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🌬️ How much force is exerted to a flag. pole with a flag in windy conditions? 🌬️

#sondreaas #education #Constitution #knowledge #physics

🇳🇴🇳🇴🇳🇴🇳🇴🇳🇴🇳🇴🇳🇴🇳🇴🇳🇴🇳🇴🇳🇴 Since 17th of May is Norway's constitution day I though it would be funny to calculate how much force that is being exerted to a flagpole when the wind blows, so let’s do some calculations🎉 📐🔍

Let’s take the following scenario:

- Dimension of flag: 2m wide and 1 meter high.
- The wind speed is: 10 m/s
- The flagpole height: 12 meters
- Flag mounted at 11 meters height
- Diameter of the Flagpoler: 0.1 meters
- Drag coefficient for the flag: 1.2
- Air density: 1.225 kg/m³

1. Wind Force on the Flag:
Fw = 0,5 * 1,225 * (10m/s)^2*1,2 * (2*1) = 147nm
1,225 is the density of the air� 10m/s is the velocity of the wind� 1,2 is the «drag coefficient for the flag
(2*1) is the flag itself�
2. Moment on the Flagpole due to the Flag:
M flag = 146* (11+0,5) = 147 * 11,5 = 1690,5 nm

3. Wind Force per Unit Length on the Flagpole:
fp = 1/2*1,225*(10)^2 *1,2*0,1 = 7,35 nm

4. Bending moment on the flagpole due to distributed load:
M pole= 7,35*x*dx* x^2/2= 7,35*72 = 529.2nm� (The formula is confusing because i am not able to write the integral sign and the limit)�
5. Total Bending Moment at the Base:
Mb = 1690.5 + 529.2 = 2219.7 nm

These calculations show the total bending moment at the BASE of the flagpole due to the wind force on the flag and the flagpole.
This was a smal flag, imagine how much force it would be if the flag was much bigger, the flagpole was higher- and it was both windy and raining, the forces would have been much higher.

I wish all a happy constitutional day! 

Best wishes Sondre Åkerøy Sundrønning
Physicist 🇳🇴🇳🇴


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