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General Characteristics of Pipe Flow II

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When fluid enters a pipe, it first passes through the entrance region, where the velocity profile adjusts due to viscous effects. In this region, a boundary layer forms along the pipe walls and grows until it fully occupies the pipe's cross-section. Once the boundary layer merges, the flow becomes fully developed, with a steady velocity profile that remains consistent along the pipe's length.
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Related Experiment Video

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Model for density waves in gravity-driven granular flow in narrow pipes.

Simen A Ellingsen¹, Knut S Gjerden, Morten Grøva

¹Department of Energy and Process Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 28, 2010

Summary

Density waves in granular flow through pipes form when wall collisions are more dissipative than particle collisions. Counterintuitively, higher flow rates occur with more grains per wave, approaching a constant in simulations.

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Published on: February 22, 2018

Area of Science:

Physics
Granular Flow Dynamics
Statistical Mechanics

Background:

Granular materials exhibit complex flow behaviors, particularly in confined geometries.
Understanding density wave formation is crucial for predicting flow rates and stability.

Purpose of the Study:

To investigate the formation criteria of density waves in gravity-driven granular flow through a narrow pipe in a vacuum.
To analyze the relationship between flow rate, wave characteristics, and collisional dissipation.

Main Methods:

Utilized a one-dimensional model incorporating two coefficients of restitution.
Performed numerical simulations to observe and analyze density wave phenomena.

Main Results:

Density waves emerge when wall-particle collision dissipation exceeds inter-particle collision dissipation.
Maximal flow rates correlate with an increasing number of grains per density wave.
The number of grains per wave tends towards a constant as particle count increases.

Conclusions:

A simple criterion governs density wave formation in this granular flow system.
The observed wave collapse in previous studies may be attributed to insufficient particle numbers for multiple wave development.