### Session JN: General Fluid Dynamics I

3:35 PM–5:58 PM, Monday, November 19, 2007
Salt Palace Convention Center Room: 251 B

Chair: Patrick Weidman, University of Colorado

Abstract ID: BAPS.2007.DFD.JN.4

### Abstract: JN.00004 : Contraction of an inviscid swirling liquid jet: Comparison with results for a rotating granular jet.

4:14 PM–4:27 PM

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#### Authors:

P.D. Weidman
In honor of the tercentenary of Leonhard Euler, we report a new solution of the Euler equations for the shape of an inviscid rotating liquid jet emanating from a tube of inner radius R$_{0}$ aligned with gravity. Jet contraction is dependent on the exit swirl parameter $\chi_{0}$ = R$_{0}$ $\Omega_{0}$/U$_{0}$ where $\Omega_{0}$ and U$_{0}$ are the uniform rotation rate and axial velocity of the liquid at the exit. The results reveal that rotation reduces the rate of jet contraction. In the limit $\chi_{0} \to$ 0 one recovers the contraction profile for a non-rotating jet and the limit $\chi_{0} \to \infty$ gives a jet of constant radius. In contrast, experiments and a kinematic model for a rotating non-cohesive granular jet show that it expands rather than contracts when a certain small angular velocity is exceeded. The blossoming profiles are parabolic in nature. The model predicts a jet of uniform radius for $\chi_{0} \to$ 0 and a jet with an initially horizontal trajectory in the limit $\chi_{0} \to \infty$.