Wind and Air: Scale an Airflow Experiment

Use Reynolds number to judge whether a small model represents a larger flow.

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Reynolds number Re = rho v L / mu compares inertial and viscous effects using dynamic viscosity mu. Similar shape does not ensure similar flow: matching Re and other relevant parameters matters. A universal transition value for every shape does not exist.

Worked example

For rho = 1.2 kg/m^3, v = 10 m/s, L = 0.1 m and mu = 0.000018 Pa s, Re is about 66667. Halving L at the same speed halves Re. Doubling speed restores that Re if the fluid properties stay fixed.

With density, reference area and drag coefficient held fixed, relative speeds of 5 and 10 meters per second give drag in the ratio 1 to 4. This model is not a universal fixed-coefficient law.

Would you believe it?

At fixed air density and swept area, doubling wind speed gives eight times the available kinetic power in the air. That does not mean a real turbine delivers eight times the electricity.

U.S. Department of Energy: wind power basics

Question 1 What is Re for the values in the example, rounded to the nearest whole number? 66667 667 6.67

Question 2 Halving L with everything else fixed changes Re by what factor? 2 1/4 1/2

Question 3 How can a half-size model match the original Re in the same fluid? Keep the original speed Double its speed Halve its speed

Question 4 Does matching Re alone guarantee similarity when compressibility matters? No, Mach number and other conditions can matter Yes, without limits Yes, regardless of shape

Question 5 Why not apply one pipe-flow transition number to every outdoor object? Re has units of seconds All outdoor flows are identical Geometry and disturbances affect transition

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