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Related Concept Videos

Magnetic Flux01:18

Magnetic Flux

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The magnetic flux measures the number of magnetic field lines passing through a given surface area. The SI unit for magnetic flux is the weber (Wb). Magnetic flux is a scalar quantity. It depends on three factors: the strength of the magnetic field B, the area through which the field lines pass, and the relative orientation of the field with the surface area.
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The concept of flux describes how much of something goes through a given area. More formally, it is the dot product of a vector field within an area. For a better understanding, consider an open rectangular surface with a small area that is placed in a uniform electric field. The larger the area, the more field lines go through it and, hence, the greater the flux; similarly, the stronger the electric field (represented by a greater density of lines), the greater the flux. On the other hand, if...
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Consider the electric field of an oppositely charged, parallel-plate system and an imaginary box between those plates. Let the bottom face of the box be ABCD, and the top face be FGHK. The electric field between the plates is uniform and points from the positive plate toward the negative plate. The calculation of this field's flux through the box's various faces shows that the net flux through the box is zero. Why does the flux cancel out here?
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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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Velocity Potential01:20

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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:
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Related Experiment Video

Updated: Mar 3, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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Gravity-Driven Flux of Particles through Apertures.

Ram Sudhir Sharma1, Alexandre Leonelli1, Kevin Zhao2

  • 1University of California, Department of Mechanical Engineering, Santa Barbara, California 93106, USA.

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|March 1, 2026
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Summary

Granular material discharge is explained by a new kinematic framework. This model separates velocity and packing effects, revealing a universal correction factor for flow deviations.

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Area of Science:

  • Granular physics
  • Fluid dynamics
  • Materials science

Background:

  • Gravity-driven granular discharge is a fundamental problem.
  • Classical descriptions rely on empirical laws with fitting parameters.
  • Disentangling mass flux into velocity and packing is crucial.

Purpose of the Study:

  • To develop a kinematic framework for granular discharge.
  • To understand deviations from free-fall limits.
  • To explain the universality of granular flow.

Main Methods:

  • Combining three-dimensional experiments and simulations.
  • Defining a dimensionless flux ratio.
  • Analyzing spherical cohesionless grains.

Main Results:

  • A dimensionless flux ratio captures confinement effects.
  • Deviations from free-fall are described by an exponential correction factor.
  • A characteristic length scale of 10-15 grain diameters modifies packing structure.

Conclusions:

  • The proposed kinematic framework explains granular discharge universality.
  • The framework moves beyond purely empirical descriptions.
  • Understanding packing structure modification is key to flow behavior.