# Calculating Air density as a function of height?

• Noone1982
In summary: This is known as the hydrostatic equation.In summary, to calculate air density as a function of height, you can use the hydrostatic equation which relates pressure and density to height, along with the ideal gas law which relates density to mass and volume.
Noone1982
Is it possible to calculate the air density as a function of height? We know that density is given as,

$$p\; =\; \frac{M}{V}$$

And that pressure is given as,

$$P\mbox{re}ssu\mbox{re}\; =\; pgh$$

But I am failing to see the connection to combine the two to get air density as a function of height. Any insight?

It's a miracle that I remember this from my hydrology course (the most boring one): $$p(h) = p_{0}e^{-\frac{gh}{RT}}$$. This is the expression for air pressure at a height h. $$p_{0}$$ is the air pressure at the sea level, T is the average temperature at the height h, and R is a gas constant for dry air.

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Noone1982 said:
Is it possible to calculate the air density as a function of height? We know that density is given as,

$$p\; =\; \frac{M}{V}$$

And that pressure is given as,

$$P\mbox{re}ssu\mbox{re}\; =\; pgh$$

But I am failing to see the connection to combine the two to get air density as a function of height. Any insight?
The pressure of the atmosphere is the weight of the air above per unit area. If you move up slightly, the weight decreases by an amount that depends on the density and change in height. You can assume the density is proportional to the pressure. Your equation

$$P\mbox{re}ssu\mbox{re}\; =\; \rho gh$$

is the change in pressure for a small change in height for which the density may be assumed constant.

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## 1. What is air density?

Air density is the amount of mass per unit volume of air. It is a measure of how tightly packed the air molecules are in a given space.

## 2. How is air density calculated?

Air density is calculated by dividing the mass of the air by its volume. The mass can be found by multiplying the air density by its volume.

## 3. What are the factors that affect air density?

The main factors that affect air density are temperature, pressure, and humidity. Generally, as temperature and humidity increase, air density decreases, while as pressure increases, air density also increases.

## 4. How does air density change with height?

Air density decreases with height. This is because as you go higher up in the atmosphere, there is less air above you, so the air molecules are less tightly packed.

## 5. Why is calculating air density important?

Calculating air density is important in a variety of fields, such as aviation, meteorology, and environmental science. It can help in determining the performance of aircraft, predicting weather patterns, and understanding air pollution levels.

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