Deriving the speed of sound is a main component of any undergraduate textbook in gas dynamics and is very important to understanding more complicated concepts! Here, I will give an honest attempt to explain and provide definitions of what it is and why it is important .I will go through the derivation of the speed of … Continue reading Definition of the Speed of Sound
Category: Basic Gas Dynamics
Derivation of the Euler Equations
In this post I am going to derive the compressible Euler equations: $latex \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \vec{V}) =0$ (1) $latex \rho \frac{\partial \vec{V}}{\partial t} + \rho \vec{V} \cdot \nabla \vec{V} = -\nabla p$ (2) $latex \rho \dot{q} = \frac{\partial}{\partial t}\rho e + \nabla \cdot \left[\rho (h+\frac{|V|^2}{2})\right]$ (3) These equations are essentially … Continue reading Derivation of the Euler Equations
Oblique Shockwaves
In this post I go over the theory of oblique shocks by building on our understand of normal shockwaves! I will give a short overview of the theory and strategy for analysis. Here is a summary of the contents of this post: Introduction to oblique shocks Analysis of the oblique shock Working relations for an oblique … Continue reading Oblique Shockwaves
Stationary Normal Shock Waves
Shock-waves are a common topic covered in undergraduate thermodynamics, fluid mechanics, and gas dynamics courses. Because shock-waves are awesome, I figured I would do one of my first posts on their basic theory. I'm going to try to cover the topic by first providing some context and a clear picture of what a shock wave … Continue reading Stationary Normal Shock Waves