Latex Equations Cribsheet

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Introduction

This page provides some introductory material for writing LaTex equations for the QNET Wiki. It is not intended to be a thorough introduction to LaTex, but is to provide some guidelines, share good practice advice and other information that aids the authoring of LaTex in this Wiki.

Editing Latex

To add an equation to an article click on the "Mathematical formula" button in the Edit toolbar.

Alternatively, use the math element in the Edit page of the article as follows:

<math>V = frac{4}{3} \pi R^{3}</math>

This should generate the expression:

CFD Equations and Expressions

There are many commonly used CFD equations and expressions used in the QNET Wiki and some of the commonly used ones are listed here. These can be either copied verbatim or used as templates for similar equations, etc.

Basic Expressions

Basic expressions here.

Reynolds Number

Prandl Number

Basic Flow Equations

Mass Continuity Equation

Eulers Equation

Navier Stokes Equations

where in the case of a Newtonian fluid:

and

Energy Transport Equation

The heat flux is given by:

Equations of State

Ideal Equation of State

Turbulence Equations

Reynolds Stress Transport Equation

Failed to parse (syntax error): {\displaystyle \frac {\partial \overline{u_{i}}}} {\partial t} + \overline{u_{j}} \frac{\partial \overline{u_{i}}}{\partial x_{j}} = - \frac{1}{\rho} \frac{\partial \overline{p}}{\partial x_{i}} + \frac{1}{\rho} \frac{\partial}{\partial x_{j}} \left( \mu \frac{\partial \overline{u_{i}}}{\frac x_{j}} - \rho \overline{u_{i}'u_{j}'} \right) }