\documentclass[10pt,a4paper]{article} % Packages \usepackage{fancyhdr} % For header and footer \usepackage{multicol} % Allows multicols in tables \usepackage{tabularx} % Intelligent column widths \usepackage{tabulary} % Used in header and footer \usepackage{hhline} % Border under tables \usepackage{graphicx} % For images \usepackage{xcolor} % For hex colours %\usepackage[utf8x]{inputenc} % For unicode character support \usepackage[T1]{fontenc} % Without this we get weird character replacements \usepackage{colortbl} % For coloured tables \usepackage{setspace} % For line height \usepackage{lastpage} % Needed for total page number \usepackage{seqsplit} % Splits long words. %\usepackage{opensans} % Can't make this work so far. Shame. Would be lovely. \usepackage[normalem]{ulem} % For underlining links % Most of the following are not required for the majority % of cheat sheets but are needed for some symbol support. \usepackage{amsmath} % Symbols \usepackage{MnSymbol} % Symbols \usepackage{wasysym} % Symbols %\usepackage[english,german,french,spanish,italian]{babel} % Languages % Document Info \author{{[}deleted{]}} \pdfinfo{ /Title (bme-cheat-sheet.pdf) /Creator (Cheatography) /Author ({[}deleted{]}) /Subject (BME Cheat Sheet) } % Lengths and widths \addtolength{\textwidth}{6cm} \addtolength{\textheight}{-1cm} \addtolength{\hoffset}{-3cm} \addtolength{\voffset}{-2cm} \setlength{\tabcolsep}{0.2cm} % Space between columns \setlength{\headsep}{-12pt} % Reduce space between header and content \setlength{\headheight}{85pt} % If less, LaTeX automatically increases it \renewcommand{\footrulewidth}{0pt} % Remove footer line \renewcommand{\headrulewidth}{0pt} % Remove header line \renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit % This two commands together give roughly % the right line height in the tables \renewcommand{\arraystretch}{1.3} \onehalfspacing % Commands \newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour \newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols \newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns \newcommand{\tn}{\tabularnewline} % Required as custom column type in use % Font and Colours \definecolor{HeadBackground}{HTML}{333333} \definecolor{FootBackground}{HTML}{666666} \definecolor{TextColor}{HTML}{333333} \definecolor{DarkBackground}{HTML}{82CAFF} \definecolor{LightBackground}{HTML}{EFF8FF} \renewcommand{\familydefault}{\sfdefault} \color{TextColor} % Header and Footer \pagestyle{fancy} \fancyhead{} % Set header to blank \fancyfoot{} % Set footer to blank \fancyhead[L]{ \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{C} \SetRowColor{DarkBackground} \vspace{-7pt} {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}} } \end{tabulary} \columnbreak \begin{tabulary}{11cm}{L} \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{BME Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{{[}deleted{]}} via \textcolor{DarkBackground}{\uline{cheatography.com/27799/cs/8137/}}} \end{tabulary} \end{multicols}} \fancyfoot[L]{ \footnotesize \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{LL} \SetRowColor{FootBackground} \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}} \\ \vspace{-2pt}{[}deleted{]} \\ \uline{cheatography.com/deleted-27799} \\ \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}} \\ \vspace{-2pt}Not Yet Published.\\ Updated 9th May, 2016.\\ Page {\thepage} of \pageref{LastPage}. \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}} \\ \SetRowColor{white} \vspace{-5pt} %\includegraphics[width=48px,height=48px]{dave.jpeg} Measure your website readability!\\ www.readability-score.com \end{tabulary} \end{multicols}} \begin{document} \raggedright \raggedcolumns % Set font size to small. Switch to any value % from this page to resize cheat sheet text: % www.emerson.emory.edu/services/latex/latex_169.html \footnotesize % Small font. \begin{multicols*}{3} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Assumptions}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{1. The fluid is Newtonian \newline % Row Count 1 (+ 1) 2. Fluid is isotropic \newline % Row Count 2 (+ 1) 3. Fluid is incompressible \newline % Row Count 3 (+ 1) 4. Fluid flow is steady state \newline % Row Count 4 (+ 1) 5. Fluid flow is laminar \newline % Row Count 5 (+ 1) 6. Fluid flow is fully developed \newline % Row Count 6 (+ 1) 7. No slip condition% Row Count 7 (+ 1) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{0.89586 cm} x{4.08114 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Units and Conversions}} \tn % Row 0 \SetRowColor{LightBackground} \seqsplit{Pressure} & 1 Pa = 1 N/m\textasciicircum{}2\textasciicircum{} = 1 \textasciicircum{}kg\textasciicircum{}/(m·s\textasciicircum{}2\textasciicircum{}) \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} & 1 atm = 101325 Pa = 2116.22 lbf/ft\textasciicircum{}2\textasciicircum{} \tn % Row Count 4 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Micropipette Aspiration}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/amj2162_1462662127_Screen Shot 2016-05-07 at 6.58.26 PM.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{where {\bf{ {\emph{n}} }} is the surface tension of the cell {[}N/m{]} \newline if given thickness then n = σt} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Buoyancy}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Equal volumes feel equal buoyant forces. \newline % Row Count 1 (+ 1) Why? Identical pressure environments and equal water displacement. \newline % Row Count 3 (+ 2) Submerged Object: Archimedes' Principle \newline % Row Count 4 (+ 1) Mass of Object - Submerged Mass = Density of Fluid x Volume of Object \newline % Row Count 6 (+ 2) Submerge object \{\{fa-long-arrow-right\}\} water level increases \newline % Row Count 8 (+ 2) Remove object from boat \{\{fa-long-arrow-right\}\} water level decreases% Row Count 10 (+ 2) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.14011 cm} x{2.83689 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Terms and Facts}} \tn % Row 0 \SetRowColor{LightBackground} Viscosity & A material property, gives proportionality of shear stress and shear rate {[}g/cm·s{]} \tn % Row Count 4 (+ 4) % Row 1 \SetRowColor{white} Absolute/Dynamic Viscosity & μ \tn % Row Count 6 (+ 2) % Row 2 \SetRowColor{LightBackground} Kinematic Viscosity & ν=μ/ρ \tn % Row Count 8 (+ 2) % Row 3 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{Non-Newtown Fluids: {\emph{τ = μγ\textasciicircum{}η\textasciicircum{}}}} \tn % Row Count 9 (+ 1) % Row 4 \SetRowColor{LightBackground} Shear Thinning (η \textless{} 1) & Faster you shear it, thinner it becomes; resistance decreases, becomes more uniform. \tn % Row Count 13 (+ 4) % Row 5 \SetRowColor{white} Shear Thickening (η \textgreater{} 1) & Faster you shear it, thicker it becomes; resistance increases. \tn % Row Count 16 (+ 3) % Row 6 \SetRowColor{LightBackground} Bingham Plastic (τ=μγ+τ\_y) & Acts like a solid until the sheet stress reaches a critical value \tn % Row Count 19 (+ 3) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Centrioidal Moments of Inertia}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/amj2162_1462660923_Screen Shot 2016-05-07 at 6.41.04 PM.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{xcp = -\textasciicircum{}{\emph{γ}}·Ixy·sinθ·Ixy\textasciicircum{}/Pcg·A = -\textasciicircum{}Ixy·sinθ\textasciicircum{}/hcg·A \newline \newline ycp = -\textasciicircum{}{\emph{γ}}·Ixx·sinθ·Ixy\textasciicircum{}/Pcg·A = -\textasciicircum{}Ixx·sinθ\textasciicircum{}/hcg·A \newline \newline F = {\emph{γ}}·hcg·A = P·A \newline \newline The center of gravity and center of pressure are different locations. \newline The force on the object occurs at the center of gravity. \newline The pressure on the object occurs at the center of pressure (use Ixx, and Ixy) \newline \newline When calculating the moment: remember the reaction forces} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Manometer}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Pressure = density\{\{fa-times\}\}gravity\{\{fa-times\}\}height = ρgh} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{If given N/m\textasciicircum{}3\textasciicircum{} or lbf/ft\textasciicircum{}3\textasciicircum{} then do {\bf{not}} add gravity} \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Change in elevation \{\{fa-long-arrow-right\}\} change in pressure} \tn % Row Count 6 (+ 2) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Within a single fluid, pressure is constant along a height} \tn % Row Count 8 (+ 2) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Specific Gravy = {[}density of X{]} / {[}density of water{]}} \tn % Row Count 10 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{move down \{\{fa-angle-right\}\} (+), move up \{\{fa-angle-right\}\} (-)} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}