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Consistency between subjects is key. If continuum mechanics is taught rigorously, but fluid mechanics rationalizes concepts erroneously, learning is compromised. Formalism cannot be replaced by incorrect simplifications.

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This creates great confusion among students: from one class to another, the same concept is explained with opposing levels of rigor. What is precise in continuum mechanics is oversimplified to the point of distortion in fluid mechanics.

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These errors are not harmless. In my continuum mechanics class, we rigorously teach the formalism and precise explanations. But in fluid mechanics, all that formalism is reduced to a pedestrian and erroneous rationalization of the theory.

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- Navier-Stokes does not apply to non-Newtonian fluids: Models like Power-Law (τ = K·γ̇ⁿ) or Carreau (μ = μ₀[1 + (λγ̇)²]^((n-1)/2)) are required.

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Technical explanation of ERROR 7: - λ: Second viscosity coefficient, measures resistance to volume changes (rapid compression/expansion). - For ideal gases, λ = -2/3 μ (Stokes' relation). - In liquids, λ ≈ 0 (incompressible).

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The full stress tensor for compressible fluids is: σᵢⱼ = -pδᵢⱼ + λ(∇·u)δᵢⱼ + 2μDᵢⱼ.

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ERROR 7: She omitted the second viscosity coefficient (λ) in Navier-Stokes and said the equation "applies to all fluids, including non-Newtonian ones." Why it's wrong: Navier-Stokes assumes: 1. Newtonian fluid (τ ∝ γ̇). 2. Linear relationship between τ and γ̇.

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Pedagogical context of ERROR 6: Applications: Materials like toothpaste, drilling mud, or fresh concrete follow this model. Key difference: Unlike an elastic solid, playdough does not regain its original shape when stress is removed. It is a fluid with stress memory.

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Technical explanation of ERROR 6: The Bingham model describes its behavior: - For τ < τ₀: Behaves like a rigid solid (no flow). - For τ ≥ τ₀: τ = τ₀ + μ·γ̇ (flows like a viscous fluid with viscosity μ). Example: Playdough has τ₀ ≈ 100–1000 Pa, depending on composition.

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ERROR 6: She said: "Playdough is a solid." Why it's wrong: Playdough is a viscoplastic material, specifically a Bingham plastic. - It does not flow until shear stress exceeds a yield stress (τ₀). - For τ > τ₀, it behaves like a viscous fluid.

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Pedagogical context of ERROR 5: Practical example: If you hit the mixture with a hammer, the high deformation rate (γ̇) generates very high apparent viscosity, making it behave like a "solid." At rest, γ̇ = 0 → low viscosity → slow flow. It is not a phase change; it is nonlinear rheological behavior.

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Mechanism: At low stress, particles are dispersed. As γ̇ increases, ordered structures form, increasing flow resistance.

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Technical explanation of ERROR 5: Non-Newtonian fluids are classified by their flow curve (τ vs. γ̇): - Shear-thickening (dilatant): τ = K·γ̇ⁿ (n > 1). Example: cornstarch + water (n ≈ 1.5–2).

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ERROR 5: She said: "Cornstarch mixed with water is a fluid when at rest, and when squeezed, it becomes solid." Why it's wrong: The mixture is a shear-thickening non-Newtonian fluid. Its viscosity increases with shear stress, but it remains a fluid. There is no phase change to solid.

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Pedagogical context of ERROR 4: Example: In Poiseuille flow (cylindrical pipe), shear stress varies linearly with radius: τ(r) = (Δp/2L)r, where Δp is the pressure difference and L is the pipe length. Pressure (p) is constant across a cross-section, but τ depends on position.

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- Deviatoric part: τᵢⱼ (shear stresses, acts tangentially). In a moving Newtonian fluid: τᵢⱼ = 2μDᵢⱼ, where Dᵢⱼ = ½(∂uᵢ/∂xⱼ + ∂uⱼ/∂xᵢ) is the deformation rate tensor.

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Technical explanation of ERROR 4: The stress tensor (σᵢⱼ) in a fluid decomposes into: - Isotropic part: -pδᵢⱼ (pressure, acts in all directions).

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Both are measured in [Pa], but they are not equivalent.

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ERROR 4: She said: "Shear is opposite to stress and is measured the same as pressure." Why it's wrong: - Shear stress (τ): Tangential component of the stress tensor. - Pressure (p): Normal component of the stress tensor, acting isotropically (in all directions).

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Technical explanation of ERROR 3: Dynamic viscosity (μ) originates from the kinetic theory of gases (for gases) or molecular interactions (for liquids). It is a direct measure of resistance to flow. Kinematic viscosity (ν) is a mathematical tool to simplify equations in fluid dynamics.

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- ν is a derived property (μ/ρ), useful for dimensional analysis.

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ERROR 3: She invented the term "real viscosity" to refer to μ. Why it's wrong: There is no classification of "real" or "unreal" for viscosity. - μ is the dynamic viscosity, an intrinsic property of the fluid that quantifies its resistance to flow.

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Technical explanation of ERROR 2: - μ appears in Newton's law of viscosity and in the Reynolds number (Re = ρUL/μ) - ν simplifies flow analysis where density is constant (e.g., Re = UL/ν) The term "kinetic viscosity" does not exist. "Kinematic" refers to motion, not a physical property of the fluid.

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- ν [m²/s]: Kinematic viscosity is defined as ν = μ/ρ.

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ERROR 2: She confused kinematic viscosity (ν) with dynamic viscosity (μ) and used the term "kinetic viscosity." Why it's wrong: - μ [Pa·s]: Dynamic (or absolute) viscosity relates shear stress (τ) to the velocity gradient in a Newtonian fluid: τ = μ (du/dy).

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Pedagogical context of ERROR 1: In the continuity equation for fluids: - Incompressible: ∇·u = 0 (constant volume). - Compressible: ∂ρ/∂t + ∇·(ρu) = 0 (variable volume). Gases are compressible fluids, and their behavior is governed by the compressible Euler or Navier-Stokes equations.

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Both are fluids. The equation of state (e.g., p = ρRT for ideal gases) describes their compressibility but does not exclude them from the fluid category.

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Technical explanation of ERROR 1: - Liquids: Almost incompressible fluids (e.g., water, ρ ≈ constant). - Gases: Compressible fluids (e.g., air, ρ varies with p and T).

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Gases meet this definition. The difference between liquids and gases is their compressibility, not their nature as fluids.

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ERROR 1: She said: "Gases are not fluids because they are not liquids." Why it's wrong: The definition of a fluid in continuum mechanics is clear: "A substance that deforms continuously under the action of shear stress, no matter how small."

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Today, I witnessed a fluid mechanics lab session where the person in charge made serious conceptual errors. Below, I will quote each error verbatim, explain why it is theoretically incorrect, and rigorously develop the correct concept.

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Eduardo Mora @moraedd.bsky.social · 10/08/2026

Créditos: El Perro de Cervantes Es importante aclarar que Adrian Bejan es ingeniero, no físico. (Cualquier parecido con la realidad, es mera coincidencia)

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Sigo escribiendo, sigo viviendo. eduardogmora.wixsite.com/edu-entre-pa... Crossposted with @openvibe.social

eduardogmora.wixsite.com

Inicio | Edu Entre Paréntesis

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Eduardo Mora @moraedd.bsky.social · 07/08/2026

Today's talk: Exergy Destruction in Concentrating Solar collectors In the presentation, a simple approach to identify the irreversibilities during the solar irradiance harnessing in concentrating devices. Crossposted with @openvibe.social

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Above all, Miroslav was a kind and generous friend. His warmth, wisdom, and passion for science inspired everyone who knew him. He will be deeply missed.

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Above all, Miroslav was a kind and generous friend. His warmth, wisdom, and passion for science inspired everyone who knew him. He will be deeply missed.

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He is best known for developing GENERIC, a universal framework for describing how physical systems evolve. His legacy in thermodynamics will endure for generations.

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Miroslav’s work revolutionized our understanding of physical systems. His contributions to Non-Equilibrium Reversible-Irreversible Coupling (NERIC) remain foundational.

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It is with deep sadness that I share the passing of Miroslav Grmela, a brilliant thermodynamics researcher and a dear friend, on June 16, 2026, at the age of 87. Crossposted with @openvibe.social

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Publicación original: mastodon.social/@greenpeace/... Crossposted with @openvibe.social

France is burning

Our hearts are with everyone forced to flee their homes, firefighters risking everything and every community living through this nightmare

You deserve better

This isn't "just nature"

Decades of burning coal, oil & gas are making wildfires more frequent and more destructive

The fossil fuel corporations behind this crisis knew

They kept drilling
They kept profiting

Communities pay the price

Time to make polluters pay: https://act.gp/3RLI2EV#MakePollutersPay#wildfires

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I'm really glad to teach again continuum mechanics at the university.

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Engineers solve these for different applications so materials does not crush (or crush, depending on the application) under certain operational conditions.

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