Exponential decay with air pressure

In summary, air pressure, P, decreases exponentially with the height, h, in meters above sea level according to the equation P = P0e-0.00012h. At the top of Mount McKinley, which is 6198 meters (about 20,330 feet) high, the air pressure is unknown without the value of P0. However, at the maximum cruising altitude of around 12,000 meters (about 39,000 feet), the air pressure is 54.8% of the pressure at sea level. The value of P0 is typically taken as the reference 1 atmosphere of pressure, or 14.696 psia (absolute pressure), 0.101325 MPa, 101
  • #1
Jacobpm64
239
0
Air pressure, P, decreases exponentially with the height, h, in meters above sea level:

P = P0e-0.00012h

where P0 is the air pressure at sea level.

(a) At the top of Mount McKinley, height 6198 meters (about 20,330 feet), what is the air pressure, as a percent of the pressure at sea level?

I think I need to know the air pressure at sea level to answer this question but I'm not given it... Does anyone know it if i need it, and if I don't.. how do i solve the problem without it?

(b) The maximum cruising altitude of an ordinary commercial jet is around 12,000 meters (about 39,000 feet). At that height, what is the air pressure, as a percent of the sea level value?

Same question for this one.
 
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  • #2
The air pressure at sea-level is taken as the reference 1 atm of pressure, or 14.696 psia (absolute pressure), or 0.101325 MPa, or 101.325 kPa, 760 mm Hg, or 760 torr (assuming Temp = 25°C/298 K)

This might be useful for future reference -
http://www.silcom.com/~aludwig/Physics/UNITS.html - find pressure near bottom of page.
 
  • #3
so I guess it doesn't matter which units I use?... I suppose atmospheres would be the best to work with.
 
  • #4
This is why I encourage people to actually Read the Problem before trying to solve it! Then you might notice that the problem asks "what is the air pressure, as a percent of the pressure at sea level?"
 

Related to Exponential decay with air pressure

1. What is exponential decay with air pressure?

Exponential decay with air pressure is a scientific phenomenon that describes the decrease in air pressure over time due to the movement and diffusion of air molecules.

2. How does temperature affect exponential decay with air pressure?

Temperature has a direct effect on air pressure, as warmer air molecules have more energy and tend to move faster and spread out, resulting in a decrease in air pressure.

3. What are some real-life examples of exponential decay with air pressure?

Examples of exponential decay with air pressure can be seen in weather patterns, as high pressure systems tend to move towards areas of low pressure. It can also be observed in the deflation of a balloon or the release of air from a compressed can.

4. How is exponential decay with air pressure measured?

Air pressure is typically measured using a barometer, which can detect changes in the pressure exerted by the atmosphere. This can also be measured using other instruments like a manometer or a pressure gauge.

5. What are the practical applications of understanding exponential decay with air pressure?

Understanding exponential decay with air pressure is important for predicting weather patterns, designing pressurized systems, and ensuring the safety of structures like buildings and airplanes. It also has applications in industries such as aviation, meteorology, and engineering.

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