Math in the News: 8/1/11
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A Bermuda High is a high-pressure air system that forms along the East Coast and causes heat waves. The downward force from the high pressure system pushes out cooler air and prevents cooler air fronts from breaking through, keeping temperatures warm. This high pressure system rotates like a cylinder and increases the air pressure through torque, similarly to how a helicopter's propellers create downward draft. Warm, moist air from the Caribbean sustains this high pressure system and prolongs the heat.
Math in the News: 8/1/11
- 1. 8/1/11
- 2. Heat Waves A Bermuda High is a high-pressure air system that starts, and stays, along the East Coast.
- 3. Heat Waves Think of the draft of air created by a helicopter’s propellers.
- 4. Heat Waves A similar phenomenon happens with the swirling air of the high pressure front.
- 5. Heat Waves The downward force comes, in part, from the torque created by the force of the wind (F) and the radius (r) of the high- pressure system.
- 6. Heat Waves The direction of torque is always perpendicular to the plane formed by the radius and the force.
- 7. Heat Waves You can think of the high-pressure system as a rotating cylinder of humid air.
- 8. Heat Waves Torque is a force and this force is applied over the column of air. Since pressure is force divided by area, then the overall effect is to increase the air pressure.
- 9. Heat Waves The downward pressure pushes out cooler air, and this persists during the high-pressure system. This causes a temperature increase.
- 10. Heat Waves The downward pressure also keeps cooler air fronts from breaking through the high- pressure system. This keeps temperatures warm.
- 11. Heat Waves A continual flow of warm, moist air from the Caribbean keeps the high-pressure system intact. This prolongs the heat.
- 12. Heat Waves The warm, moist air from Caribbean is heavier than cool, dry air. This causes an increase in pressure and temperature.
- 13. Heat Waves But how much pressure does the high-pressure system add to the regions affected by this system?
- 14. Heat Waves Pressure is the ratio of the downward force and the area of the high-pressure system. For a cylinder the pressure formula changes to this.
- 15. Heat Waves As we saw earlier, the downward force from the pressure system is the torque. Express torque in force units.
- 16. Heat Waves Torque is the product of angular momentum (I) and angular acceleration (α). For a rotating disk, the torque formula is as shown here.
- 17. Heat Waves Use this formula for torque in the pressure equation.
- 18. Heat Waves We cannot directly measure the mass but we can estimate mass using the density of air and volume of the cylinder.
- 19. Heat Waves Inputting the mass equation into the pressure equation and simplifying yields a fairly simple equation.
- 20. Heat Waves This graph shows the pressure as a function of radius, with parameters for h, α, and ρ. The horizontal graph shows standard pressure.
- 21. Heat Waves As the radius increases, so does the air pressure, and as a result, so does the temperature.