A4 Math Link – How Pressure Changes With Altitude

You already know that atmospheric pressure decreases as altitude increases simply because there are fewer and fewer air particles at higher elevations. But what is the exact relationship between atmospheric pressure and altitude? The data below represents average atmospheric pressure over a range of altitudes.

Atmospheric Pressure (hPa/mb) Altitude (km)
   
1013.25 0.00
954.61 0.50
898.76 1.00
845.59 1.50
795.01 2.00
746.91 2.50
701.21 3.00
657.80 3.50
616.60 4.00
577.52 4.50
540.48 5.00
505.39 5.50
472.17 6.00
440.75 6.50
411.05 7.00
382.99 7.50
356.51 8.00
331.54 8.50
308.00 9.00
285.84 9.50
264.99 10.00

Plot a graph of Atmospheric Pressure vs. Altitude for this data. Draw a curve of best fit through your data points. Extrapolate your curve of best fit to an altitude of at least 14 km. (Hint: Atmospheric Pressure is your dependent variable, so it acts as your y coordinate. Altitude is your independent variable and is your x coordinate.)

  1. Use the graph to fill in the following table. Click on each location name in order to travel to that location.

    Location Altitude (km) Atmospheric Pressure (hPa/mb)
         
    Calgary, Alberta 1.1 889
    Albuquerque, New Mexico 1.6 831
    Mt. Shasta, California (summit) 4.3 585
    average cruising altitude of a commercial jet 11.0 227

    Note: Answers for the atmospheric pressure may vary slightly from the sample values given here because of accuracy in reading the graph. Values should, however, be fairly close to these.

  1. What is your home elevation?
  2. Answers will vary depending on your home location.

  3. What is the average atmospheric pressure at this elevation?
  4. Answers will vary depending on the elevation used.

  5. Your graph of atmospheric pressure vs. altitude does not express a linear relationship. What do you think is the reason for this?
  6. The graph for atmospheric pressure vs. altitude is nonlinear because air is compressible. This means that the atmosphere is packed more densely at lower altitude. A small change in altitude at low elevation takes you through a large mass of atmosphere with a corresponding large drop in pressure. A similar change in higher elevations has a much smaller drop in pressure because the change in the mass of the atmosphere is much smaller.