\[ \begin{align}\begin{aligned}\newcommand\blank{~\underline{\hspace{1.2cm}}~}\\% Bold symbols (vectors) \newcommand\bs[1]{\mathbf{#1}}\\% Poor man's siunitx \newcommand\unit[1]{\mathrm{#1}} \newcommand\num[1]{#1} \newcommand\qty[2]{#1~\unit{#2}}\\\newcommand\per{/} \newcommand\squared{{}^2} \newcommand\cubed{{}^3} % % Scale \newcommand\milli{\unit{m}} \newcommand\centi{\unit{c}} \newcommand\kilo{\unit{k}} \newcommand\mega{\unit{M}} % % Percent \newcommand\percent{\unit{\%}} % % Angle \newcommand\radian{\unit{rad}} \newcommand\degree{\unit{{}^\circ}} % % Time \newcommand\second{\unit{s}} \newcommand\s{\second} \newcommand\minute{\unit{min}} \newcommand\hour{\unit{h}} % % Distance \newcommand\meter{\unit{m}} \newcommand\m{\meter} \newcommand\inch{\unit{in}} \newcommand\foot{\unit{ft}} % % Force \newcommand\newton{\unit{N}} \newcommand\kip{\unit{kip}} % kilopound in "freedom" units - edit made by Sri % % Mass \newcommand\gram{\unit{g}} \newcommand\g{\gram} \newcommand\kilogram{\unit{kg}} \newcommand\kg{\kilogram} \newcommand\grain{\unit{grain}} \newcommand\ounce{\unit{oz}} % % Temperature \newcommand\kelvin{\unit{K}} \newcommand\K{\kelvin} \newcommand\celsius{\unit{{}^\circ C}} \newcommand\C{\celsius} \newcommand\fahrenheit{\unit{{}^\circ F}} \newcommand\F{\fahrenheit} % % Area \newcommand\sqft{\unit{sq\,\foot}} % square foot % % Volume \newcommand\liter{\unit{L}} \newcommand\gallon{\unit{gal}} % % Frequency \newcommand\hertz{\unit{Hz}} \newcommand\rpm{\unit{rpm}} % % Voltage \newcommand\volt{\unit{V}} \newcommand\V{\volt} \newcommand\millivolt{\milli\volt} \newcommand\mV{\milli\volt} \newcommand\kilovolt{\kilo\volt} \newcommand\kV{\kilo\volt} % % Current \newcommand\ampere{\unit{A}} \newcommand\A{\ampere} \newcommand\milliampereA{\milli\ampere} \newcommand\mA{\milli\ampere} \newcommand\kiloampereA{\kilo\ampere} \newcommand\kA{\kilo\ampere} % % Resistance \newcommand\ohm{\Omega} \newcommand\milliohm{\milli\ohm} \newcommand\kiloohm{\kilo\ohm} % correct SI spelling \newcommand\kilohm{\kilo\ohm} % "American" spelling used in siunitx \newcommand\megaohm{\mega\ohm} % correct SI spelling \newcommand\megohm{\mega\ohm} % "American" spelling used in siunitx % % Inductance \newcommand\henry{\unit{H}} \newcommand\H{\henry} \newcommand\millihenry{\milli\henry} \newcommand\mH{\milli\henry} % % Power \newcommand\watt{\unit{W}} \newcommand\W{\watt} \newcommand\milliwatt{\milli\watt} \newcommand\mW{\milli\watt} \newcommand\kilowatt{\kilo\watt} \newcommand\kW{\kilo\watt} % % Energy \newcommand\joule{\unit{J}} \newcommand\J{\joule} % % Composite units % % Torque \newcommand\ozin{\unit{\ounce}\,\unit{in}} \newcommand\newtonmeter{\unit{\newton\,\meter}} % % Pressure \newcommand\psf{\unit{psf}} % pounds per square foot \newcommand\pcf{\unit{pcf}} % pounds per cubic foot \newcommand\pascal{\unit{Pa}} \newcommand\Pa{\pascal} \newcommand\ksi{\unit{ksi}} % kilopound per square inch \newcommand\bar{\unit{bar}} \end{aligned}\end{align} \]

Dec 03, 2024 | 272 words | 3 min read

2.2.1. Task 1

Learning Objectives

By the end of this exercise, you will be able to apply your mathematical and analytical skills to optimize the dimensions of a cylindrical storage tank. You will demonstrate proficiency in using cell referencing for calculations, organizing data effectively, and interpreting results to answer critical questions about the design.

Introduction

Fig. 2.3 Cylinder for Task 1.

A team of engineers is designing a storage tank in a cylindrical shape. The total available surface area of the cylinder (\(A\)) is \(\qty{2000}{\sqft}\). The team’s objective is to make this cylinder hold the maximum possible volume. The dimensions for the cylinder are shown in Fig. 2.3.

Equations used:

• Volume: \(V = \pi R^2 H\)

• Surface area: \(A = 2 \pi R^2 + 2 \pi R H = \qty{2000}{\foot\squared}\)

Task Instructions

1. Open the answer sheet ex2_team_1_teamnumber.xlsx. Save it with your team number replacing teamnumber in the file name.

2. On the Input Section of the sheet, you will see possible radii of the storage tank. Under the Calculation Section, calculate the possible height \(H\) and volume \(V\) for each radius \(R\).

   1. Use cell referencing to perform the calculations.

   2. Organize and format your work, so it is easy to follow. Be sure to include units.

3. Copy the following questions into the Output Section of the spreadsheet and then add your answers.

   1. Which radius \(R\) and height \(H\) combination results in the largest volume \(V\)?

   2. Are the dimensions from the previous question acceptable considering maximizing volume and transportation to a new site? Why or why not?

4. Save the ex2_team_1_teamnumber.xlsx file as ex2_team_1_values_teamnumber.pdf displaying the values and ex2_team_1_formulas_teamnumber.pdf displaying the formula.

5. Submit both files to Gradescope.

Important

When organizing your work in MS Excel:

• Use cell referencing to perform the calculations

• Use descriptive variable names

• Include column and row headings with units

• Organize and format your work so it is easy to follow