Fluid Cylinders or Jets

A slow-moving, thin cylindrical stream of water issuing from a faucet can often be seen to become nonuniform in diameter at some distance below the faucet and eventually to break up into drops. In a similar manner the beads on a spider s web are formed by instability of a cylinder of sticky liquid surrounding the thread leaving the spider s body. This instability is sometimes used in industrial processes to disperse one fluid in another by injecting it in the form of a jet. 

If effects of gravity are neglected, the equation of motion simplifies to 

Taking the divergence of this equation and invoking the continuity equation V v = 0, we find 

The solution to this equation, which remains finite at r = 0, is given by 

In a similar manner we take the radial velocity to have the form 

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