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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.
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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,...
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Laminar flow represents a smooth, orderly fluid motion where particles move along parallel paths, resulting in minimal mixing between layers. Streamlined particle paths characterize this flow regime and occur under conditions where viscous forces dominate over inertial forces. The distinction between laminar, transitional, and turbulent flow is primarily determined by the Reynolds number, a dimensionless quantity calculated as:
General External Flow Characteristics01:26

General External Flow Characteristics

The study of external flow is essential for creating structures and objects that interact efficiently and safely with moving fluids, such as air or water. When a body is immersed in a flowing fluid, it experiences two primary forces: drag, which opposes motion along the flow direction, and lift, which acts perpendicular to the flow. The shape, size, and orientation of the object influence these forces.Streamlined and Blunt Bodies in External FlowObjects in fluid flow are classified as...
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Coupled air/granular flow in a linear Hele-Shaw cell.

Ø Johnsen1, R Toussaint, K J Måløy

  • 1Department of Physics, University of Oslo, P.O. Box 1048, Blindern, 0316 Oslo, Norway.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 21, 2008
PubMed
Summary

Air injection into granular materials creates distinct flow patterns. This study identifies four hydrodynamic regimes, revealing coupled air-grain flows and channelization that significantly alter material permeability.

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Area of Science:

  • Physics
  • Fluid Dynamics
  • Materials Science

Background:

  • Pattern formation in granular materials is crucial for understanding multiphase flows.
  • Hele-Shaw cells provide a controlled environment for studying granular dynamics.

Purpose of the Study:

  • To experimentally investigate pattern formation during air injection into granular media.
  • To characterize the dynamics and features of these patterns.
  • To classify behaviors based on key parameters.

Main Methods:

  • Experimental investigation using a linear Hele-Shaw cell.
  • Fast image analysis for pattern characterization.
  • Sensitive pressure measurements for dynamic analysis.
  • Classification based on injection pressure and plate opening.

Main Results:

  • Four distinct hydrodynamic regimes were identified.
  • Strong coupling and instability observed between air and grain flows in certain parameter regions.
  • Evidence of channelization within the granular material.
  • Significant large-scale permeability variations due to channelization.

Conclusions:

  • Air injection in granular materials leads to complex pattern formation.
  • Flow behavior is highly dependent on injection pressure and plate opening.
  • Channelization significantly impacts the effective permeability of the granular medium.