Question

A flag pole 20 m tall with a diameter of 0.12 m has at its top a flag which measures 2 m tall and 2.5 m wide.a) Calculate the aerodynamic force on the combination pole and flag is the wind speed measured at the top of the pole is 20 m/s.b) Discuss factors which may cause your calculation to be higher or lower than the actual force.

Answer 1

Answer:

a) the aerodynamic force is 1.083x10⁴N

b) If the CL factor changes, the response also changes, since the aerodynamic force is dependent on said factor

Explanation:

Given data:

v=20m/s

Apole=20*0.12=2.4m²

Aflag=2*2.5=5m²

The total area is:

Atotal=2.4+5=7.4m²

The properties of the air at 30°C are:

v=1.6036x10⁻⁵m²/s

ρ=1.1649kg/m³

a) First, we need to calculate the coefficient of lift:

$C_{L} =2\pi sin\theta$

Here, θ=90°, thus, the expression is:

$C_{L} =2\pi$

The mathematical expression to calculate the aerodynamic force is:

$F_{L} =\frac{1}{2} C_{L} \rho Av^{2} =\pi *\rho *A*v^{2} =\pi *1.1649*7.4*20^{2} =1.083x10^{4} N$

b) If the CL factor changes, the response also changes, since the aerodynamic force is dependent on said factor