# Formula for atmostpheric pressure

IS there a formula for atmospheric pressure based on height? Should I have posted this in another section?

enigma
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It depends on the range of heights you're looking for. The pressures, temperatures, and densities are variable, but can be approxomated into zones (one of the reasons they have names like Troposphere, Ionosphere, etc.)

Your best bet is to go to a standard atmosphere table to get mean values for the hights you're designing for.

I don't know if there is one online, but I do know there is one in the appendices of Introduction to Flight by John Anderson.

enigma
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I found the formula for low (less than 11km) altitudes.

$$\frac{p}{p_1} = \frac{T}{T_1}^{-\frac{g_0}{aR}}$$

in the low altitude you are in a temperature gradient region, and T varies with altitude like $$T = T_1+a(h-h1)$$

$$g_0$$ is the acceleration of gravity at sea level
R is the gas constant (287 for air in SI units)
a is the slope of the temperature gradient, equal to -6.5e-3 K/m for the low altitude gradient.

for p1 and T1, you use the pressure and temperature at standard atmospheric sea level conditions: 1 atm and 288.16K.
h1 is 0m for this gradient region

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Bystander
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Originally posted by enigma
(snip)R is the gas constant (287 for air in SI units)(snip)

Huh? This is a new one --- do aeros tabulate separate "R" values for different gases?

enigma
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I didn't have the big cap R.

It's the ideal gas constant divided by the molecular mass.

EDIT: sorry, should have called it the specific gas constant

and no, we don't usually tabulate the R's, but we do need to know the molecular masses of commonly used fluids.

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Bystander
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(I hate it when people sidetrack threads, but this is intriguing.)

The "specific gas constant" is useful/expedient in what sort of applications then? Jet/nozzle flow?

enigma
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Yeah,

Everything from the calculation for the speed of sound

$$a=\sqrt{\gamma * \frac{R}{m} * T}$$

to the calculations of flame temperature (through Cp and Cv)

(more lengthy than I really want to enter into the Latex editor)

Bystander
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Has this ever resulted in confusing situations? Someone taking the "specific gas constant" for one system as being really a constant and applying it to another system?

enigma
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-YES!

seriously though, the only time I ever use the ideal gas constant is right before I divide it by the molecular mass. I can't think of a single time in the last 2 years where it's been standing alone.

It is used merely to bring the ideal gas constant into "human sized" units: switching from J/(kg mol*K) into J/kg*K

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Bystander
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Methinks I'll open a new thread in aero in a couple days --- there are a couple questions that need to ferment a bit.

nautica
Originally posted by Bystander
Has this ever resulted in confusing situations? Someone taking the "specific gas constant" for one system as being really a constant and applying it to another system?

Should not be too confusing, so long as you understand which units you are using.

Nautica

Originally posted by mattmns
IS there a formula for atmospheric pressure based on height?
mattmns,
what you're looking for is probably the formula
p(h) = exp(-&rho;0gh/p0).
(symbols should be obvious).
This is called the barometric formula.