Questions: The Reynolds Number and Flow Regimes

Question 1

Which combination of changes would most increase the Reynolds number for flow in a pipe?

• A. Decrease flow velocity and increase fluid viscosity
• B. Increase pipe diameter and decrease fluid viscosity
• C. Decrease pipe length and increase fluid density
• D. Increase viscosity and decrease flow velocity

Answer: (B)

Re = ρVL/μ. Increasing pipe diameter L increases Re; decreasing viscosity μ increases Re (it appears in the denominator). Both changes push Re upward. Options A and D both decrease Re (lower V and higher μ each reduce Re). Option C is a trap — pipe length does not appear in Re for internal pipe flow; the characteristic length is the diameter.

Question 2

Re ≈ 2300 is the universal critical Reynolds number above which any flow becomes turbulent.

• T. True
• F. False

Answer: False

Re ≈ 2300 is the critical value specifically for internal pipe flow (circular cross-section), where transition from laminar to turbulent begins. Different geometries have different critical values: for flow over a flat plate, transition occurs around Re ≈ 500,000 (using distance from leading edge as L); for flow past a sphere, wake instabilities appear around Re ≈ 1. The critical Re depends fundamentally on geometry and flow configuration.

Question 3

What physical competition does the Reynolds number describe, and how does this ratio explain why turbulence occurs at high Re?

Model answer: The Reynolds number compares inertial forces (which amplify disturbances and sustain chaotic motion) to viscous forces (which damp disturbances and restore ordered flow). At low Re, viscosity dominates — perturbations decay, and flow stays laminar. At high Re, inertia overpowers viscosity — small disturbances grow rather than decay, eventually producing the eddying, chaotic motion of turbulence.

This inertia-vs-viscosity interpretation is more useful than the formula alone. It explains why highly viscous fluids (honey, heavy oils) remain laminar at speeds that would be turbulent in water: their large μ keeps Re low even at moderate velocities. It also explains why small-scale flows (blood in capillaries, flow in microfluidic channels) are almost always laminar — the small characteristic length L keeps Re tiny regardless of speed.