Atmospheric pressure decreases
exponentially with altitude.
|
We are actually
living near the bottom of an ocean of air.
At sea level, the
weight of the air presses on us with a pressure of
approximately 14.7 lbs/in2.
At higher altitudes,
less air means less weight and less pressure.
Pressure and density of air decreases with
increasing elevation.
Pressure varies smoothly from the
earth's surface to the top of the mesosphere.
This table compiled by NASA gives a rough idea of
air pressure at various altitudes (as a fraction of
one atmosphere).
|
fraction
of 1 atm |
average altitude |
| (m) |
(ft) |
| 1 |
0 |
0 |
| 1/2 |
5,486.3 |
18,000 |
| 1/3 |
8,375.8 |
27,480 |
| 1/10 |
16,131.9 |
52,926 |
| 1/100 |
30,900.9 |
101,381 |
| 1/1000 |
48,467.2 |
159,013 |
| 1/10000 |
69,463.6 |
227,899 |
| 1/100000 |
96,281.6 |
283,076 |
|
|
Determining
atmospheric pressure: |
 |
where:
p = atmospheric pressure
(measured in bars)
h = height (altitude)
p0 = is pressure at
height h = 0 (surface pressure)
h0 = scale height
|
|
|
This equation shows
that the atmospheric pressure decays exponentially
from its value at the surface of the body where the
height h is equal to 0.
When h0
= h, the pressure has decreased to a value of
e-1 times its value at the surface.
|
|
The surface pressure on Earth is approximately 1 bar, and
the scale height of the atmosphere is approximately 7
kilometers. |
|
Problems:
1.
Estimate the pressure at an altitude of 3
kilometers in Earth's atmosphere.
Answer:
2. Estimate the pressure at an altitude equivalent to
the height of Mount Everest (the highest point on Earth).
The altitude of Mount Everest is 8,848 meters. (Change
meters to kilometers.)
3.
Estimate the pressure at an altitude
equivalent to the height of Mount
Kilimanjaro, 5,895 meters.
4.
Estimate the pressure in the Earth's
stratosphere at a height of 35 kilometers.
This pressure will be approximately
equivalent to the pressure on Mars.
5.
Using your graphing calculator and the NASA
table at the top, prepare a scatter plot of
the altitude in kilometers (x-axis)
and the air pressure (y-axis).
Find an exponential model equation for this
data.
6.
Using your findings from questions 1, 2, 3
and 4, prepare a scatter plot of the
altitude in kilometers and the air pressure.
Find an exponential model equation for this
data.
7.
Compare the three equations you have
obtained comparing altitude and air
pressure. What are the similarities?
What are the differences? Explain.
