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In a steady flow:
- a)Streamlines and path lines are identical but are different from streaklines
- b)Streaklines and pathlines are identical but are different from streamlines
- c)Streamlines, streaklines, and pathlines can be different from each other
- d)None of the above
Correct answer is option 'D'. Can you explain this answer?
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In a steady flow:a)Streamlines and path lines are identical but are d...
Streamlines are a family of instantaneously tangent curves to the velocity vector of the flow. These show the direction in which a massless fluid element will travel at any point in time.
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Streaklines are the loci of points of all the fluid particles that have passed continuously through a particular spatial point in the past. Thus, dye steadily injected into the fluid at a fixed point extends along a streak line.
Pathlines are the trajectories that individual fluid particles follow. These can be thought of as "recording" the path of a fluid element in the flow over a certain period. The fluid streamlines will determine the direction the path takes at each moment in time.
For steady flow, path lines, streamlines, and streaklines coincide.
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In a steady flow:a)Streamlines and path lines are identical but are d...
In a steady flow, the terms streamlines, streaklines, and pathlines are used to describe the behavior of fluid particles. These terms help us understand the movement and flow patterns of fluids.
Streamlines:
- Streamlines are imaginary lines that represent the instantaneous direction of the fluid flow at a given point.
- They are always tangent to the velocity vector of the fluid at every point.
- Streamlines do not provide any information about the actual path followed by individual fluid particles.
Streaklines:
- Streaklines are the paths traced by fluid particles as they move through a flow field over a certain period of time.
- They represent the history of the fluid particles and show the path they have taken.
- Streaklines are obtained by injecting a dye or a tracer into the fluid and observing the movement of the colored streak over time.
Pathlines:
- Pathlines are the actual paths followed by individual fluid particles over a certain period of time.
- They show the complete trajectory of a fluid particle.
- Pathlines can be obtained by tracking the movement of a specific fluid particle using techniques like particle tracking or using numerical simulations.
Relation between Streamlines, Streaklines, and Pathlines:
- Streamlines, streaklines, and pathlines can all be different from each other in a steady flow.
- Streamlines represent the instantaneous flow direction at a given point and are always tangent to the velocity vector.
- Streaklines show the paths traced by fluid particles over time, and they can be different from streamlines because they represent the history of fluid particles.
- Pathlines represent the actual paths followed by fluid particles over time and can also be different from streamlines and streaklines because they show the complete trajectory of individual fluid particles.
Conclusion:
Therefore, in a steady flow, streamlines, streaklines, and pathlines are all different from each other, and the correct answer to the given question is option 'D' - None of the above.
Streamlines:
- Streamlines are imaginary lines that represent the instantaneous direction of the fluid flow at a given point.
- They are always tangent to the velocity vector of the fluid at every point.
- Streamlines do not provide any information about the actual path followed by individual fluid particles.
Streaklines:
- Streaklines are the paths traced by fluid particles as they move through a flow field over a certain period of time.
- They represent the history of the fluid particles and show the path they have taken.
- Streaklines are obtained by injecting a dye or a tracer into the fluid and observing the movement of the colored streak over time.
Pathlines:
- Pathlines are the actual paths followed by individual fluid particles over a certain period of time.
- They show the complete trajectory of a fluid particle.
- Pathlines can be obtained by tracking the movement of a specific fluid particle using techniques like particle tracking or using numerical simulations.
Relation between Streamlines, Streaklines, and Pathlines:
- Streamlines, streaklines, and pathlines can all be different from each other in a steady flow.
- Streamlines represent the instantaneous flow direction at a given point and are always tangent to the velocity vector.
- Streaklines show the paths traced by fluid particles over time, and they can be different from streamlines because they represent the history of fluid particles.
- Pathlines represent the actual paths followed by fluid particles over time and can also be different from streamlines and streaklines because they show the complete trajectory of individual fluid particles.
Conclusion:
Therefore, in a steady flow, streamlines, streaklines, and pathlines are all different from each other, and the correct answer to the given question is option 'D' - None of the above.
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In a steady flow:a)Streamlines and path lines are identical but are different from streaklinesb)Streaklines and pathlines are identical but are different from streamlinesc)Streamlines, streaklines, and pathlines can be different from each otherd)None of the aboveCorrect answer is option 'D'. Can you explain this answer?
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