Streamline formula derivation | streamline kaise nikalne | derivation of streamline formula

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Difference between path line and streamline
Difference between streamline and streakline
Difference between pathline and streakline
In fluid dynamics, streamline, pathline, and streakline are three fundamental concepts used to visualize and analyze fluid flow. Here's a comparison between streamline and pathline:
Streamline:
1. Definition: An imaginary line that represents the direction of fluid flow at a given instant.
2. Description: Streamlines are tangent to the velocity vector at each point.
3. Purpose: Show the direction of fluid flow.
4. Time-dependent: No, streamlines are instantaneous.
5. Equation: ∂r/∂t = u (where u is the velocity vector)
Pathline:
1. Definition: The trajectory of a fluid particle over time.
2. Description: Pathlines show the actual path traveled by a fluid particle.
3. Purpose: Show the history of fluid particle movement.
4. Time-dependent: Yes, pathlines are time-dependent.
5. Equation: dx/dt = u (where x is the position vector)
Key differences:
1. Time dependency: Streamlines are instantaneous, while pathlines are time-dependent.
2. Direction: Streamlines show the direction of fluid flow, while pathlines show the actual path traveled.
3. Information: Streamlines provide information about the flow field, while pathlines provide information about individual fluid particles.
Streakline:
(A third concept, streakline, shows the location of fluid particles that have passed through a fixed point.)
Comparison Table:
| | Streamline | Pathline | Streakline |
| --- | --- | --- | --- |
| Definition | Direction of flow | Trajectory of fluid particle | Location of particles passing through a fixed point |
| Time-dependent | No | Yes | Yes |
| Purpose | Show flow direction | Show particle history | Show particle location |
Applications:
- Fluid dynamics
- Aerodynamics
- Hydrodynamics
- Chemical engineering
- Biological systems
Do you have any specific questions about streamlines, pathlines, or streaklines in fluid dynamics?