Bubbles Rising in a Tube and Jets Falling from a Nozzle.

Abstract

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 Garabedin's findings. There exists a unique solution for each value of the Froude number F=U/(gh)1/2 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)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1984
Accession Number
ADA139266

Entities

People

  • J. M. Vanden-broeck

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Analytic Functions
  • Coefficients
  • Continents
  • Equations
  • Experimental Data
  • Flow
  • Froude Number
  • Geographic Regions
  • Infinite Series
  • Mathematics
  • Military Research
  • North America
  • North Carolina
  • Security
  • Two Dimensional
  • United States
  • Wisconsin

Fields of Study

  • Mathematics
  • Physics

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Fluid Dynamics.
  • Underwater engineering and Marine Technology.