Tuesday, November 20, 2007

Doublet, Source or Sink

Warning geekiness will follow, if not interested just skip to next section. Source or sink? Well as it turns out a doublet it both. It is where you have a source at –B and a sink at B then you let B → 0. So basically you have a source (radial flow outward) and a sink (radial flow inward) in the same place, the flow resembles a dipoles field lines. Why do I mention this, well as it happens if you have a doublet and put it in a uniform flow (a flow at constant speed) the system mathematically models a cylinder in a uniform flow. Now the cool thing that arises from this is what is called the D’Alembert’s Paradox, which is if you solve for the net force acting on the “cylinder” it works out to be zero which can’t be right since the constant flow should apply a force. This was solved by Ludwig Prandtl who introduced the concept of boundary layers, this allowed for there to be a force. Now the really cool geeky thing about this is that if you can make a doublet and use a superfluid for your fluid you can theoretically get no net force on the cylinder in a uniform flow.

Now on to the fun for everyone part. Based upon the stuff above (which you don’t need to read) if you add a vortex to the system, that is take a spinning cylinder in a flow you get a lift force acting perpendicular to the initial flow, this is called the Magnus Effect. From all this you get Anton Flettner who invented the Flettner Rotor Ship.

This actually crossed the Atlantic. He also invented a rotor mill (which I can't find a good picture of), which used the same principle as the ship; it was a windmill that for the paddles had spinning cylinders.

Sorry about the massive amount of technical geeky stuff in this post.

1 comment:

  1. want to know how source + sink is a doublet. any help is appreciated.