A cylindrical fairing of radius m is made from two half-shells bolted together along…
PHYSICS · Subjective · Fermi University Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow · Kinematics, conservation laws and ideal flow
Fluids and Continuum Physics, Ch Potential flow, complex potentials and lift
Problem
A cylindrical fairing of radius a=0.25 m is made from two half-shells bolted together along the plane x=0, which contains the axis and is perpendicular to the wind. The wind blows at U=30 m s−1 along +x, the air has density ρ=1.2 kg m−3 and is treated as incompressible and inviscid, and the flow is steady, two-dimensional in the (x,y) plane and irrotational, with the surface pressure that of ideal flow past a circular cylinder. The interior of the fairing is vented, so the air inside is at rest at the far-field pressure p∞ on both inner faces. The weight of the air is ignored. Find the magnitude and direction of the net pressure force per unit length of fairing that the bolts must carry on the upstream half-shell, that is on the half of the surface with x<0 (polar angles 90∘≤θ≤270∘, with θ measured anticlockwise from +x).