Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Probabilistic computation of Poiseuille flow velocity fields

Published

Author(s)

Fern Y. Hunt, J. F. Douglas, Javier Bernal

Abstract

Velocity fields for Poiseuille flow through tubes having general cross section are calculated using a path integral method involving the first‐passage times of random walks in the interior of the cross sectional domain D of the pipe. This method is applied to a number of examples where exact results are available and to more complicated geometries of practical interest. These examples include a tube with ‘‘fractal'' cross section and open channel flows. The calculations demonstrate the feasibility of the probabilistic method for pipe flow and other applications having an equivalent mathematical description (e.g., torsional rigidity of rods, membrane deflection). The example of flow through a fractal pipe shows an extended region of diminished flow velocity near the rough boundary which is similar to the suppressed vibration observed near the boundaries of fractal drums.
Citation
Journal of Mathematical Physics
Volume
36
Issue
5

Citation

Hunt, F. , Douglas, J. and Bernal, J. (1995), Probabilistic computation of Poiseuille flow velocity fields, Journal of Mathematical Physics, [online], https://doi.org/10.1063/1.531044 (Accessed April 15, 2024)
Created April 30, 1995, Updated October 12, 2021