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If the velocity potential function ϕ for a flow satisfies the Laplace equation δ2ϕ⁄δx2 + δ2ϕ⁄δy2 + δ2ϕ⁄δz2 = 0 then the flow is
- a)unsteady, incompressible, rotational
- b)steady, compressible, rotational
- c)steady, incompressible, irrotational
- d)unsteady, compressible, irrotational
Correct answer is option 'C'. Can you explain this answer?
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If the velocity potential function ϕ for a flow satisfies the Laplace...
Velocity potential function is defined only for irrotational flows, whether the flow is steady or unsteady, compressible or incompressible. If it also satisfies Laplace equation then the flow is also incompressible.
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Most Upvoted Answer
If the velocity potential function ϕ for a flow satisfies the Laplace...
Laplace's equation is a partial differential equation that describes a scalar field in terms of its second derivatives. In fluid dynamics, the velocity potential function represents the flow field of a fluid, and it satisfies Laplace's equation.
The Laplace equation in three dimensions can be written as:
∇²ϕ = δ²ϕ/δx² + δ²ϕ/δy² + δ²ϕ/δz² = 0
where ∇² is the Laplacian operator.
Based on the given equation, we can determine the characteristics of the flow:
a) Unsteady, Incompressible, Rotational:
If the flow is unsteady, the velocity potential function would depend on time. However, the given equation does not have any time-dependent terms, implying that the flow is steady.
Rotational flow refers to the presence of vortices or fluid rotation. The Laplace equation does not allow for fluid rotation, so the flow cannot be rotational.
b) Steady, Compressible, Rotational:
As mentioned earlier, the flow is steady since the equation does not have any time-dependent terms.
Compressible flow involves changes in fluid density. However, the Laplace equation does not consider density variations, so the flow cannot be compressible.
c) Steady, Incompressible, Irrotational:
Steady flow has a constant velocity at any given point in the flow field. As the equation does not have any time-dependent terms, the flow is steady.
Incompressible flow implies that the fluid density remains constant. The Laplace equation does not account for density changes, so the flow is incompressible.
Irrotational flow means that there is no fluid rotation or vorticity. Since the Laplace equation does not allow for fluid rotation, the flow is irrotational.
Therefore, the correct answer is option 'C': steady, incompressible, irrotational.
The Laplace equation in three dimensions can be written as:
∇²ϕ = δ²ϕ/δx² + δ²ϕ/δy² + δ²ϕ/δz² = 0
where ∇² is the Laplacian operator.
Based on the given equation, we can determine the characteristics of the flow:
a) Unsteady, Incompressible, Rotational:
If the flow is unsteady, the velocity potential function would depend on time. However, the given equation does not have any time-dependent terms, implying that the flow is steady.
Rotational flow refers to the presence of vortices or fluid rotation. The Laplace equation does not allow for fluid rotation, so the flow cannot be rotational.
b) Steady, Compressible, Rotational:
As mentioned earlier, the flow is steady since the equation does not have any time-dependent terms.
Compressible flow involves changes in fluid density. However, the Laplace equation does not consider density variations, so the flow cannot be compressible.
c) Steady, Incompressible, Irrotational:
Steady flow has a constant velocity at any given point in the flow field. As the equation does not have any time-dependent terms, the flow is steady.
Incompressible flow implies that the fluid density remains constant. The Laplace equation does not account for density changes, so the flow is incompressible.
Irrotational flow means that there is no fluid rotation or vorticity. Since the Laplace equation does not allow for fluid rotation, the flow is irrotational.
Therefore, the correct answer is option 'C': steady, incompressible, irrotational.
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If the velocity potential function ϕ for a flow satisfies the Laplace equation δ2ϕ⁄δx2 + δ2ϕ⁄δy2 + δ2ϕ⁄δz2 = 0 then the flow isa) unsteady, incompressible, rotationalb) steady, compressible, rotationalc) steady, incompressible, irrotationald) unsteady, compressible, irrotationalCorrect answer is option 'C'. Can you explain this answer?
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If the velocity potential function ϕ for a flow satisfies the Laplace equation δ2ϕ⁄δx2 + δ2ϕ⁄δy2 + δ2ϕ⁄δz2 = 0 then the flow isa) unsteady, incompressible, rotationalb) steady, compressible, rotationalc) steady, incompressible, irrotationald) unsteady, compressible, irrotationalCorrect 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 If the velocity potential function ϕ for a flow satisfies the Laplace equation δ2ϕ⁄δx2 + δ2ϕ⁄δy2 + δ2ϕ⁄δz2 = 0 then the flow isa) unsteady, incompressible, rotationalb) steady, compressible, rotationalc) steady, incompressible, irrotationald) unsteady, compressible, irrotationalCorrect 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 If the velocity potential function ϕ for a flow satisfies the Laplace equation δ2ϕ⁄δx2 + δ2ϕ⁄δy2 + δ2ϕ⁄δz2 = 0 then the flow isa) unsteady, incompressible, rotationalb) steady, compressible, rotationalc) steady, incompressible, irrotationald) unsteady, compressible, irrotationalCorrect answer is option 'C'. Can you explain this answer?.
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