Which of the following is correct?a)Pathlines of two particles in an o...
Explanation: The pathline of a particle in an one-dimensional flow is a straight line along the direction it moves. If the two particles move along the same direction, their pathlines will be parallel to each other and will never intersect.
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Which of the following is correct?a)Pathlines of two particles in an o...
Introduction:
In fluid mechanics, the concept of pathlines is used to describe the trajectory followed by individual fluid particles over a period of time. Pathlines can be visualized as the actual path traced by a series of particles as they move through a flow field. The question asks about the possibility of pathlines of two particles in a one-dimensional flow intersecting.
Understanding one-dimensional flow:
One-dimensional flow refers to a flow field where fluid particles move along a single direction. In this type of flow, the velocity of the fluid particles varies only in one dimension, typically along the x-axis. Therefore, the flow can be considered as uniform in all other directions except along the x-axis.
Explanation:
To determine whether pathlines of two particles in a one-dimensional flow can intersect, we need to consider the nature of one-dimensional flow and the behavior of fluid particles within it.
1. One-dimensional flow:
In a one-dimensional flow, the velocity of fluid particles varies only in one direction, while it remains constant in all other directions. This means that the particles are moving parallel to each other along the same direction.
2. Pathlines:
Pathlines describe the path followed by individual fluid particles as they move through a flow field. These paths are determined by integrating the velocity field over time. Pathlines can be thought of as the actual trajectory traced by particles in a flow.
3. Possibility of intersection:
a) Option a: Pathlines of two particles in a one-dimensional flow can never intersect.
This statement is incorrect because in a one-dimensional flow, particles move parallel to each other along the same direction. As a result, their pathlines will never cross or intersect.
b) Option b: Pathlines of two particles in a one-dimensional flow can never intersect if the two particles move along the same direction.
This statement is correct. Since the particles move along the same direction, their pathlines will never intersect.
c) Option c: Pathlines of two particles in a one-dimensional flow can intersect only if the two particles move along different directions.
This statement is incorrect. In a one-dimensional flow, particles move along the same direction. Therefore, their pathlines will not intersect, regardless of whether they move at different velocities.
d) Option d: Pathlines of two particles in a one-dimensional flow can intersect only if the two particles move along the same direction.
This statement is incorrect. As mentioned earlier, pathlines of particles in a one-dimensional flow will never intersect, regardless of their direction of motion.
Conclusion:
The correct option is c) Pathlines of two particles in a one-dimensional flow can intersect only if the two particles move along different directions. In a one-dimensional flow, particles move parallel to each other along the same direction, and their pathlines will never intersect. The possibility of pathline intersection arises only when particles move along different directions, which is not the case in a one-dimensional flow.
Which of the following is correct?a)Pathlines of two particles in an o...
I think 1 is correct answer..,
what do you say poori ??
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