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Which of these is the linearized perturbation velocity potential equation over a thin airfoil in a supersonic flow?(a) λ^2(ϕxx + ϕyy) = 0(b) ϕxx + ϕyy = 0(c) λ^2ϕxx + ϕyy = 0(d) λ^2ϕxx + ϕxy = 0I had been asked this question in semester exam.My doubt stems from Linearized Supersonic Flow topic in division Linearized and Conical Flows of Aerodynamics

Answer» RIGHT answer is (C) λ^2ϕxx + ϕyy = 0

For explanation: For a supersonic flow over a thin airfoil, the two dimensional linearized perturbation velocity POTENTIAL equation is given by

λ^2ϕxx + ϕyy = 0

In this equation the PERTURBATIONS are assumed to be small with the VALUE of λ = \(\sqrt {M_∞^2 – 1}\).


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