097 – Bottle Tornado

Water vortex  

Bathtub swirl

 

Introduction to:  

  • Vortex
  • Rotational hyperboloid
  • Centrifugal force/centripetal force
  • Conservation of angular momentum
  • Vortex funnel  

Material:  

  • 2 plastic bottles (= PET bottles, recommendation: volume 1.5 liters, absolutely transparent!)   
  • Hard plastic connector, commercially available 

Or  

  • 2 lids  
  • Hot glue with gun 
  • Sandpaper
  • Scissors  

 Instructions: 

  • Take the finished connector  

Or make one yourself:  

  • Roughen the surface of the two lids with sandpaper and glue them together  
  • Use the scissors to drill a hole in the center of the lids. The diameter should be about 5 mm.  
  • Fill one of the two bottles with water, leaving about five centimeters of air at the top.  
  • Screw the second, empty bottle onto the top of the connector.  
  • Turn the two bottles over so that the full bottle comes up.  
  • Spin the water in the top bottle by swirling. This requires some practice. Swirl the bottle like a large glass of water, always in a circle, as if you were stirring in a large saucepan.  
  • Keep the bottles still and watch! 

Observation:  

  • A vortex funnel forms in the upper bottle  

Tips:  

  • If the connection isn’t completely tight, place a bowl underneath it or experiment outdoors.  
  • Experiment with turning the bottle slower or faster  

Didactic potential:  

  • The bathtub vortex exerts a great fascination!  
  • The shape of the vortex can be explained theoretically with secondary school mathematics: The vortex is a consequence of the conservation of angular momentum:  

1. Task:

  • Explain why a water particle m in a water vortex rotates faster (i.e. greater rotational velocity v ) the closer it gets to the axis of rotation! This happens when it is sucked into the vortex.   

2. Task:

  • Show: The surface forms a rotational hyperboloid!  
  • Note: The inclination of the water surface (angle α ) results from the sum of the forces of centrifugal force and the weight force of the volumetric piece. (Forces in the rotating reference frame)