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Which of these is the linearized perturbation velocity potential equation over a thin airfoil in a subsonic compressible flow?(a) β^2(ϕxx + ϕyy) = 0(b) ϕxx + ϕyy = 0(c) β^2ϕxx + ϕyy = 0(d) β^2ϕxx + ϕxy = 0I had been asked this question by my school teacher while I was bunking the class.This key question is from Linearized Subsonic Flow topic in division Linearized and Conical Flows of Aerodynamics

Answer»

Correct answer is (c) β^2ϕxx + ϕyy = 0

Easy explanation: For a compressible SUBSONIC flow over a thin airfoil, the TWO dimensional linearized perturbation velocity potential EQUATION is given by

β^2ϕxx + ϕyy = 0

In this equation the perturbations are ASSUMED to be small with the value of β = \(\sqrt {1 – M_∞^{2}} \).



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