# Streamlines, streaklines and pathlines

1. Jan 30, 2010

### R Power

Hi PFians

I searched net for hours about understanding the concept of streamlines, streaklines and pathlines but I am still under confusion.
1.) See, streamlines are tangent to velocity vector at everypoint. Right? Now velocity is a characteristic of a moving fluid particle. So, shouldn't streamlines equivalent to path lines.
e.g take a particle moving in a circle, path traced by that particle is a circle or we can say circle is the pathline for that particle. Right? Also circle is tangent to velocity vector for the particle at a certain instant. So , circle or pathline is same as fieldline(streamline in case of fluid particle) for the particle because streamline is tangent to velocity vector by definition. Now these two are same in steady flows but not in unsteady flows. Why? These both are same things, then why different in unsteady flows.

2. In case of steady flow streaklines are also same as pathlines. Why and how? Consider particles moving from origin towards infinity in x-y plane at differerent angles in straight lines and with different speeds but the flow is steady. Here velocity vectors of particles will concide with the straight pathlines. So these pathlines should be the streamlines. Now the locus particles that have moved from a fixed certain point over certain time will be a line or curve intersecting all the pathlines and streamlines. This locus will be streakline. So how streamline , streakline and pathline all three concide in steady flow???????????

2. Jan 30, 2010

### Brian_C

See Anderson's book on Aerodynamics. Streamlines show the instantaneous direction of fluid flow at every point, while pathlines show the trajectory taken by a single fluid element over an interval of time. Streamlines are essentially a "photograph" of the flow taken at an instant in time, while pathlines are a "time exposure" of the flow of a fixed particle. Streaklines are the locus of fluid elements that pass through a given point. Different fluid particles passing through the same point will not follow the same path if the velocity at that point is changing with time. In a streakline, you are connecting the instantaneous positions of particles that have followed different trajectories (for unsteady flow).

3. Jun 25, 2010

### raghuram_306

Up to my understanding...i explained my self for the reason how streak lines in steady flow will be identical with the stream lines and path lines like this...
In a steady flow the velocity vector for all particles is same that means a fluid particle leaving a fixed point will have some velocity and since the next particle leaving the same point will have the same velocity,it will follow the path of the first particle and wont move away from that path . So if you consider the positions of these two particles after some time they will stay one after another,on the path which is traced by the first particle. So if you draw a line joining these two particles (Definition of streak line) that will gives you nothing but the path of the first particle nothing but the path line of that particle.
Since the velocity of the two particles is not changing at any fixed point it is a steady flow streamline (imaginary line joining the fixed points in a fluid flow) .

Last edited: Jun 25, 2010