Pressure in a viscous liquid versus non-viscous fluids

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Discussion Overview

The discussion centers on the differences in pressure definitions and behaviors between viscous and non-viscous fluids, particularly in the context of fluid dynamics and rheology. Participants explore the implications of viscosity on pressure orientation and the foundational principles governing fluid behavior.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant references Hc Verma's definition of pressure for non-viscous fluids and questions why this definition does not apply to viscous fluids, specifically regarding the dependence of pressure on orientation.
  • Another participant introduces the constitutive equation for Newtonian fluids, highlighting its role in fluid dynamics and stating that it encompasses both shear and normal stresses, suggesting a more complex behavior in viscous fluids.
  • A later reply acknowledges a lack of familiarity with the constitutive equation, indicating a gap in understanding among some participants regarding advanced fluid dynamics concepts.
  • Another participant suggests consulting "Transport Phenomena" by Bird et al. for further study on the topic.

Areas of Agreement / Disagreement

Participants express differing levels of familiarity with advanced fluid dynamics concepts, and there is no consensus on the implications of viscosity on pressure orientation. The discussion remains unresolved regarding the specific effects of viscosity on pressure definitions.

Contextual Notes

Some participants may lack foundational knowledge of rheological equations, which could limit their understanding of the discussion. The conversation also reflects varying levels of expertise in fluid dynamics.

Who May Find This Useful

This discussion may be useful for students and professionals interested in fluid dynamics, particularly those exploring the differences between viscous and non-viscous fluids and the underlying principles of rheology.

Kashmir
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Hc verma, concepts of Physics, vol 1 pg 258
"We define pressure of fluid at the point A as : ##P= F/\Delta S##
For a homogeneous and non-viscous fluid, this quantity does not depend on orientation of ##\Delta S## and hence we talk of pressure at a point".

Why did the author stress that the definition holds only for non-viscous fluids?
What happens to viscous fluids? Does the pressure depend on orientation in viscous fluids ?
 
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Are you familiar with with the constitutive equation (rheological equation of state) for a Newtonian fluid in 3D in terms of the fluid viscosity, "pressure," and velocity gradient tensor? This is the more general version of Newton's law of viscosity that we learned about in freshman physics, and forms the basis of most of the fluid dynamics that we work with in practice. It includes not only shear stresses, but normal stress as well. The Newtonian fluid model reduces to an isotropic stress tensor (pressure) in the limit of static equilibrium.
 
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Chestermiller said:
Are you familiar with with the constitutive equation (rheological equation of state) for a Newtonian fluid in 3D in terms of the fluid viscosity, "pressure," and velocity gradient tensor? This is the more general version of Newton's law of viscosity that we learned about in freshman physics, and forms the basis of most of the fluid dynamics that we work with in practice. It includes not only shear stresses, but normal stress as well. The Newtonian fluid model reduces to an isotropic stress tensor (pressure) in the limit of static equilibrium.
Thank you.
No, I've not studied it.
 
Kashmir said:
Thank you.
No, I've not studied it.
See Transport Phenomena by Bird et al
 

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