User contributions for Nian

16 March 2026

• 13:4213:42, 16 March 2026 diff hist +1,483 N The entropy equation Created page with "Category:Compressible flow Category:Governing equations __TOC__ \section{The Entropy Equation} \noindent From the second law of thermodynamics\\ \begin{equation} \frac{De}{Dt}=T\frac{Ds}{Dt}-p\frac{D}{Dt}\left(\frac{1}{\rho}\right) \label{eq:second:law} \end{equation}\\ \noindent From the energy equation on differential non-conservation form internal energy formulation\\ \[\frac{De}{Dt} = \dot{q} - \frac{p}{\rho}(\nabla\cdot\mathbf{v})\]\\ \noindent The co..."
• 13:4113:41, 16 March 2026 diff hist +1,481 N Crocco's equation Created page with "Category:Compressible flow Category:Governing equations __TOC__ \section{Crocco's Equation} \noindent The momentum equation without body forces\\ \[\rho\frac{D\mathbf{v}}{Dt}=-\nabla p\]\\ \noindent Expanding the substantial derivative\\ \[\rho\frac{\partial \mathbf{v}}{\partial t}+\rho\mathbf{v}\cdot\nabla\mathbf{v}=-\nabla p\]\\ \noindent The first and second law of thermodynamics gives\\ \[T\nabla s =\nabla h-\frac{\nabla p}{\rho}\]\\ \noindent Insert..."
• 13:3813:38, 16 March 2026 diff hist +54 N Governing equations on differential form Nian moved page Governing equations on differential form to Governing equations on differential form current Tag: New redirect
• 13:3813:38, 16 March 2026 diff hist 0 m Governing equations on differential form Nian moved page Governing equations on differential form to Governing equations on differential form
• 13:3713:37, 16 March 2026 diff hist +39 Compressible flow No edit summary
• 13:3613:36, 16 March 2026 diff hist +251 Compressible flow No edit summary
• 13:2413:24, 16 March 2026 diff hist +11,896 N Governing equations on differential form Created page with "Category:Compressible flow Category:Governing equations __TOC__ \section{Governing Equations on Differential Form} \subsection{Conservation of Mass} \noindent Apply Gauss's divergence theorem on the surface integral in Eqn. \ref{eq:governing:cont:int} gives\\ \[\oiint_{\partial \Omega}\rho \mathbf{v}\cdot \mathbf{n} dS=\iiint_{\Omega}\nabla\cdot(\rho\mathbf{v})d\mathscr{V}\]\\ \noindent Also, if $\Omega$ is a fixed control volume\\ \[\frac{d}{dt}\iiint_{\O..."
• 13:2213:22, 16 March 2026 diff hist +8,432 N Governing equations on integral form Created page with "Category:Compressible flow Category:Governing equations __TOC__ \section{Governing Equations on Integral Form} \begin{figure}[ht!] \begin{center} \includegraphics[]{figures/standalone-figures/Chapter02/pdf/control-volume.pdf} \caption{Generic control volume} \label{fig:generic:cv} \end{center} \end{figure} \noindent The governing equations stems from mass conservation, conservation of momentum and conservation of energy \subsection{The Continuity Equation}..."
• 12:2112:21, 16 March 2026 diff hist +368 N Reference flow states Created page with "Category:Compressible flow Category:One-dimensional flow Category:Reference flow states __TOC__ \section{Reference Flow States} \subsection{Stagnation Flow Properties} \[h_o=h+\dfrac{1}{2}u^2\Rightarrow Cp T_o=C_p T +\dfrac{1}{2}u^2\Rightarrow \dfrac{T_o}{T}=1+\dfrac{1}{2C_p}M^2\gamma RT=1+\dfrac{\gamma-1}{2}M^2\] \subsection{Sonic Flow Properties}"
• 12:1912:19, 16 March 2026 diff hist +6,468 N Thermodynamic processes Created page with "Category:Compressible flow Category:Thermodynamics __TOC__ \section{Thermodynamics} \subsection{Specific Heat Relations} \noindent For thermally perfect and calorically perfect gases\\ \begin{equation} \begin{aligned} &C_p=\frac{dh}{dT}\\ &C_v=\frac{de}{dT} \end{aligned} \label{eq:specificheat} \end{equation}\\ \noindent From the definition of enthalpy and the equation of state $p=\rho RT$\\ \begin{equation} h=e+\frac{p}{\rho}=e+RT \label{eq:enthalpy} \end..."
• 10:1510:15, 16 March 2026 diff hist +2 Normal-shock relations →The Hugoniot Equation
• 10:1410:14, 16 March 2026 diff hist −21,439 One-dimensional inviscid flow Replaced content with "Category:Compressible flow Category:One-dimensional flow Category:inviscid flow __TOC__ {{:Acoustic waves}} {{:Shock waves}} {{:Normal-shock relations}}" Tag: Replaced
• 10:1110:11, 16 March 2026 diff hist +128 Normal-shock relations No edit summary
• 10:1010:10, 16 March 2026 diff hist +8,654 N Normal-shock relations Created page with " ==Normal Shock Relations== Rewriting the continuity equation (Eqn. \ref{eq:governing:cont}) <math display="block"> \frac{\rho_2}{\rho_1}=\frac{u_1}{u_2}=\frac{u_1^2}{u_1 u_2}=\left\{{a^*}^2=u_1u_2\right\}=\frac{u_1^2}{{a^*}^2}={M^*_1}^2 </math> Eqn. \ref{eq:MachStar} in Eqn. \ref{eq:Normal:density:a} gives <math display="block"> \frac{\rho_2}{\rho_1}=\frac{(\gamma+1)M_1^2}{2+(\gamma-1)M_1^2} </math> To get a corresponding relation for the pressure ratio over the s..."
• 10:0810:08, 16 March 2026 diff hist +28 N Acoustic waves Nian moved page Acoustic waves to Acoustic waves current Tag: New redirect
• 10:0810:08, 16 March 2026 diff hist 0 m Acoustic waves Nian moved page Acoustic waves to Acoustic waves
• 10:0710:07, 16 March 2026 diff hist +25 N Shock waves Nian moved page Shock waves to Shock waves current Tag: New redirect
• 10:0710:07, 16 March 2026 diff hist 0 m Shock waves Nian moved page Shock waves to Shock waves
• 10:0710:07, 16 March 2026 diff hist +129 Shock waves No edit summary
• 10:0610:06, 16 March 2026 diff hist +7,711 N Shock waves Created page with "==Shock Waves== <!-- \begin{figure}[ht!] \begin{center} \includegraphics[]{figures/standalone-figures/Chapter03/pdf/shock-wave.pdf} \caption{Stationary normal shock} \label{fig:shock} \end{center} \end{figure} --> The starting point is to set up the governing equations for one-dimensional steady compressible flow over a control volume enclosing the normal shock (Fig. \ref{fig:shock:cv}). <!-- \begin{figure}[ht!] \begin{center} \includegraphics[]{figures/standalone-fig..."
• 10:0510:05, 16 March 2026 diff hist +27 Acoustic waves No edit summary
• 10:0410:04, 16 March 2026 diff hist +5,235 N Acoustic waves Created page with "Category:Compressible flow Category:One-dimensional flow Category:inviscid flow __TOC__ ==Acoustic Waves== <!-- \begin{figure}[ht!] \begin{center} \includegraphics[]{figures/standalone-figures/Chapter03/pdf/acoustic-wave.pdf} \caption{sound wave} \label{fig:soundwave} \end{center} \end{figure} --> In Fig. \ref{fig:soundwave}, station 1 represents the flow state ahead of the sound wave and station 2 the flow state behind the sound wave. Set up the continui..."
• 08:3108:31, 16 March 2026 diff hist +1 Compressible flow No edit summary
• 08:2908:29, 16 March 2026 diff hist +37 Compressible flow No edit summary

14 March 2026

• 15:4015:40, 14 March 2026 diff hist +5,120 One-dimensional inviscid flow No edit summary
• 09:2109:21, 14 March 2026 diff hist +51 Compressible flow No edit summary
• 09:0209:02, 14 March 2026 diff hist 0 One-dimensional inviscid flow No edit summary
• 09:0109:01, 14 March 2026 diff hist −152 One-dimensional inviscid flow No edit summary

13 March 2026

• 19:4019:40, 13 March 2026 diff hist +11,412 One-dimensional inviscid flow No edit summary
• 19:3119:31, 13 March 2026 diff hist +61 One-dimensional inviscid flow No edit summary
• 19:2219:22, 13 March 2026 diff hist 0 N Category:Compressible flow Created blank page
• 19:1919:19, 13 March 2026 diff hist +31 N Compressible flow Nian moved page Compressible flow to Compressible flow over redirect current Tag: New redirect
• 19:1919:19, 13 March 2026 diff hist 0 m Compressible flow Nian moved page Compressible flow to Compressible flow over redirect
• 14:3714:37, 13 March 2026 diff hist 0 m Compressible flow Nian moved page Compressible flow to Compressible flow
• 14:3014:30, 13 March 2026 diff hist +31 One-dimensional inviscid flow No edit summary
• 14:2414:24, 13 March 2026 diff hist +37 Compressible flow No edit summary
• 14:2314:23, 13 March 2026 diff hist −28 One-dimensional inviscid flow No edit summary
• 14:0514:05, 13 March 2026 diff hist +9 One-dimensional inviscid flow No edit summary
• 14:0314:03, 13 March 2026 diff hist +5,152 N One-dimensional inviscid flow Created page with " == Acoustic Wave == <!-- \begin{figure}[ht!] \begin{center} \includegraphics[]{figures/standalone-figures/Chapter03/pdf/acoustic-wave.pdf} \caption{sound wave} \label{fig:soundwave} \end{center} \end{figure} --> In Fig. \ref{fig:soundwave}, station 1 represents the flow state ahead of the sound wave and station 2 the flow state behind the sound wave. Set up the continuity equation for one-dimensional flows between 1 and 2. If we could change frame of reference and fol..."
• 13:5313:53, 13 March 2026 diff hist 0 Flowpedia No edit summary
• 13:4913:49, 13 March 2026 diff hist 0 MediaWiki:Mainpage No edit summary current
• 13:4813:48, 13 March 2026 diff hist +87 N Flowpedia Created page with "* Incompressible Flow * Compressible Flow"
• 13:1813:18, 13 March 2026 diff hist 0 MediaWiki:Mainpage No edit summary Tag: Manual revert
• 13:1713:17, 13 March 2026 diff hist −61 MediaWiki:Mainpage No edit summary Tags: Manual revert Reverted
• 13:1613:16, 13 March 2026 diff hist +4 MediaWiki:Mainpage No edit summary Tag: Reverted
• 13:1613:16, 13 March 2026 diff hist +57 MediaWiki:Mainpage No edit summary Tag: Reverted
• 12:1912:19, 13 March 2026 diff hist 0 MediaWiki:Mainpage No edit summary Tag: Reverted
• 12:1712:17, 13 March 2026 diff hist +9 N MediaWiki:Mainpage Created page with "Main Test"
• 08:4208:42, 13 March 2026 diff hist +55 N Incompressible flow init Tag: Visual edit
• 08:4108:41, 13 March 2026 diff hist +53 N Compressible flow init Tag: Visual edit