Flag pole

Homework Help
1

a flag pole 17 m high is cylindrical in shape with dia=100mm. wind blows past the pole with 15m/s vel, and the air temperature is 30C. What is the bending moment about the base of the pole

2

This text is generated by AI trained by Professor Brian J. Kirby on his lectures, videos, notes, message board responses, and textbook

PK Bot’s answer:

  1. PURPOSE OF THE EXERCISE:
    Demonstrate the application of aerodynamic loading and bending moment calculation using a distributed drag force on a cylindrical structure.

  2. ENGINEERING CONTEXT:
    This problem is representative of the wind-load analysis needed in structural design. Once mastered, you can apply these techniques to size wind-resistant supports or design flagpoles and similar structures subject to crosswind loading.

  3. PHYSICAL CONTEXT:
    The dominating effect is the drag force arising from the conversion of the dynamic pressure of the wind into a distributed load along the pole’s exposed surface.

  4. ASSUMPTIONS:
    Assume steady, uniform wind velocity with incompressible air at 30°C (take \rho\approx1.164\,\mathrm{kg/m^3}) and a typical drag coefficient for a smooth cylinder (e.g. C_d\approx1.2); also assume the drag force is uniformly distributed along the height of the pole.

  5. DRAWINGS:
    A simple sketch is recommended: draw a vertical cylinder (height H=17\,\mathrm{m}, diameter d=0.1\,\mathrm{m}) with a uniform wind velocity U=15\,\mathrm{m/s} acting perpendicular to the axis, and indicate the distributed drag force whose resultant acts at the midpoint of the height.

  6. SOLUTION TECHNIQUE:
    Calculate the total drag force using

F_d=\tfrac{1}{2}\,C_d\,\rho\,U^2\,A\,,

where the projected area is

A=H\,d=17\,\mathrm{m}\times0.1\,\mathrm{m}=1.7\,\mathrm{m^2}\,.

Substitute the values:

F_d=\tfrac{1}{2}\,(1.2)(1.164\,\mathrm{kg/m^3})(15\,\mathrm{m/s})^2(1.7\,\mathrm{m^2})\,.

Evaluate

F_d\approx 0.6\times1.164\times225\times1.7\approx267\,\mathrm{N}\,.

For a uniformly distributed load, the bending moment at the base is the drag force multiplied by the distance from the base to the load’s line of action (i.e. at half the height):

M_{base}=F_d\left(\frac{H}{2}\right)=267\,\mathrm{N}\times\frac{17\,\mathrm{m}}{2}\,.

Thus,

M_{base}\approx267\,\mathrm{N}\times8.5\,\mathrm{m}\approx2270\,\mathrm{N\cdot m}\,.
  1. REFLECTION:
    This analysis shows that with the assumed parameters the flagpole is subject to a bending moment of approximately 2270\,\mathrm{N\cdot m}. The approach, based on uniform drag and a typical drag coefficient, is standard for preliminary wind load calculations in structural design.

In formulating this response, I consulted the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked the sections according to their relevance. If they are marked as relevant, I encourage you to explore them:

Textbook sections:

  1. Chapter 9.3: Why We Use Irrotational Flow Analysis Part 5 (HIGHLY RELEVANT)
  2. Chapter 9 Fundamentals: Derivation of Thin Airfoil Theory (RELEVANT)
  3. Chapter 10 Fundamentals: There is a fundamental mathematical reason why the assumptions that your fl… (RELEVANT)
  4. Chapter 7.3: Integral Conservation of Momentum Part 2 (RELEVANT)
  5. Chapter 9.3: Why We Use Irrotational Flow Analysis Part 1 (RELEVANT)

Disclaimer:

See What is Professor Kirby Bot for information about Professor Kirby Bot and its answers.