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mattmns

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mattmns

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Ambitwistor

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http://teacher.nsrl.rochester.edu/phy_labs/AppendixD/AppendixD.html

However, it neglects the fact that gravity decreases with height, it neglects temperature differences, etc. The real atmosphere is messy.

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enigma

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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

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enigma

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

[tex] \frac{p}{p_1} = \frac{T}{T_1}^{-\frac{g_0}{aR}} [/tex]

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

[tex]g_0[/tex] 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

[tex] \frac{p}{p_1} = \frac{T}{T_1}^{-\frac{g_0}{aR}} [/tex]

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

[tex]g_0[/tex] 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?

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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.

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

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enigma

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Everything from the calculation for the speed of sound

[tex]a=\sqrt{\gamma * \frac{R}{m} * T} [/tex]

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

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

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Bystander

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enigma

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*thinks back to Intro to Aerodynamics*

-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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Originally posted by Bystander

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

Nautica

- #13

arcnets

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mattmns,Originally posted by mattmns

IS there a formula for atmospheric pressure based on height?

what you're looking for is probably the formula

p(h) = exp(-ρ

(symbols should be obvious).

This is called the barometric formula.

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