Videos of “Lift, Boundary layer separation, and curve balls”

Here are the videos from the “Lift, Boundary layer separation, and curve balls” demonstration. The GIF titles link to the full videos.

Launch

release

Flight

flight

This one is a little hard to follow. The balls are orange and appear near the top left corner. The ball only rises a little bit and the camera angle makes it hard to see. If you watch carefully you see that the flight appears a lot flatter than a pure projectile motion (because of the perspective the ball appears to float in mid-air at one point)would lead to, indicating that there is a vertical lift force. This is better watched on the full video.

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Lift, Boundary layer separation, and curve balls

Getting a ball (e.g. a cricket ball, soccer ball, tennis ball, or baseball) to move laterally is somewhat difficult (though I find it all too easy with a golf ball). The fluid mechanics of this phenomenon is quite interesting and provides insight in to how boundary layer separation influences both drag and lift. Here is a simple demonstration for showing how to get a ball to move upward after release by putting backspin on it.

Equipment

  1. A ping-pong ball
  2. Some sort of track. I used a 30 inch wall mounted shelving frame piece that you can get at a hardware store (I used this one http://www.lowes.com/ProductDisplay?productId=3006188)

Photo Jan 18, 9 10 20 AM

Figure 1. Equipment.

Demonstration

  1. Hold the bottom of the track and rest the ball on top of your hand (see figure 2 below).
  2. Rotate your wrist rapidly so that the ball is forced up the track and forwards (see figure 3 below)

With a bit of practice you can get the ball to fly off the end of the track roughly horizontally and then rise up due to the lift force

R1

Figure 2. Initial setup.

R2

Figure 3. Launching the ball by rapidly rotating the track.

Explanation

The key to the explanation is that the rotation of the ball leads to asymmetric boundary layer separation. As you flick your wrist and rotate the track the ball is accelerated and forced up the track. Friction with the track imparts a backspin to the ball such that, as the ball leaves the end of the track, it is rotating in a clockwise direction as shown in figure 3. The backspin on the ball means that the lower side of the ball is moving faster than the upper part of the ball (see figure 4 below). As a result, provided you are in the right Reynolds number regime such that the separation point is  Re dependent, the boundary layer on the top of the ball will stay attached over a greater distance than the boundary layer on the lower side (see figure 4 below). As a result the airflow will be deflected downward by the ball.

cureve sep

Figure 4. The rotation of the ball causes the underside to move faster and the underside boundary layer to separate further upstream than on the top.

If you draw a control volume around the ball with the control volume moving with the ball then the C. V.  inflow is in the direction of flight and the outflow is deflected downward. Therefore, the ball must be applying a downward force on the airflow to create the downward component of the outflow momentum. As a result, the airflow must be applying a force vertically upward in reaction. This lift force drives the ball upward.

curve CV

Figure 5. Control volume moving with the ball showing the inflow, the deflected outflow and the force that the ball applies to the flow to generate the downward momentum.

The demonstration requires very little equipment but is a little fiddly. You need to use a ping-pong ball as it is light enough that the lift force can overcome the balls weight and move it upward. An alternate way to do this is to spin it sideways and get it to move laterally. The implications of this physics are discussed with actual numbers in “The physics of baseball” by R. K. Adir. The origin of this particular demonstration is unknown though I have seen basic descriptions of it in a few different books.

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

 

Videos of “Spin up, boundary layers, and tracking tea leaves”

Here are the videos of the “Spin up, boundary layers, and tracking tea leaves” demonstration. The video titles link to the full videos.

spinning up

tcup

stopping a fully spun up cup

tcfulldown

stopping a partially spun up cup

tcpartdown

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

Spin up, boundary layers, and tracking tea leaves

Background:

Boundary layers play an important role in many fluid mechanics applications including drag, lift, and flow in conduits. This demonstration illustrates the role of boundary layers as part of the classic spin-up problem. The demonstration is a cheap and easy version of one written up by Nicholas Rott in the book ‘Experiments in fluid mechanics’ (out of print but worth getting a second hand copy of). The demonstration uses tea leaves to visualize the secondary vortex that forms during spin-up. See here for more on tea cup fluid dynamics.

Equipment:

  • Turntable (Lazy Susan)
  • Bag of tea
  • Scissors
  • Half-filled glass of water
  • Tape (to secure the glass to the turntable)

Procedure:

  1. Place the tea bag in a glass of hot water to wet the tea leaves.
  2. Fasten the half-filled glass of water to the turntable with tape.
  3. Using the scissors, cut open the used tea bag and dump roughly half of the tea leaves into the glass of water fastened to the turntable.
  4. Spin the turntable quickly, so that the tea leaves move to the outer edge of the glass. Keep spinning until the water is fully spun up (at least thirty seconds for the glass we used you will need to test this out prior to using the demonstration).
  5. After the elapsed thirty seconds, stop the turntable abruptly.
  6. The tea leaves should move from the outer edge and settle in a heap in the center of the bottom of the glass.
  7. Alternatively, if you do not allow the water in the cup to fully spin up, when you stop it the tea leaves will form a circle at the edge of the secondary vortex (see analysis below).

CAUTION: If not attached well, the glass of water can slide off of the turntable when rotated.

The images below show the tea leaves location when, from left to right, the cup is being spun up, the cup is stopped having been fully spun up, and the cup has been stopped after partial spin up.

spinupspindownfullspindownpart

Analysis (qualitative)

When, starting from rest, the cup is initially spun, a boundary layer forms along the base of the cup. This drives the fluid in a circumferential direction. However, in the absence of any force to balance the resulting normal acceleration, the water in the boundary layer is driven radially outward. This drives the tea leaves to the edge of the cup. The radial outflow is then forced up the side of the cup, though the tea leaves stay in the corner at the base as they are denser than the water.

The vertical flow then turns back in toward the cup center and then down when it reaches the water surface. This creates a cylindrical vortex around the edge of the cup (see figure below). Inside the cylindrical vortex is a non-rotating core with a flat water surface.

partialup

Over time, the cylindrical vortex grows toward the center of the cup until there is no longer a non-rotating core and the water surface is curved all the way across (see figure below). At this point the flow is fully spun up and the tea leaves should still be at the corner of the cup.

fullup

When the cup is abruptly stopped, the water in contact with the base also stops moving. There is, therefore, no longer anything driving the flow radially outward. Instead, there is a hydrostatic pressure gradient toward the center of the cup due to the curved water surface (the water surface remains curved as all the fluid outside the boundary layer does not know the cup has stopped and is still rotating). Therefore, the flow in the bottom boundary layer reverses and the tea leaves are driven into the center of the cup (see figure below).

spindown

In the event that the cup is not fully spun up (step 7 in the procedure section), the hydrostatic pressure gradient only extends from the side of the cup to the edge of the cylindrical vortex (recall that the water surface in the non-rotating core is horizontal). Therefore, the lower boundary layer only flows radially inward to the edge of the cylindrical vortex. The tea leaves thus accumulate at the inner edge of the cylindrical vortex (see figure below).

partialdown

This is a remarkably robust experiment. It is almost impossible for it not to work (provided that the cup is secured to the center of the turntable). Thanks to Alex, and Meredith for putting together this write up and demonstration. Videos to follow soon.

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.