4.You are designing a wind tunnel model of a sport aircraft. If the full scale r

Question

4.You are designing a wind tunnel model of a sport aircraft. If the full scale reference length (wing chord) is 4 ft and a 30% scale size wind tunnel model fis into your wind tunnel, and you are simulating sea level flight but your wind tunnel is in the mountains at 2,000 feet altitude, what speed do you have to test the model to simulate a full scale velocity of 150 mph to properly scale the boundary layer thickness at the trailing edge? Be careful of units of mph vs. ft/sect Show all work on a separate page. An atmospheric calculator can be found at http://www.onlineconversion.com/atmosphere.htm

Explanation / Answer

given, full scale reference cord, c = 4ft
30% scale model is to be used
so reference length c' = 0.3*4 = 1.2 ft
now, pressure at sea level, Po = 2116.22 Pa
Altitude for testing, h = 2,000 ft
Pressure at altitude h , P = 1967.68 lb/ft^2
Density at sea level, rhoo = 0.00237 sl/ft^3
Density at altitude h, rho = 0.00224 sl/ft^3
full scale speed = vo = 150 mph
wind tunnel speed = v

now reynold's number for both the conditions should be the same
reynold's numebr is defined as R = rho*v*L/mu ( mu is dynamic viscosity)
dynamic visocity at sea level, muo = 3.73719712*10^-7 lb sec ft^2
dynamic visocity at h, mu = 3.69713348*10^-7 lb sec ft^2

hence
rhoo*vo*c/muo = rho*v*c'/mu

0.00237*150*4/3.73719712*10^-7 = 0.00224*v*1.2/ 3.69713348*10^-7
hence v = 523.34666 mph
hence the model has to be tested at a wind tunnel speed of 523.34666 mph

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