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A large-scale model is used to study the aerodynamic effect of scales which cover the surface of the wings of butterflies. It is given that the typical height of the scales is 0.1 mm and the typical maximum speed of the butterfly is 0.5 m/s. The model is to be tested in a channel filled with glycerin at 20°C. For convenience in flow visualization and in order for the wing model to fit in the facility, the scale model height should be 10 mm.
a) Determine the maximum speed of glycerin flow for the tests.
b) At extremely low Reynolds numbers, aerodynamic forces should not be normalized by the "inertia force", which is negligible, but by the "viscous force", which is proportional to the viscosity, μ. Use dimensional analysis to determine a dimensionless expression for the drag force on the butterfly scales.


Contributed by Stavros Tavoularis, Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada. Image from Science Museum of Minnesota.

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