A light aircraft of mass and wingspan climbs out at through air of density

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow · Kinematics, conservation laws and ideal flow

Fluid Dynamics, Ch Vorticity: its sources, its field and the motion of vortices

Problem

A light aircraft of mass 1200 kg1200\,\mathrm{kg} and wingspan b=10 mb=10\,\mathrm{m} climbs out at U=50 m s−1U=50\,\mathrm{m\,s^{-1}} through air of density ρ=1.20 kg m−3\rho = 1.20\,\mathrm{kg\,m^{-3}}. Its trailing vortices roll up into a pair separated by b0=0.8bb_0 = 0.8b. Take g=9.8 m s−2g=9.8\,\mathrm{m\,s^{-2}}. ((a)) Find the circulation Γ0\Gamma_0 of the trailing vortices, using Γ0=W/(ρUb0)\Gamma_0 = W/(\rho U b_0). ((b)) Find the downwash at the wing's mid-span, Γ0/(πb0)\Gamma_0/(\pi b_0). ((c)) Find the rate at which the pair sinks far behind the aircraft, Γ0/(2πb0)\Gamma_0/(2\pi b_0).

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