Atmospheric pressure, defined as the force exerted by the air above a surface per unit area, can be calculated using a specific formula that considers altitude.
Understanding the Formula
The core formula used for approximating atmospheric pressure at different altitudes is:
P = 101325 ( 1 − 2.25577 × 10 − 5 ( h ) ) 5.25588
Where:
- P is the atmospheric pressure in Pascals (Pa).
- 101325 is the standard atmospheric pressure at sea level in Pascals.
- h is the altitude above sea level in meters.
- 2.25577 × 10-5 is a constant derived from atmospheric properties.
- 5.25588 is another constant related to the atmospheric model used.
This formula provides a practical means for approximating how air pressure decreases as altitude increases.
How to Use the Formula:
- Determine the altitude (h): Identify the elevation above sea level in meters at which you want to calculate the atmospheric pressure.
- Plug the altitude into the formula: Substitute the value of 'h' into the equation.
- Calculate the pressure (P): Perform the calculation according to the mathematical operations, making sure to follow order of operations.
Example Calculation:
Let's calculate the air pressure at an altitude of 10,000 meters. Using the formula mentioned in reference 2, and example shown in reference 5:
P = 101325 ( 1 − 2.25577 × 10 − 5 ( 10000 ) ) 5.25588
P = 101325 ( 1 − 0.225577 ) 5.25588
P = 101325 ( 0.774423 ) 5.25588
P ≈ 101325 * 0.26085
P ≈ 26436 Pa (approximately) as shown in reference 6.
Therefore, according to this calculation, the air pressure at 10,000 meters is approximately 26436 Pa.
Key Points:
- This formula is an approximation. Actual atmospheric pressure can vary based on temperature, weather conditions, and other factors.
- The formula assumes a standard atmosphere model.
- The formula is best suited for altitudes where the assumption of hydrostatic equilibrium holds true.
Practical Insights
- Aviation: Pilots use altimeters that rely on atmospheric pressure to determine their altitude. Understanding how pressure changes with altitude is crucial for flight safety.
- Meteorology: Atmospheric pressure readings are essential for predicting weather patterns. Changes in pressure indicate approaching storms or clear weather.
- Outdoor Activities: Hikers and mountaineers need to be aware of how atmospheric pressure changes at higher altitudes, as it affects the amount of oxygen available and can contribute to altitude sickness.
| Altitude (meters) | Approximate Pressure (Pa) |
|---|---|
| 0 | 101325 |
| 1000 | 89875 |
| 5000 | 54048 |
| 10000 | 26436 |
