GATE 2011 AEROSPACE ENGINEERING (Q 41-50)

  1. Consider the inviscid, adiabatic flow of air at free stream conditions, M1 = 2, p1 = 1 atm and T1 = 288 K around a sharp expansion corner (θ = 20°) as shown below. The Prandtl-Meyer function, ν, is given as a function of Mach number, M, as  Assume air to be calorically perfect with γ = 1.4. The Mach number, M2 downstream of the expansion corner is approximately
    1. 2.00
    2. 1.76
    3. 2.83
    4. 3.14

    Answer:- 2.83
    Putting the value M1 in given equation, we have ν(M1) = 26.38°
    Now, ν(M2) = ν(M1) + 20°
    ⇒ ν(M2) = 46.38°, which is correspond to M2 = 2.83.
    Note: The Mach number downstream of an expansion corner is always higher than upstream Mach number.

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