Stream lines and path lines always coincide in case of laminar flow.



In fluid mechanics, stream lines and path lines are two different concepts used to represent the motion of fluid particles in a flow field. Understanding the difference between the two is crucial in analyzing fluid flows.



- Stream lines are defined as the instantaneous lines that are tangent to the velocity vector of a fluid particle at any given point in the flow field.
- They represent the direction and magnitude of fluid particle velocities at a specific moment in time.
- Stream lines are always tangent to the velocity vector and do not cross each other.
- They can be visualized by injecting dye or smoke into the flow and observing the path followed by the dye or smoke.



- Path lines, on the other hand, represent the actual path taken by a fluid particle as it moves through the flow field over a period of time.
- They are the integral curves of the velocity vector field and describe the trajectory of a specific fluid particle.
- Path lines can be obtained by tracking the position of a fluid particle over time.
- They can be visualized by releasing a dye or tracer particle into the flow and tracking its motion.



In steady flow conditions, the stream lines and path lines coincide.

- Steady flow refers to a flow field where the velocity at any given point remains constant over time.
- In such flows, the position of a fluid particle does not change with time, and thus the path line coincides with the stream line.
- This means that the direction and magnitude of fluid particle velocities are constant along the stream lines.
- The stream lines represent the instantaneous path followed by a fluid particle, which is the same as the path followed over time.



Laminar flow is a type of flow characterized by smooth and orderly motion of fluid particles.

- In laminar flow, fluid particles move in parallel layers with little or no mixing between the layers.
- The flow is highly organized, and the fluid particles move in a predictable manner.
- Laminar flow is commonly observed at low velocities and high viscosities.

Therefore, in laminar flow, where the flow is steady and the motion of fluid particles is highly ordered, the stream lines and path lines coincide. However, in turbulent flow, where the flow is unsteady and highly chaotic, the stream lines and path lines do not coincide.