Questions: Fluid Properties and the Continuum Hypothesis

Question 1

Mercury is about 13.6 times denser than water, yet it flows much more easily through a tube. Which property explains this difference in flow behavior?

• A. Density
• B. Bulk modulus
• C. Dynamic viscosity
• D. Surface tension

Answer: (C)

Ease of flow under shear is governed by viscosity, not density. Mercury has a dynamic viscosity of about 1.5 mPa·s — similar to water — while motor oil has viscosity 100–1000 times higher than water, even though oil is less dense. Density determines mass per unit volume, while viscosity measures resistance to shearing deformation. These are independent properties.

Question 2

The continuum hypothesis is a universal physical law that applies to most fluids at most scale.

• T. True
• F. False

Answer: False

The continuum hypothesis is an engineering approximation, not a universal law. It breaks down when the Knudsen number (mean free path divided by characteristic length scale) is not small — for example, in gas flows at very low pressures, in micro/nanoscale channels, or in rarefied atmospheric conditions at high altitude. At these scales, the discrete molecular nature of matter must be modeled explicitly.

Question 3

What is kinematic viscosity, and why is it sometimes more useful than dynamic viscosity?

Model answer: Kinematic viscosity ν = μ/ρ is dynamic viscosity divided by density. It is useful because many flow equations (like the Reynolds number) involve the ratio μ/ρ naturally, so using ν simplifies the expressions. It also directly characterizes how momentum diffuses through a fluid relative to its inertia.

Dynamic viscosity μ measures absolute resistance to shear. Kinematic viscosity ν = μ/ρ normalizes by density, giving a measure of momentum diffusivity. The Reynolds number Re = ρVL/μ = VL/ν, so kinematic viscosity appears directly in dimensionless flow parameters. For problems involving fluid inertia and viscous forces together, ν is the natural quantity.