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Related Concept Videos

Steady, Laminar Flow in Circular Tubes01:23

Steady, Laminar Flow in Circular Tubes

Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is purely axial,...
Irrotational Flow01:28

Irrotational Flow

Irrotational flow is characterized by fluid motion where particles do not rotate around their axes, resulting in zero vorticity. For a flow to be irrotational, the curl of the velocity field must be zero. This imposes specific conditions on velocity gradients. For instance, to maintain zero rotation about the z-axis, the gradient condition:
Design Example: Flow of Oil Through Circular Pipes01:25

Design Example: Flow of Oil Through Circular Pipes

Understanding fluid flow behavior through pipes is critical in fluid mechanics, especially in applications like oil transportation through pipelines. Hagen-Poiseuille's law provides an exact solution derived from the Navier-Stokes equations for steady, incompressible, and laminar flow within a circular pipe. Hagen-Poiseuille's law helps determine the necessary pressure drop across a pipeline section by determining parameters like pipe length, radius, oil viscosity, and the desired volumetric...
Thin-Walled Hollow Shafts01:15

Thin-Walled Hollow Shafts

In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution of...
Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
Couette Flow01:22

Couette Flow

Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...

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Updated: Jul 4, 2026

Uncoupling Coriolis Force and Rotating Buoyancy Effects on Full-Field Heat Transfer Properties of a Rotating Channel
10:03

Uncoupling Coriolis Force and Rotating Buoyancy Effects on Full-Field Heat Transfer Properties of a Rotating Channel

Published on: October 5, 2018

Granular flow in rotating cylinders with noncircular cross sections.

D V N Prasad1, D V Khakhar

  • 1Department of Chemical Engineering, Indian Institute of Technology-Bombay, Powai, Mumbai 400076, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 4, 2008
PubMed
Summary

Rotating cylinders with non-circular cross-sections enhance granular material mixing. The study reveals how particle flow layers change with rotation, improving chaotic advection and tracer mixing in granular materials.

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10:03

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Area of Science:

  • Physics
  • Fluid Dynamics
  • Materials Science

Background:

  • Granular material flow in rotating cylinders is crucial for mixing applications.
  • Understanding particle dynamics in confined geometries is complex.
  • Previous studies often focused on circular cross-sections.

Purpose of the Study:

  • To experimentally and theoretically investigate granular flow in rotated cylinders with varying cross-sectional shapes.
  • To analyze the impact of geometry on particle layer dynamics and mixing efficiency.
  • To develop and validate a predictive model for layer thickness variations.

Main Methods:

  • Experimental flow visualization of glass beads in quasi-two-dimensional mixers.
  • Development of a depth-averaged flow model.
  • Analytical perturbation solution and numerical simulations.
  • Comparison of theoretical predictions with experimental measurements.

Main Results:

  • Particle flow is confined to a shallow surface layer that periodically changes in thickness and length.
  • Chaotic advection and improved mixing of passive tracers are observed.
  • The model accurately predicts layer thickness profiles, especially for circular cylinders.
  • Non-circular geometries show larger variations in layer thickness compared to circles.
  • Theoretical predictions align well with experimental data for scaled midlayer thickness variation.

Conclusions:

  • The study provides a comprehensive understanding of granular flow in rotated cylinders with diverse cross-sections.
  • The developed model and solutions offer accurate predictions for layer dynamics.
  • Geometric variations significantly influence mixing efficiency through modulation of chaotic advection.
  • Findings are applicable to the design of advanced granular mixers and material processing equipment.