Question

EXAMPLE 7-8 Lift on a Wing Some aeronautical engineers are designing an airplane and wish to predict the lift produced by their new wing design (Fig. 7-31). The chord length L of the wing is 1.12 m, and its planform area A (area viewed from the top when the wing is at zero angle of attack) is 10.7 m2. The prototype is to fly at V = 52.0 m/s close to the ground where T = 25°C. They build a one- tenth scale model of the wing to test in a pressurized wind tunnel. The wind tunnel can be pressurized to a maximum of 5 atm. At what speed and pres- sure should they run the wind tunnel in order to achieve dynamic similarity? SOLUTION We are to determine the speed and pressure at which to run the wind tunnel in order to achieve dynamic similarity.

Answer 1

variables are , f2= f( Us Log Cid) F = lift force on wing | de- flued viscoste v=fluid speed c=speed of sound he=chord length influed 8= fluid density I d-angle of altaa a of the wing FC Lee Le seca E l nee me lel no of primary dimensions (J)=3 Kentj=7–354 Sets can be, Le&S (ar) c.4&p velocity is more common , so choose OLC&P CJ-3 T=FL va colga 76,= (MILLE 3 CL ENQI Calyo Cros (3) 91=2, 6212 GFt T = FL (modified) - SV2A = lift coeffc

T2 = levar LE2gc2 T2= (MCE) CLED92 (1) 32 (m! (3) C2 a2=,6237, C2=4 Teza e re the remotes number Iz= SVLC (modified) a *3=U = mach no=Ma Maade angle of attack a= A LA = f(Re, ma,a) t5124 Reynolds number similarity gives mach no would differ by a factor of . c=346 m/s 10 at 25°c ma=52 346 -0.15 (Subsonid Ma = 115 Supersonic) not possible (model) at 5atm, Vwindtunnel =2v prototype =104 mis Ma = 104 codes 346 3 0.301 ". Approximately a speed of 100 mys at P5 atm 8259