Bubbles Rising in a Tube and Jets Falling from a Nozzle.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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The shape of a two-dimensional bubble rising at a constant velocity U in a tube of width h is computed. The flow is assumed to be inviscid and incompressible. The problem is solved numerically by collocation. The results confirm Garabedins findings. There exists a unique solution for each value of the Froude number FUgh12 smaller than a critical value I sub c. Here g denotes the acceleration of gravity. It is found that I sub c 0.36. In addition the problem of a jet emerging from a vertical nozzle is considered. It is shown that the slope of the free surface at the separation points is horizontal for F F sub c and vertical for F F sub c. Graphs and tables of the results are included. Author
- Numerical Mathematics
- Fluid Mechanics