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:

Basic Mathematical Expressions

Algebraic Equations

The above example shows a typical algebraic expression that uses a mixture of fractions and exponents. Fractions are generated using the frac expression with the numerator and denominator as two arguments:

<math>
a = \frac{b+c}{d}
</math>

Differential Equations

Ordinary and partial derivative expressions can be generated in the obvious way using the frac operator:


while exponents are written with the symbol '^':

<math>
   E = mc^{2}
</math>


The curly braces '{}' are optional but may be required to remove ambiguities or aid readability in LaTex expressions.


Subscripts are defined using the '_' symbol.


<math>
    \sigma_{kk}
</math>

is rendered as:


Arrays of equations

<math>
\begin{array}{lcl}
      a + b + c + d & = & e + f + \\
                    &   & g + h
\end{array}
</math>



More information on basic mathematical expressions can be found at the MediaWiki web site here and here.

CFD Equations and Expressions

There are many 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 from the article source or used as templates for similar equations, etc.


Basic Expressions

Reynolds Number


Prandl Number


Basic Flow Equations

Mass Continuity Equation


Eulers Equation


Navier Stokes Equations

where in the case of a Newtonian fluid:

and


Reynolds Averaged Navier-Stokes Equation


Energy Transport Equation

The heat flux is given by:


Equations of State

Ideal Equation of State


Turbulence Equations

Standard Two Equation Model

Kinematic eddy viscosity:

Turbulent Kinetic Energy transport equation:

Dissipation Rate transport equation:

Coefficients and Auxilliary Relations:

where

and


Reynolds Stress Transport Equation