# 2.3.1: Hypotheses

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

Hypothesis 2.1 (Standard atmosphere)

The basic typotheses of ISA are:

• Complies with the perfect gas equation:
$p = \rho RT, \label{eq2.3.1.1}$
where $$R$$ is the perfect gas constant for air ($$R = 287.053 [J/kg\ K]$$), $$p$$ is the pressure, $$\rho$$ is the density, and $$T$$ the temperature.
• In the troposphere the temperature gradient is constant.
$\begin{array} {c} {\text{Troposphere } (0 \le h < 11000 [m])} \\ {T = T_0 - \alpha h,} \end{array}$
where $$T_0 = 288.15 [K], \alpha = 6.5 [K/km]$$.
• In the tropopause and the inferior stratosphere the temperature is constant.
$\begin{array} {c} {\text{Tropopause and inferior stratosphere } (11000 [m] \le h < 20000 [m])} \\ {T = T_{11}} \end{array}$
where $$T_{11} = 216.65[K]$$.
• The air pressure at sea level ($$h = 0$$) is $$p_0 = 101325 [Pa]$$. In Equation ($$\ref{eq2.3.1.1}$$), the air density at sea level yields $$\rho_0 = 1.225 [kg/m^3]$$.
• The acceleration due to gravity is constant ($$g = 9.80665 [m/s^2]$$).
• The atmosphere is in calm with respect to Earth.

This page titled 2.3.1: Hypotheses is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by Manuel Soler Arnedo via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.