Which of these is a wrong expression for the total circulation around a thin symmetric airfoil?(a) Γ=\(\int_0^c\)γ(ξ)dξ(b) Γ=\(\frac {c}{2} \int_0^{\pi }\)γ(θ)sin⁡θ dθ(c) Γ=cαV∞\(\int_0^c\)(1+cosθ)dθ(d) Γ=cαV∞\(\int_0^{\pi }\)(1+cosθ)dθI had been asked this question in semester exam.I need to ask this question from The Symmetric Airfoil topic in chapter Incompressible Flow over Airfoils of Aerodynamics

Which of these is a wrong expression for the total circulation around

1.	Which of these is a wrong expression for the total circulation around a thin symmetric airfoil?(a) Γ=\(\int_0^c\)γ(ξ)dξ(b) Γ=\(\frac {c}{2} \int_0^{\pi }\)γ(θ)sin⁡θ dθ(c) Γ=cαV∞\(\int_0^c\)(1+cosθ)dθ(d) Γ=cαV∞\(\int_0^{\pi }\)(1+cosθ)dθI had been asked this question in semester exam.I need to ask this question from The Symmetric Airfoil topic in chapter Incompressible Flow over Airfoils of Aerodynamics
Answer» Right choice is (c) Γ=cαV∞\(\int_0^c\)(1+cosθ)dθ The best explanation: Using the transformation ξ=\(\frac {c}{2}\)(1-cosθ), where 0&leq;θ&leq;π, CORRESPONDING to 0&leq;ξ&leq;c in γ(θ) and INTEGRATING gives the TOTAL circulation Γ.

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