Pressure and normal stress in fluid mechanics

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SUMMARY

The discussion clarifies the distinction between pressure and normal stress in fluid mechanics. Pressure is defined as the force exerted by surrounding fluids on an infinitesimal fluid cell, while normal stress encompasses both pressure and additional normal viscous stresses that arise during fluid deformation. In static equilibrium, only pressure contributes to the stress, but in dynamic scenarios, viscous stresses must also be considered. The overall stress tensor is a combination of isotropic pressure and non-isotropic viscous stresses for incompressible fluids.

PREREQUISITES
  • Understanding of fluid mechanics principles
  • Familiarity with stress tensors in continuum mechanics
  • Knowledge of static and dynamic fluid equilibrium
  • Concept of viscous stresses in fluid dynamics
NEXT STEPS
  • Study the derivation of the stress tensor in fluid mechanics
  • Learn about the Navier-Stokes equations for viscous fluid flow
  • Explore the concept of shear stress and its effects on fluid behavior
  • Investigate the differences between isotropic and non-isotropic stresses
USEFUL FOR

Students of fluid mechanics, engineers working with fluid dynamics, and researchers focusing on stress analysis in fluids will benefit from this discussion.

asteroid21
Hi, everyone.
I am learning fluid mechanics. One book says that for a infinitesimal fluid cell, surface force includes
1) the pressure, which is imposed by the outside fluids surrounding the concerned fluid cell
2) the shear and normal stress, which result in shear deformation and volume change, respectively.

But I think normal stress is pressure. Can anyone help me clarify?
Thank you.
 
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If the fluid is in static equilibrium, then only the pressure contributes. But, if the fluid is deforming, then there are viscous stresses in the fluid over and above the pressure; both go into determining the force per unit area. The overall stress tensor is a linear combination of the pressure (which is isotropic) and the viscous stresses, which, for an incompressible fluid, are not isotropic. The normal stress on an element of area is the sum of the pressure plus the normal viscous stress.

Chet
 

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