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Related Concept Videos

Density, Specific Weight, Specific Gravity and Compressibility of Fluid01:27

Density, Specific Weight, Specific Gravity and Compressibility of Fluid

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Density, specific weight, specific gravity, and compressibility are fundamental properties of fluids. Density is the mass per unit volume, characterizing the mass of a fluid system. It influences buoyancy, pressure, flow dynamics, viscosity, thermal conductivity, and sound propagation. For instance, in pipeline design, accurate density measurements ensure that the pipeline can handle the fluid's mass.
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Shearing Stress01:19

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Shearing stress, denoted by the Greek letter tau (τ), is stress caused by forces acting transversely on an object. These forces create internal ones within the entity in the plane where the external forces are applied. The resultant of these internal forces is the shear in the section.
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Components of Stress01:23

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Stress analysis under multiple loading conditions is intricate, necessitating a comprehensive grasp of normal and shearing stresses. Consider a small cube at point O, subjected to stress on all six faces, visible or not. Normal stress components σx, σy, σz act perpendicularly to the x, y, and z axes. Shearing stress components τxy and τxz are exerted on faces perpendicular to these axes.
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Shearing Stresses in a Beam: Problem Solving01:14

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A cantilever beam with a rectangular cross-section under distributed and point loads experiences shearing stresses. The analysis begins by identifying the loads acting on the beam. Then, the reactions at the beam's fixed end are calculated using equilibrium equations. The vertical reaction is a combination of the distributed and point loads, while the moment reaction is the sum of their moments. The shear force distribution along the beam, resulting from these loads, is established by creating...
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Elastic Strain Energy for Shearing Stresses01:20

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As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
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Related Experiment Video

Updated: Feb 10, 2026

The Assembly and Application of 'Shear Rings': A Novel Endothelial Model for Orbital, Unidirectional and Periodic Fluid Flow and Shear Stress
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Shear-density coupling for a compressible single-component yield-stress fluid.

Markus Gross1, Fathollah Varnik

  • 1Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany.

Soft Matter
|May 23, 2018
PubMed
Summary

This study models yield stress fluid flow, revealing how density and velocity changes create flow heterogeneity. At high densities and low shear rates, distinct regions of high/low density and shear rate emerge in steady states.

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Area of Science:

  • Soft Matter Physics
  • Rheology
  • Fluid Dynamics

Background:

  • Yield stress fluids exhibit complex flow behaviors not fully captured by standard models.
  • Understanding flow heterogeneity is crucial for applications involving colloidal glasses and similar materials.

Purpose of the Study:

  • To develop and analyze a hydrodynamic model for single-component yield stress fluid flow.
  • To investigate the emergence of flow heterogeneity under specific conditions (low shear rates, high densities).

Main Methods:

  • Utilized a Herschel-Bulkley-type constitutive model coupled with density and velocity gradient fluctuations.
  • Analyzed linearized hydrodynamic equations and cubic dispersion relations for fluctuation dynamics.
  • Examined mechanical equilibrium conditions and dynamical evolution under various boundary conditions.

Main Results:

  • Identified a regime of growing flow heterogeneity at specific densities and shear rates.
  • Observed the formation of spatially inhomogeneous stationary profiles with coexisting high/low density and shear rate regions.
  • Demonstrated that steady states result from a balance between shear-induced density variations and relaxation via sound waves.

Conclusions:

  • The model successfully predicts flow heterogeneity in yield stress fluids, particularly in colloidal glasses.
  • The interplay between density fluctuations and shear is key to understanding non-uniform flow states.
  • The study provides criteria for steady-state solutions and insights into dynamic flow evolution.