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In an incompressible flow, the:
- a)density should remain fixed
- b)velocity field needs to be divergence free
- c)vorticity vector should be null
- d)streamline and path line should be similar
Correct answer is option 'A'. Can you explain this answer?
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In an incompressible flow, the:a)density should remain fixedb)velocit...
In an incompressible fluid flow, the density of fluid element will not change during the motion and it serves as the property of fluid flow and not of fluid. Incompressible flow does not imply that the fluid itself is incompressible. Even compressible fluids can give a good approximation – be modelled as an incompressible flow
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Thus continuity equation reduces to
∇ · v = 0
Most Upvoted Answer
In an incompressible flow, the:a)density should remain fixedb)velocit...
Incompressible Flow:
In fluid dynamics, incompressible flow refers to the flow of a fluid in which the density remains constant throughout the flow field. This means that the density of the fluid does not change with respect to time or position. Incompressible flow is a common assumption made in many fluid dynamics problems, as it simplifies the analysis and allows for the use of certain mathematical models.
Explanation of the Options:
a) Density should remain fixed: This option is correct for incompressible flow. In an incompressible flow, the density of the fluid remains constant. This means that the mass of the fluid within any given volume does not change as the fluid flows. The conservation of mass equation, also known as the continuity equation, is used to describe the incompressibility of the flow.
b) Velocity field needs to be divergence free: This statement is true for both incompressible and compressible flows. The divergence of the velocity field represents the rate of change of density in the flow. In an incompressible flow, the density is constant, so the divergence of the velocity field is zero. This condition is known as the continuity equation, and it is a fundamental equation in fluid dynamics.
c) Vorticity vector should be null: This statement is not necessarily true for incompressible flow. Vorticity is a measure of the local rotation of fluid particles in the flow. In an incompressible flow, the vorticity can be non-zero, indicating the presence of rotation in the flow. However, it is important to note that in irrotational flow, the vorticity vector is indeed zero.
d) Streamline and path line should be similar: This statement is not necessarily true for incompressible flow. Streamlines represent the instantaneous direction of the velocity vector at each point in the flow field. Pathlines, on the other hand, represent the actual path traced by a fluid particle as it moves with the flow. In general, streamlines and pathlines can be different in an incompressible flow.
Conclusion:
In summary, the correct answer is option 'a' - the density should remain fixed. In an incompressible flow, the density of the fluid remains constant throughout the flow field. The other options, while related to fluid dynamics, do not necessarily apply exclusively to incompressible flow.
In fluid dynamics, incompressible flow refers to the flow of a fluid in which the density remains constant throughout the flow field. This means that the density of the fluid does not change with respect to time or position. Incompressible flow is a common assumption made in many fluid dynamics problems, as it simplifies the analysis and allows for the use of certain mathematical models.
Explanation of the Options:
a) Density should remain fixed: This option is correct for incompressible flow. In an incompressible flow, the density of the fluid remains constant. This means that the mass of the fluid within any given volume does not change as the fluid flows. The conservation of mass equation, also known as the continuity equation, is used to describe the incompressibility of the flow.
b) Velocity field needs to be divergence free: This statement is true for both incompressible and compressible flows. The divergence of the velocity field represents the rate of change of density in the flow. In an incompressible flow, the density is constant, so the divergence of the velocity field is zero. This condition is known as the continuity equation, and it is a fundamental equation in fluid dynamics.
c) Vorticity vector should be null: This statement is not necessarily true for incompressible flow. Vorticity is a measure of the local rotation of fluid particles in the flow. In an incompressible flow, the vorticity can be non-zero, indicating the presence of rotation in the flow. However, it is important to note that in irrotational flow, the vorticity vector is indeed zero.
d) Streamline and path line should be similar: This statement is not necessarily true for incompressible flow. Streamlines represent the instantaneous direction of the velocity vector at each point in the flow field. Pathlines, on the other hand, represent the actual path traced by a fluid particle as it moves with the flow. In general, streamlines and pathlines can be different in an incompressible flow.
Conclusion:
In summary, the correct answer is option 'a' - the density should remain fixed. In an incompressible flow, the density of the fluid remains constant throughout the flow field. The other options, while related to fluid dynamics, do not necessarily apply exclusively to incompressible flow.
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In an incompressible flow, the:a)density should remain fixedb)velocity field needs to be divergence freec)vorticity vector should be nulld)streamline and path line should be similarCorrect answer is option 'A'. Can you explain this answer?
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