GATE 2011 AEROSPACE ENGINEERING (Q 21-30)

  1. Consider a potential flow with free stream velocity V, over a spinning circular cylinder of radius R and circulation Γ. The stream function, ψ, where ψ = 0 on the cylinder surface, in cylindrical coordinates (r,θ) is given by
  2. A turbojet powered aircraft is flying at Mach number 0.8 at an altitude of 10 km. The inlet and exit areas of the engine are 0.7 m2 and 0.4 m2 respectively. The exhaust gases have velocity of 500 m/s and pressure of 60 kPa. The free stream pressure, density and speed of sound are 26.5 kPa, 0.413 kg/m3 and 299.5 m/s respectively. The thrust of the engine (in kN) is _____
    Ca = Maaa = 0.8 × 299.5 = 239.6 m/s
    ṁ = ρaAinletCa = 0.413 × 0.7 × 239.6 = 69.268 kg/s
    F = ṁ(Cj – Ca) + Aj(pj – pa)
    =69.268(500 – 239.6) + 0.4(60000-26500) = 31437.387 N = 31.437 kN
  3. A low speed wind tunnel has a contraction ratio of 14:1 and the cross-sectional area of the test section is 1 m2. The static pressure difference between the settling chamber and the test section is 40 cm of water column. Assume g = 9.81 m/s2, ρair = 1.2 kg/m3 and ρwater = 1000 kg/m3. The speed of air in the test section (in m/s) is _____
    p + (1/2)ρairV2 = p0
    (1/2)ρairV2 = p0 − p
    (1/2)ρairV2 = ρwaterghw
    (1/2)ρairV2 = 1000*9.81*(40*10-2) = 3924
    V = (3924*2/1.2)0.5 = 80.87 m/s

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