If U₀ is the free stream velocity and the velocity on the surface of the cylinder (UC) of radius r due to circulation (Γ) is Γ/(2πr), then for irrotational flow, the lift coefficient would be
- A2π U₀/UC
- Bπ UC/U₀
- Cπ U₀/UC
- D2π UC/U₀Correct
Solution
Concept
Magnus effect
Formula
L = ρ U₀ Γ; CL = L/(½ρU₀²·2r)
Step-by-step solution
1. Lift per unit length L = ρ U₀ Γ. 2. CL = ρ U₀ Γ/(½ ρ U₀² · 2r) = Γ/(U₀ r). 3. Γ = 2π r UC, so CL = 2π UC/U₀.
Explanation
The lift coefficient is based on projected area 2r.
Shortcut
CL = 2π UC/U₀.
Correct answer: D) 2π U_C/U₀