Incompressible & Compressible Aerodynamics

Induced velocity w at a point zz = zz1 along the lifting line can be calculated using the formula ww(zz1) = - 1 4𝜋𝜋 ∫ ddΓ ddzz ss -ss 1 zz-zz1 ddzz. Given Γ2 Γoo2 + zz2 ss2 = 1, wherezz, Γoo and sare given in figure below. For theabove semi-elliptic distribution of circulation, Γ, the downwash velocity at any point zz1,for symmetric flight can be obtained as, ww(zz1) = Γoo 4𝜋𝜋ss [𝜋𝜋 + zz1II], where II = zz1 ∫ ddzz �ss2-zz2�zz-zz1� ss -ss . Which of the following options is correct if the induced drag is DDii (given ∫ �1 - zz2 ss2 ss -ss ddzz = 𝜋𝜋ss 2 ) (A)I=0 and DDii = 8𝜌𝜌Γoo 2 𝜋𝜋 (B)I= 1 and DDii = 8𝜌𝜌Γoo 2 𝜋𝜋 (C)I=0 and DDii = 𝜋𝜋𝜌𝜌Γoo 2 8 (D)I= 1 and DDii = 𝜋𝜋𝜌𝜌Γoo 2 8