Answer:
27.35m
Explanation:
We need first to consider the expression for the lift force, at which is,
[tex]F_y = - \rho Ul\Gamma[/tex]
Where
[tex]F_y[/tex]= Lift force
[tex]\rho[/tex]= density of air
[tex]\Gamma[/tex] = vortex strength
However the vortex strength is given by the equation,
[tex]\Gamma = 2\pi av_{\theta}[/tex]
Where,
a= 1m, radios of cylinder
[tex]v_{\theta}= 20 Km/hr=5.5m/s[/tex], the velocity of cylinder surface.
[tex]\Gamma = 2\pi (1)(5.5) = 34.90m^2/s[/tex]
In the U.S Standard Atmosphere Table, the density of Air to 2000m is [tex]1.007kg/m^3,[/tex]
[tex]U= 150Km/hr = 41.6m/s, F_y = 40000N, \Gamma = 34.90m^2/s[/tex]
Substituting in first equation we have,
[tex]40000 = -(1.007)(41.6)l(34.90)[/tex]
Solving for l, we have,
[tex]l=-27.35m[/tex]
Therefore the required length of wing cylinder is 27.35m
