A new fighter aircraft with a length of 10 m is designed to fly at a cruise speed of 200 m/s under standard atmospheric conditions at sea level, for which the speed of sound may be taken as 340 m/s. It is desired to estimate the drag on the aircraft from wind tunnel tests on a small-scale model. Two large wind tunnels are available for the tests: i) a wind-tunnel using air at essentially standard atmospheric conditions and ii) a cryogenic wind tunnel using nitrogen at a temperature of -90°C and a pressure of 500 kPa; under such conditions, the density of nitrogen is 7.7 kg/m³ , its kinematic viscosity is 1.56×10^-6 m²/s and the speed of sound is 295 m/s.
a) Identify the dimensionless parameters that should be matched during the tests for complete dynamic similarity. Then identify a dimensionless parameter that can be used to estimate the drag force on the actual aircraft from the wind tunnel tests.
b) Is it possible to conduct dynamically similar tests using a small-scale model in the air facility? If so, estimate the length of the model and the speed of the air flow.
c) Is it possible to conduct dynamically similar tests using a small-scale model in the cryogenic facility? If so, estimate the length of the model and the speed of the nitrogen flow. Then estimate the numerical factor by which the drag on the model must be multiplied to provide the drag on the actual aircraft.

Contributed by Stavros Tavoularis, Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada. Image from 1Free Wallpaper.com