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Related Concept Videos

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.
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:
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...
Velocity Potential01:20

Velocity Potential

In steady, incompressible flow through a long, straight pipe with a uniform cross-section, the flow in the central region (far from the pipe walls) is irrotational. This irrotational nature means that fluid particles do not rotate around their axes, and a scalar function called the velocity potential, represented by ϕ, can be used to describe their movement. In irrotational flows, the velocity field V is defined as the gradient of the velocity potential:
Dimensionless Groups in Fluid Mechanics01:15

Dimensionless Groups in Fluid Mechanics

Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in...

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Related Experiment Video

Updated: Jun 14, 2026

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

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Published on: February 3, 2014

Appearance of three dimensionality in wall-bounded MHD flows.

R Klein1, A Pothérat

  • 1Applied Mathematics Research Centre, Coventry University, Priory Street, Coventry CV1 5FB, United Kingdom.

Physical Review Letters
|April 7, 2010
PubMed
Summary

Researchers experimentally observed how three dimensionality emerges in magnetohydrodynamic flows. Inertia drives these phenomena, offering insights into geophysical and astrophysical fluid dynamics.

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Related Experiment Videos

Last Updated: Jun 14, 2026

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

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Published on: February 3, 2014

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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Published on: July 19, 2016

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Published on: August 26, 2019

Area of Science:

  • Fluid Dynamics
  • Magnetohydrodynamics
  • Plasma Physics

Background:

  • Wall-bounded flows often exhibit two-dimensional characteristics.
  • Understanding the transition to three-dimensionality is crucial for complex fluid systems.

Purpose of the Study:

  • To experimentally characterize the emergence of three dimensionality in wall-bounded magnetohydrodynamic (MHD) flows.
  • To identify and differentiate mechanisms leading to three-dimensional behavior.

Main Methods:

  • Experimental analysis of a square array of vortices in a cubic container.
  • Observation of vortex breakdown and disruption phenomena.

Main Results:

  • Identified 'weak' three dimensionality via differential rotation within 2D vortices.
  • Observed 'strong' three dimensionality through vortex disruption, leading to steady 3D vortex arrays and scale-selective breakdown in chaotic flows.

Conclusions:

  • Inertia is the primary driver for the observed three-dimensional phenomena in MHD flows.
  • These findings are relevant to two-dimensionalizing flows in geophysics and astrophysics, such as rotating or stratified flows.