the text makes a big deal about saying fluids don’t have friction, but I don’t get what the big deal is – why is it wrong to say that there is fluid friction or skin friction
This text is generated by AI trained by Professor Brian J. Kirby on his lectures, videos, notes, message board responses, and textbook
PK Bot’s answer:
The distinction between viscosity and friction is important in fluid mechanics because they describe different physical phenomena, even though they both dissipate mechanical energy as heat.
Viscosity vs. Friction:
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Viscosity is a property of fluids that describes how they resist deformation due to internal shear stresses. It is a measure of a fluid’s resistance to flow and is related to the velocity gradients within the fluid. Viscous stresses arise from the relative motion of fluid layers and are linear with respect to the velocity gradient in Newtonian fluids. Viscosity is an intrinsic property of the fluid and is present throughout the fluid domain.
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Friction, on the other hand, typically refers to the force resisting the relative motion of solid surfaces in contact. It is characterized by coefficients of static and dynamic friction, which are not present in Newtonian fluids like air or water. Friction forces are generally nonlinear and depend on the normal force between the surfaces.
Why the Distinction Matters:
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Boundary Layers: In fluid mechanics, the term “skin friction” is often used to describe the viscous drag on a solid surface due to the no-slip condition, where the fluid velocity at the boundary matches the velocity of the solid surface. This is a viscous effect, not a frictional one in the traditional sense. Here, “friction” is a metaphor. Using the word “friction” is harmless as long as you know that really the phenomenon is viscous, and “friction” is being used because viscosity is dissipative like friction. Professor Kirby’s text says that this metaphor is misleading.
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Misleading Intuition: Comparing viscosity to friction can be misleading because it suggests that the same principles apply to both phenomena. For example, in a Couette flow, the shear stress on different planes arises from the same viscous effect, which does not have a direct analogy in solid friction. Specifically, a Couette flow with a nonzero \partial u /\partial y term feels both a nonzero \tau_{yx} term (this stress is analogous to the friction stress on solids sliding relative to each other) and a nonzero \tau_{xy} term (this is the term that into fluids forget about when they use friction to try to intuit the dyadic nature of the stress).
In summary, although both viscosity and friction dissipate energy, they do so through different mechanisms. Understanding this distinction is crucial for accurately analyzing and predicting fluid behavior, especially in engineering applications involving boundary layers and flow over surfaces.
In formulating this response, I consulted the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked the sections based on their relevance. If they are marked as relevant, I encourage you to explore them:
Textbook sections:
- Appendix F.1: Pressure and Viscosity Part 3 (HIGHLY RELEVANT)
- Chapter 10.3: Boundary Layers: Overview Part 3 (HIGHLY RELEVANT)
- Chapter 10 Fundamentals: There is a fundamental mathematical reason why the assumptions that your fl… (HIGHLY RELEVANT)
- Chapter 3 Engineering Models: Temporal and Spatial Averaging in the Continuum Model of Fluid Mechani… (HIGHLY RELEVANT)
- Chapter 2 Engineering Models: Temporal and Spatial Averaging in the Continuum Model of Fluid Mechani… (HIGHLY RELEVANT)
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