Introduction
The area-Mach number relation (AMR from now on), is important when analyzing nozzle flows. In this post, I’m not going to go through the derivation of the equation because I derive it in this video. I will be taking the final equation and showing you a few different methods of solution, along with some MATLAB code that you can use in your own programs. Below is the equation we will be looking at.
(1) ![\begin{equation*} \left( \frac{A}{A^*} \right) ^2 = \frac{1}{M^2} \left[ \frac{2}{\gamma + 1} \left(1+\frac{\gamma -1}{2} M^2 \right) \right]^{\frac{\gamma + 1}{\gamma -1}} \end{equation*}](https://www.joshtheengineer.com/wp-content/ql-cache/quicklatex.com-2773e5c5d1ec76fa589b2d954fc6382d_l3.png "Rendered by QuickLaTeX.com")
The term 
is the area ratio, 
is the Mach number, and 
is the specific heat ratio. There are two ways of looking at this equation. The first is that the area ratio is a function of Mach number, and the second is that the Mach number is a function of the area ratio. It all depends on what you have and what you want to calculate.