Dimensions of Material and Transport Coefficients
A constitutive coefficient's dimensions are defined by the physical law relating flux, stress, strain, gradient, or response; the same descriptive word can denote different coefficients, so the defining equation is essential.
Why this shows up in the exam
Selecting material data · Checking transport equations · Comparing elastic and fluid coefficients
Learn the idea
Coefficients such as viscosity, elasticity, conductivity, and diffusivity inherit dimensions from their constitutive laws. Material coefficients are conversion rules between a driving cause and a response, so isolate the coefficient in the relevant law instead of guessing.
🧠 Memory hook: Isolate the coefficient in the law that defines it.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- [eta] = M L⁻¹ T⁻¹ — dynamic viscosity from shear stress = eta times velocity gradient
- [Y] = M L⁻¹ T⁻² — Young modulus from stress divided by strain
- [D] = L² T⁻¹ — diffusivity from diffusion scaling
How to approach it
- 1Identify the named constitutive law
- 2Solve algebraically for the coefficient
- 3Substitute dimensions including gradients
Common slip-ups that cost marks
- •Confusing dynamic and kinematic viscosity
- •Assuming every modulus is dimensionless
- •Using conductivity without identifying thermal or electrical context
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A quantity Q is defined as Q = force^1 / speed^2. Which dimensional formula represents Q?
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