The difference between path lines, streak lines and streamlines is often hard to visualize. There is a great video illustrating the differences between path lines and streak lines for an unsteady flow but the flow gets a little complex at times. I use a larger scale demonstration with Ping-Pong balls acting as the fluid particles. This one takes a little more equipment and a fair bit of clean up.
- Lots of Ping-Pong balls (50+)
- A bucket
- A Ping-Ping ball gun capable of shooting 10 or so balls at a time.
- An air compressor
The Ping-Pong ball gun can be made from a four foot length of 1½” PVC pipe capped at one end. Attach a quarter turn valve to the cap and a compressed air connector to the valve (see picture below). You will need either a compressed air line or a portable air compressor in the class room to fire the gun.
Path lines (the trajectory of an individual particle)
Write the definition of a path line on the board. Load a single ball into the gun. Ask the class to take a mental image of where the ball is at each of the times that you call out during flight. Fire the ball across the front of the class room in front of the white board (use orange balls if you have a white board or white balls if you have a chalk board). While the ball is in flight, quickly count out loud from 1 up to say 5 or 6 (the actual number is not important). After the flight draw a series of circles on the board (one for each number you counted) roughly following the arc of the ball’s flight. Label them as (t=1), (t=2), … with (t=1) being the circle nearest the outlet of the gun. The labels refer to the locations of the ball at the times called out. Draw a line through circles to form the path line.
Streak line (a line connecting all the particles that have passed through a single point)
Write the definition of a streak line on the board. Load about 10 balls into the gun. Ask the class to take a mental image of where all the balls are when you call out ‘NOW’ during flight. Fire the balls across the front of the board and call ‘NOW’ when the balls are in the air. After they have landed draw up a series of circles in an arc across the board. Label them (P1), (P2), … with (P1) being the particle that came out of the gun first. The labels indicate the order in which they left the gun. Draw a line connecting the circles to form the streak line.
Streamline (a line that is instantaneously tangent to the velocity vectors of the flow)
Write the definition of a streamline on the board. Tell the class that you are going to throw a bucket full of balls across the front of the room and ask them to take a mental image of where each ball is and what its velocity is when you call “NOW”. Throw the balls across the front of the room and call out “NOW” when the balls are in the middle of the board. Once they have landed, draw a whole series of circles all over the board with arrows for the velocity vectors. Draw the vectors such that you can draw lines tangent to the arrows passing through multiple balls. I typically draw up about 20-30 circles. I often ask the class if the drawing is accurate. Then draw a series of streamlines that pass through the circles and are tangent to the velocity vectors.
At the end of the class I ask each student to pick up a couple of balls each to help tidy up.
The demonstration usually gets a good laugh, particularly when 100+ balls get thrown across the front of the room (I think the students don’t actually believe I am going to throw the whole bucket full). However, it does illustrate that a path line is formed over time (the counting during flight) as a single particle moves through space, whereas the other two lines are snap shots in time (when you shout “NOW”) connecting multiple particles.
Videos to follow shortly.