# Calculating air pressure from altitude, RH and temperature?

• Alfreds9
In summary, the question asks about determining pressure and O2 partial pressure at altitude using real-world data such as relative humidity and temperature, rather than generic formulas based on sea level temperature and standard temperature lapse rate. The closest formula found accounts for these factors but assumes dry air, which is not accurate. The question also asks if there is a formula specifically for this purpose or if it needs to be put together from aviation books. The response notes that humidity has a minimal effect on air density and explains why sea level temperature and lapse rate are commonly used for rough calculations. However, meteorologists routinely measure temperature profiles at different altitudes for more accurate results.
Alfreds9

## Homework Statement

[/B]
This is a practical problem, no homework question.

I'd like to determine pressure (and O2 partial pressure) at altitude, yet following a more realistic real-world calc including measured data like relative humidity (RH) and temperature at that altitude, yet all I can find are more generic formulas accounting sealevel temperature and standard temperature lapse rate, which seem a less accurate approach given that I'd have to guess sealevel temperature while measuring RH and temperature at a certain height is direct rather than computed data.

## Homework Equations

Closest I can find is:

where

• sea level standard atmospheric pressure p0 = 101325 Pa
• sea level standard temperature T0 = 288.15 K
• Earth-surface gravitational acceleration g = 9.80665 m/s2.
• temperature lapse rate L = 0.0065 K/m
• universal gas constant R = 8.31447 J/(mol·K)
• molar mass of dry air M = 0.0289644 kg/mol
or reversing this one:

## The Attempt at a Solution

• However both seem rather inaccurate to me since they assume dry air which luckily never occurs in realworld (moist air is surely less dense) and I can easily measure both RH and temperature at my altitude (and/or calculate dew point) rather than estimate them from sealevel temp and lapse rate.

I've found some online calculator/forms however I'm not skilled enough to read the sourcecode and get the equations from there.

Does the formula I'm looking for exist or it has to be put together from aviation books I'm not aware of?
Thank you

Allison

The humidity of the air has very little effect on the vertical pressure profile. That's why it's typically not included. What do you think the mole fraction of water vapor is in the air at ground level with a 50 % humidity at 25 C? How much does this affect the average molecular weight of the air?

I see thank you, maybe I'm mistaken with air density lowered by humidity. However, why is there no measured T rather than resorting to sealevel T and lapse rate?

Alfreds9 said:
I see thank you, maybe I'm mistaken with air density lowered by humidity. However, why is there no measured T rather than resorting to sealevel T and lapse rate?
Vertical temperature profiles are routinely measured by meteorologists on a daily and even hourly basis. The sea level T and lapse rate just provide average values over time for rough calculations.

## 1. What is the formula for calculating air pressure from altitude, RH, and temperature?

The formula for calculating air pressure from altitude, RH, and temperature is: P = P₀e^(-gMh/RT), where P is the air pressure at the given altitude, P₀ is the air pressure at sea level, g is the acceleration due to gravity, M is the molar mass of air, h is the altitude, R is the gas constant, and T is the temperature in Kelvin.

## 2. How does altitude affect air pressure?

As altitude increases, the air pressure decreases. This is because the air molecules at higher altitudes are less compressed and therefore exert less pressure on their surroundings. At sea level, the air pressure is typically around 1013.25 millibars, but at an altitude of 18,000 feet, it decreases to around 500 millibars.

## 3. What is the relationship between temperature and air pressure?

The relationship between temperature and air pressure is inverse. As temperature increases, air molecules gain more energy and move faster, causing them to exert more pressure on their surroundings. On the other hand, as temperature decreases, air molecules move slower and exert less pressure. This is why hot air balloons rise – the hot air inside has a lower density and therefore exerts less pressure than the surrounding cooler air.

## 4. How does relative humidity (RH) affect air pressure?

Relative humidity (RH) does not have a direct effect on air pressure. However, it can affect the density of air, which in turn can affect air pressure at a given altitude. When the air is more humid, it contains more water vapor, which has a lower density than dry air. This decrease in air density can result in a slight decrease in air pressure at the same altitude.

## 5. Is it necessary to consider all three variables – altitude, RH, and temperature – when calculating air pressure?

Yes, it is necessary to consider all three variables when calculating air pressure. Each of these variables has a direct or indirect effect on air pressure, and leaving one out could result in an inaccurate calculation. For example, not accounting for altitude would result in the same air pressure being calculated for different altitudes, which is not accurate. Therefore, all three variables should be taken into consideration when calculating air pressure.

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