity potential is given by:
∇²φ = 0
where ∇² is the Laplacian operator and φ is the velocity potential.
Streamlines and Equipotential Lines
Streamlines are imaginary lines that represent the path of fluid particles in a flow field. They are always tangent to the velocity vector at any point in the flow field. Equipotential lines, on the other hand, represent regions of constant velocity potential.
It can be shown that streamlines and equipotential lines are always mutually perpendicular to each other in two-dimensional potential flow. This is a consequence of the fact that the velocity vector is always tangent to the streamline, and the gradient of the velocity potential is always perpendicular to the equipotential line.
Interchangeability of Stream Function and Potential Function
In two-dimensional potential flow, the stream function and the velocity potential are related to each other through the following equations:
u = ∂ψ/∂y v = -∂ψ/∂x φ = ∂ψ/∂x φ = -∂ψ/∂y
where u and v are the x and y components of the velocity vector, and x and y are the coordinates in the flow field.
From these equations, it can be seen that the stream function determines the velocity components, while the velocity potential determines the streamlines. Therefore, the stream function and the velocity potential are not interchangeable.
Correct Statements
From the above explanations, we can conclude that the correct statements are:
1. Laplace equation for stream function must be satisfied.
2. Laplace equation for velocity potential must be satisfied.
3. Streamlines and equipotential lines are mutually perpendicular.
Therefore, the correct answer is option 'C' - 1, 2, and 3 are correct.
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Consider the following statements:For a two-dimensional potential flow1. Laplace equation for stream function must be satisfied.2. Laplace equation for velocity potential must be satisfied.3. Streamlines and equipotential lines are mutually perpendicular.4. Stream function and potential function are not interchangeable.a)1 and 4 are correctb)2 and 4 are correctc)1, 2 and 3 are correctd)2, 3 and 4 are correctCorrect answer is option 'C'. Can you explain this answer?
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Consider the following statements:For a two-dimensional potential flow1. Laplace equation for stream function must be satisfied.2. Laplace equation for velocity potential must be satisfied.3. Streamlines and equipotential lines are mutually perpendicular.4. Stream function and potential function are not interchangeable.a)1 and 4 are correctb)2 and 4 are correctc)1, 2 and 3 are correctd)2, 3 and 4 are correctCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Consider the following statements:For a two-dimensional potential flow1. Laplace equation for stream function must be satisfied.2. Laplace equation for velocity potential must be satisfied.3. Streamlines and equipotential lines are mutually perpendicular.4. Stream function and potential function are not interchangeable.a)1 and 4 are correctb)2 and 4 are correctc)1, 2 and 3 are correctd)2, 3 and 4 are correctCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements:For a two-dimensional potential flow1. Laplace equation for stream function must be satisfied.2. Laplace equation for velocity potential must be satisfied.3. Streamlines and equipotential lines are mutually perpendicular.4. Stream function and potential function are not interchangeable.a)1 and 4 are correctb)2 and 4 are correctc)1, 2 and 3 are correctd)2, 3 and 4 are correctCorrect answer is option 'C'. Can you explain this answer?.
Consider the following statements:For a two-dimensional potential flow1. Laplace equation for stream function must be satisfied.2. Laplace equation for velocity potential must be satisfied.3. Streamlines and equipotential lines are mutually perpendicular.4. Stream function and potential function are not interchangeable.a)1 and 4 are correctb)2 and 4 are correctc)1, 2 and 3 are correctd)2, 3 and 4 are correctCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Consider the following statements:For a two-dimensional potential flow1. Laplace equation for stream function must be satisfied.2. Laplace equation for velocity potential must be satisfied.3. Streamlines and equipotential lines are mutually perpendicular.4. Stream function and potential function are not interchangeable.a)1 and 4 are correctb)2 and 4 are correctc)1, 2 and 3 are correctd)2, 3 and 4 are correctCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements:For a two-dimensional potential flow1. Laplace equation for stream function must be satisfied.2. Laplace equation for velocity potential must be satisfied.3. Streamlines and equipotential lines are mutually perpendicular.4. Stream function and potential function are not interchangeable.a)1 and 4 are correctb)2 and 4 are correctc)1, 2 and 3 are correctd)2, 3 and 4 are correctCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Consider the following statements:For a two-dimensional potential flow1. Laplace equation for stream function must be satisfied.2. Laplace equation for velocity potential must be satisfied.3. Streamlines and equipotential lines are mutually perpendicular.4. Stream function and potential function are not interchangeable.a)1 and 4 are correctb)2 and 4 are correctc)1, 2 and 3 are correctd)2, 3 and 4 are correctCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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Consider the following statements:For a two-dimensional potential flow1. Laplace equation for stream function must be satisfied.2. Laplace equation for velocity potential must be satisfied.3. Streamlines and equipotential lines are mutually perpendicular.4. Stream function and potential function are not interchangeable.a)1 and 4 are correctb)2 and 4 are correctc)1, 2 and 3 are correctd)2, 3 and 4 are correctCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Consider the following statements:For a two-dimensional potential flow1. Laplace equation for stream function must be satisfied.2. Laplace equation for velocity potential must be satisfied.3. Streamlines and equipotential lines are mutually perpendicular.4. Stream function and potential function are not interchangeable.a)1 and 4 are correctb)2 and 4 are correctc)1, 2 and 3 are correctd)2, 3 and 4 are correctCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Consider the following statements:For a two-dimensional potential flow1. Laplace equation for stream function must be satisfied.2. Laplace equation for velocity potential must be satisfied.3. Streamlines and equipotential lines are mutually perpendicular.4. Stream function and potential function are not interchangeable.a)1 and 4 are correctb)2 and 4 are correctc)1, 2 and 3 are correctd)2, 3 and 4 are correctCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider the following statements:For a two-dimensional potential flow1. Laplace equation for stream function must be satisfied.2. Laplace equation for velocity potential must be satisfied.3. Streamlines and equipotential lines are mutually perpendicular.4. Stream function and potential function are not interchangeable.a)1 and 4 are correctb)2 and 4 are correctc)1, 2 and 3 are correctd)2, 3 and 4 are correctCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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