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If for a flow, a stream function
- exists and satisfies the Laplaceequation, then which one of the following is the correctstatement?
- a)The continuity equation is satisfied and the flow is irrotational.
- b)The continuity equation is satisfied and the flow is rotational.
- c)The flow is irrotational but does not satisfy the continuity equation.
- d)The flow is rotational.
Correct answer is option 'A'. Can you explain this answer?
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If for a flow, a stream function exists and satisfies the Laplaceequat...
Ans (a) if a stream function
- exists means a possible case of flow, if it satisfies the Laplace equation then flow is irrotational.
Most Upvoted Answer
If for a flow, a stream function exists and satisfies the Laplaceequat...
Explanation:
Stream function:
- Stream function is a function that describes the flow of a fluid in two dimensions.
- It is defined as the scalar function whose gradient is perpendicular to the velocity vector at every point.
- Mathematically, it is defined as ψ(x,y) such that u = ∂ψ/∂y and v = -∂ψ/∂x, where u and v are the velocities in x and y directions respectively.
Laplace equation:
- Laplace equation is a partial differential equation that describes the steady-state behavior of a system.
- In fluid mechanics, it is used to describe the behavior of fluids that are not changing over time.
- Mathematically, it is defined as ∇^2ψ = 0, where ∇^2 is the Laplacian operator.
Continuity equation:
- Continuity equation is a fundamental principle of fluid mechanics that states that the mass flow rate of a fluid is conserved.
- Mathematically, it is defined as ∂ρ/∂t + ∇.(ρv) = 0, where ρ is the density, t is time, and v is the velocity vector.
Irrotational flow:
- An irrotational flow is a flow in which the fluid particles move along paths that are parallel to each other, and there is no rotation of the fluid around any axis.
- Mathematically, it is defined as ∇ x v = 0, where v is the velocity vector.
Rotational flow:
- A rotational flow is a flow in which the fluid particles move along paths that are not parallel to each other, and there is rotation of the fluid around some axis.
- Mathematically, it is defined as ∇ x v ≠ 0, where v is the velocity vector.
Answer:
- If a stream function exists and satisfies the Laplace equation, then it implies that the velocity vector can be expressed in terms of the stream function.
- Using this expression, it can be shown that the continuity equation is automatically satisfied.
- Moreover, since the curl of the velocity vector is zero, it implies that the flow is irrotational.
- Therefore, option 'A' is the correct statement.
Stream function:
- Stream function is a function that describes the flow of a fluid in two dimensions.
- It is defined as the scalar function whose gradient is perpendicular to the velocity vector at every point.
- Mathematically, it is defined as ψ(x,y) such that u = ∂ψ/∂y and v = -∂ψ/∂x, where u and v are the velocities in x and y directions respectively.
Laplace equation:
- Laplace equation is a partial differential equation that describes the steady-state behavior of a system.
- In fluid mechanics, it is used to describe the behavior of fluids that are not changing over time.
- Mathematically, it is defined as ∇^2ψ = 0, where ∇^2 is the Laplacian operator.
Continuity equation:
- Continuity equation is a fundamental principle of fluid mechanics that states that the mass flow rate of a fluid is conserved.
- Mathematically, it is defined as ∂ρ/∂t + ∇.(ρv) = 0, where ρ is the density, t is time, and v is the velocity vector.
Irrotational flow:
- An irrotational flow is a flow in which the fluid particles move along paths that are parallel to each other, and there is no rotation of the fluid around any axis.
- Mathematically, it is defined as ∇ x v = 0, where v is the velocity vector.
Rotational flow:
- A rotational flow is a flow in which the fluid particles move along paths that are not parallel to each other, and there is rotation of the fluid around some axis.
- Mathematically, it is defined as ∇ x v ≠ 0, where v is the velocity vector.
Answer:
- If a stream function exists and satisfies the Laplace equation, then it implies that the velocity vector can be expressed in terms of the stream function.
- Using this expression, it can be shown that the continuity equation is automatically satisfied.
- Moreover, since the curl of the velocity vector is zero, it implies that the flow is irrotational.
- Therefore, option 'A' is the correct statement.
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If for a flow, a stream function exists and satisfies the Laplaceequation, then which one of the following is the correctstatement?a)The continuity equation is satisfied and the flow is irrotational.b)The continuity equation is satisfied and the flow is rotational.c)The flow is irrotational but does not satisfy the continuity equation.d)The flow is rotational.Correct answer is option 'A'. Can you explain this answer?
Question Description
If for a flow, a stream function exists and satisfies the Laplaceequation, then which one of the following is the correctstatement?a)The continuity equation is satisfied and the flow is irrotational.b)The continuity equation is satisfied and the flow is rotational.c)The flow is irrotational but does not satisfy the continuity equation.d)The flow is rotational.Correct answer is option 'A'. 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 If for a flow, a stream function exists and satisfies the Laplaceequation, then which one of the following is the correctstatement?a)The continuity equation is satisfied and the flow is irrotational.b)The continuity equation is satisfied and the flow is rotational.c)The flow is irrotational but does not satisfy the continuity equation.d)The flow is rotational.Correct answer is option 'A'. 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 If for a flow, a stream function exists and satisfies the Laplaceequation, then which one of the following is the correctstatement?a)The continuity equation is satisfied and the flow is irrotational.b)The continuity equation is satisfied and the flow is rotational.c)The flow is irrotational but does not satisfy the continuity equation.d)The flow is rotational.Correct answer is option 'A'. Can you explain this answer?.
If for a flow, a stream function exists and satisfies the Laplaceequation, then which one of the following is the correctstatement?a)The continuity equation is satisfied and the flow is irrotational.b)The continuity equation is satisfied and the flow is rotational.c)The flow is irrotational but does not satisfy the continuity equation.d)The flow is rotational.Correct answer is option 'A'. 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 If for a flow, a stream function exists and satisfies the Laplaceequation, then which one of the following is the correctstatement?a)The continuity equation is satisfied and the flow is irrotational.b)The continuity equation is satisfied and the flow is rotational.c)The flow is irrotational but does not satisfy the continuity equation.d)The flow is rotational.Correct answer is option 'A'. 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 If for a flow, a stream function exists and satisfies the Laplaceequation, then which one of the following is the correctstatement?a)The continuity equation is satisfied and the flow is irrotational.b)The continuity equation is satisfied and the flow is rotational.c)The flow is irrotational but does not satisfy the continuity equation.d)The flow is rotational.Correct answer is option 'A'. Can you explain this answer?.
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