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Below I have attached my code for a report i am writing along with the error codes it is giving me AND the "lab2bib.bib" file that i am using. I am having so many issues with getting bibliographies to work.... PLEASE HELP. When i run the .bib file it tells that it cannot find the lab2bib.aux file as well.

The citation i am trying to make as a test rigth above the "Appendices" section.

documentclass[letterpaper,10pt]{article}

input kvmacros % For Karnaugh Maps (K-Maps)

usepackage{apacite}

usepackage{graphicx} % For images

usepackage{amsmath}

usepackage{indentfirst}

usepackage{gensymb}

usepackage[nottoc]{tocbibind}

usepackage{varwidth}

usepackage{float}    % For tables and other floats

usepackage{verbatim} % For comments and other

usepackage{amsmath}  % For math

usepackage{amssymb}  % For more math

usepackage{fullpage} % Set margins and place page numbers at bottom center

usepackage{listings} % For source code

usepackage{subfig}   % For subfigures

usepackage[usenames,dvipsnames]{color} % For colors and names

usepackage[pdftex]{hyperref}           % For hyperlinks and indexing the PDF

hypersetup{ % play with the different link colors here

    colorlinks,

    citecolor=blue,

    filecolor=blue,

    linkcolor=blue,

    urlcolor=blue % set to black to prevent printing blue links

}



definecolor{mygrey}{gray}{.96} % Light Grey

lstset{ 

    language=[ISO]C++,              % choose the language of the code ("language=Verilog" is popular as well)

   tabsize=3,                             % sets the size of the tabs in spaces (1 Tab is replaced with 3 spaces)

    basicstyle=tiny,               % the size of the fonts that are used for the code

    numbers=left,                   % where to put the line-numbers

    numberstyle=tiny,              % the size of the fonts that are used for the line-numbers

    stepnumber=2,                   % the step between two line-numbers. If it's 1 each line will be numbered

    numbersep=5pt,                  % how far the line-numbers are from the code

    backgroundcolor=color{mygrey}, % choose the background color. You must add usepackage{color}

    %showspaces=false,              % show spaces adding particular underscores

    %showstringspaces=false,        % underline spaces within strings

    %showtabs=false,                % show tabs within strings adding particular underscores

    frame=single,                    % adds a frame around the code

    tabsize=3,                      % sets default tabsize to 2 spaces

    captionpos=b,                   % sets the caption-position to bottom

    breaklines=true,                % sets automatic line breaking

    breakatwhitespace=false,        % sets if automatic breaks should only happen at whitespace

    %escapeinside={%*}{*)},        % if you want to add a comment within your code

    commentstyle=color{BrickRed}   % sets the comment style

}





newcommand{Hz}{textsl{Hz}}

newcommand{KHz}{textsl{KHz}}

newcommand{MHz}{textsl{MHz}}

newcommand{GHz}{textsl{GHz}}

newcommand{ns}{textsl{ns}}

newcommand{ms}{textsl{ms}}

newcommand{s}{textsl{s}}







% TITLE PAGE CONTENT %%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

newcommand{labno}{01}

newcommand{labtitle}{Surface Tension Laboratory}

newcommand{authorname}{Zackary Schexnider, Leland Smith}

newcommand{professor}{Dr. Borquist}

newcommand{classno}{MEMT313-001}

% END TITLE PAGE CONTENT %%%%%%%%%%%%%%%%%%%%





begin{document}  % START THE DOCUMENT!



begin{titlepage}

begin{center}

{LARGE textsc{Laboratory No. labno:} \ vspace{4pt}}

{Large textsc{labtitle} \ vspace{4pt}} 

rule[13pt]{textwidth}{1pt} \ vspace{150pt}

{large By: authorname \ vspace{10pt}

Instructor: professor \ vspace{10pt}

 classno \ vspace{10pt}

large December 3, 2018 }

end{center}

end{titlepage}

% END TITLE PAGE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



tableofcontents

newpage

listoffigures



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section{Objective}

Calculate surface tension in filtered water versus SAE 30W oil using a replicable experiment design. Compare the calculations to known values given in the text and provide improvement suggestions for the flawed design.



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section{Background and Theory}



subsection{Surface Tension and Capillary Rise Explained}



Surface tension is most commonly observed when filling containers with liquid. The moment before the drink spills over the sides there is a “bubble” shaped mass of liquid at the top of the container. This is due to surface tension which can be visualized as an elastic membrane stretched over the free side of a liquid. All particles within a liquid exert attraction upon one another. Particles on the interior of the liquid mass are attracted from all sides creating a net force of zero. Particles on the edges of the liquid do not have a net force of zero due to the lack of surrounding particles. The lack of surrounding forces on the outer particles is the reason that surface tension is present.vspace{3mm}



This phenomenon can be observed in many real-world scenarios. These include: Bugs traveling along the surface of water, waterproof tents, droplets of water from a sink, and many more.vspace{3mm} 



The concept that is specific to this experiment is called Capillary Rise. It is caused by the characteristics of a solid-liquid-gas interface. When glass and water interface, there is an adhesion force present. When the radius of the glass capillary tube is small enough, the adhesion force overcomes the cohesion force in the water causing it to move upwards in the tube. This is only true for certain liquids. Depending on the viscosity, the liquid could depress below the surface of the liquid.vspace{3mm}



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subsection{Equation Derivation}



The equation for surface tension in the capillary rise scenario is derived using static analysis of the forces acting on the meniscus. The forces acting tangential of the meniscus endpoints are represented as $$pi R sigma cos(theta)$$ where the tube radius is $R$, surface tension is $sigma$, and angle of contact is $theta$. This equation is multiplied by $2$ to account for both meniscus endpoints.

The downward force acting upon the center of the meniscus is represented as $$gamma pi R^2 h$$ where the specific weight is $gamma$, the radius is $R$, and the height from liquid surface to the top of the meniscus is $h$.vspace{3mm}

These forces are set equal to make the equation: $$2 pi R sigma = gamma pi R^2 h$$ vspace{3mm}

This equation can then be solved for the final surface tension equation:

$$sigma=frac{hgamma R}{2 cos(theta)}$$



subsection{Surface Tension and Surface Energy}



Surface Energy, $frac{Energy}{Area}$, and Surface Tension, $frac{Force}{Length}$, are two interconnected concepts that are opposite in magnitudes relative to the contact angle $theta$. When surface tension is High, Surface Energy is Low and vice versa. This relationship is non-intuitive, but can be visualized by realizing the increase in $area$ constitutes a decrease in $length$.



subsection{Dismissed Designs}



begin{enumerate}

        item "Fulcrum Method" - This design is executed by incrementally adding rice grains into the weighing tray that act as a increasing counterweight to find the breaking point of the surface tension. 

    begin{figure}[H]   

        begin{center}

      includegraphics[width=0.5textwidth]{Option1.png}

   end{center}

   caption{Fulcrum Method}

   label{figure1}

   end{figure}





  begin{varwidth}[t]{.5textwidth}

underline{Positives:}

begin{itemize}

item Intuitive

item Visually Immersive

item Easy Assembly

item Simple data gathering



end{itemize}

end{varwidth}% <---- Don't forget this %

hspace{4em}% <---- Don't forget this %

begin{varwidth}[t]{.5textwidth}

underline{Negatives:}

begin{itemize}

item Not Precise

item Results vary due to impulse of rice addition

item Large amount of components

item Difficult to precisely replicate



end{itemize}

end{varwidth}

newpage    

    item "Stalagmometer Method" - This method requires the purchase of two seperate stalagmometers for the oil and water. The fluids are different viscosities which requires different size Stalagmometers.



    begin{figure}[H]   

        begin{center}

      includegraphics[width=0.2textwidth]{Option3.png}

   end{center}

   caption{Stalagmometer Method}

   label{figure2}

   end{figure}



    begin{varwidth}[t]{.5textwidth}

underline{Positives:}

begin{itemize}

item Most precise

item Stable

item Easy to replicate 

item Simple assembly



end{itemize}

end{varwidth}% <---- Don't forget this %

hspace{4em}% <---- Don't forget this %

begin{varwidth}[t]{.5textwidth}

underline{Negatives:}

begin{itemize}

item Expensive

item Delicate transportation

item Different sizes required for different viscosities

item Use of mouth required for most models (repulsive to some)



end{itemize}

end{varwidth}



    end{enumerate}



%%%%%%%%%%%%%

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subsection{Design Choice Reasoning}



The “Capillary Rise Method” was chosen as the experiment design because of its stability, precision, replicability, and intuitiveness. This design allows for a precise measurement due to the clear acrylic plate. The acrylic plate allows for the angle of vision to be exactly perpendicular with the meniscus. This feature, coupled with the side by side comparison, enables the experimenter to test two liquids simultaneously. These design elements set this option above the rest in all categories.



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newpage

section{Procedure}



begin{figure}[H]

   begin{center}

      includegraphics[width=0.6textwidth]{Option2.png}

   end{center}

caption{Capillary Method}

label{figure3}

end{figure}



subsection{Equipment}



begin{enumerate}

item Container - A preferably clear/transparent container is used to hold the liquid(s) for measuring.  Kitchen glassware, like a cup, would suffice although most glasses are circular and could be difficult to secure the height measuring device.  The size of the container is not a factor in the calculations.  The container used in this experiment is hand crafted from 1” thick pine wood boards, clear acrylic plate for an easy read of height measurements, wood screws as fasteners, polyurethane coating to stop absorption into the wood, and a silicone sealer to inhibit leaks. The dual compartment design is only needed for simultaneous testing.

item Length Measuring Tool - A length measuring tool is used to measure the capillary rise of the liquid(s).  A ruler is the ideal tool to determine the height of the risen liquid in the capillary tubes.  This height difference, measured between the surface of the liquid to the top of the meniscus inside the capillary tube, will be h in the surface tension equation.

item Capillary Tubes (made by Pyrex, Part #9530-4) - 0.8-1.1mm diameter capillary tubes are used to determine the capillary rise of the liquid(s) being measured. The tubes need to be open on both sides so air can exit as liquid enters. 

item Mounting Device - The capillary tubes need to be secured to the length measuring tool, so no accidental movement occurs during the experiment.  Rubber bands are an easy and cheap method for securing the tubes to the ruler.

item Desired Liquid(s) to Measure - The only liquids used in this experiment are filtered water and SAE 30W oil.  Some physical properties of these liquids can be found in Figure ref{4}.  The surface tension values in this table will be compared to our calculated values.

end{enumerate}



begin{figure}[H]

   begin{center}

      includegraphics[width=0.9textwidth]{Tablevalues.png}

   end{center}

caption{Physical Properties}

label{4}

end{figure}



subsection{Experiment}

begin{enumerate}





item To begin the experiment, the container needs to be completely clean and dry, so no impurities mix with the liquid.  Any impurities could potentially alter the surface tension and corrupt the data collected.  Once the container is prepped and placed on a flat, leveled surface, water is poured into the left compartment of the container and SAE 30W oil into the right compartment.  The liquids are filled to half of the containers volume.  

item Two opened ended capillary tubes are secured, by rubber bands, to two rulers; one capillary tube per ruler.  The capillary tubes are placed at a high enough level on the ruler so that half of the tubes will be submerged when placed in liquid.  

item One ruler is placed in the water-filled compartment of the container and the other ruler in the oil-filled compartment.  The rulers are placed with the tubes facing the acrylic plate on the container so that height of the liquid in the capillary tube can be seen. 

item The liquids in the capillary tubes rise higher than the level of the liquid in the individual compartments.  The liquids in the capillary tubes continue to rise for about a minute but eventually come to a halt.  Once the water and oil quit rising in their respective tubes, the height difference is recorded.  The height difference is measured from the surface of the liquids to the top-most point of the meniscuses in the capillary tubes.  The collection of height data is Step 4.

item Repeat Steps 2-4 two more times with unused or acetone cleaned capillary tubes to get a total of three heights for each liquid.  This collected data will be used to calculate an average height for water and an average height for the SAE 30W oil.

end{enumerate}



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newpage

section{Results}



begin{figure}[H]

   begin{center}

      includegraphics[width=0.9textwidth]{Heightvalues.png}

   end{center}

caption{Collected Height Data}

label{5}

end{figure}



textbf{underline{From Figure ref{4}:}}vspace{3mm}



$gamma_{water}=9800 frac{N}{m^3}$ 



$gamma_{30Woil}=8950 frac{N}{m^3}$vspace{3mm} 



textbf{underline{Other Given Values:}}vspace{3mm}



$theta=0degree$, The angle of the meniscus, measured from vertical, is zero because we assume the glass capillary tube is unused or cleaned with acetone.vspace{3mm}



$R=0.0005m$, The diameter of the capillary tube is given from the manufacturer.  Since the diameter can vary from 0.8mm to 1.1 mm, we assume the diameter is 1mm to keep calculations easy.vspace{3mm}



textbf{underline{Solve for Surface Tensions:}}vspace{3mm}



$ h_{avgwater} = frac{ 2 sigma_{water} cos(theta)}{ gamma_{water} R }$vspace{3mm}



$0.0185m = frac{2 sigma_{water}}{9800 frac{N}{m^3} 0.0005m}$vspace{3mm}



$sigma_{water}=boxed{0.045 frac{N}{m^3}}$vspace{10mm}



$ h_{avg30W} = frac{ 2 sigma_{30W} cos(theta)}{ gamma_{30W} R }$vspace{3mm}



$0.0115m = frac{2 sigma_{30W}}{8950 frac{N}{m^3} 0.0005m}$vspace{3mm}



$sigma_{30W}=boxed{0.025 frac{N}{m^3}}$vspace{3mm}





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newpage

section{Discussion & Conclussion}



Overall, the replicable experiment design gives promising values of capillary rise heights which are used to calculate surface tension of the varying liquids, water and 30W oil.  The final surface tension results are compared to the proven values in Figure ref{4} from the text.  The calculated surface tensions,

 $sigma_{water} = 0.045 frac{N}{m^3}$  and $sigma_{30W} = 0.025 frac{N}{m^3}$, are slightly lower than the given values from text, $sigma_{Actualwater} = 0.0734 frac{N}{m^3}$ and $sigma_{Actual30W} = 0.036 frac{N}{m^3}$.  Note that the proven surface tensions of water and 30W oil in Figure ref{4} are measured at $15.6 degree C $ while the location of the experiment was at room temperature, $72 degree F$ or $22.22 degree C$. vspace{3mm}



Temperature was over looked as a contributing factor to the surface tension because there are no “visible” temperature dependent variables in the surface tension equation.  The reason why surface tension and temperature are inversely proportional is due to the cohesive forces decreasing when molecular thermal energy increases.vspace{3mm}



This design flaw is contributing factor to why the calculated surface tensions are lower than those from Figure ref{4}.  This flaw can easily be avoided by making sure that the temperature of the experiment’s enviroment matches that of the proven surface tensions environment temperature.vspace{3mm} 



The capillary action of these fluids is desirable in small scale pumping systems. Once the fluid rises, it starts a perpetual suction that will drive a pumping system without any work input required. Water would be more desirable in this scenario because is has more capillary action resulting in greater surface tension. cite{Nobody06}



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newpage

section{Appendices}



subsection{Original Data and Calculations}



begin{figure}[H]

   begin{center}

      includegraphics[width=0.8textwidth]{Calculations.jpg}

   end{center}

caption{Original Data and Calculations}

label{6}

end{figure}







bibliographystyle{plain}

bibliography{lab2bib}











end{document}

lab2bib.bib file:

@misc{ Nobody06,

       author = "Nobody Jr",

       title = "My Article",

       year = "2006" }