Quick Look
Grade Level: 9 (912)
Time Required: 3 hours 45 minutes
(1 week, about five 45minute class periods; see note in Procedure section)
Expendable Cost/Group: US $0.00
Group Size: 4
Activity Dependency:
Subject Areas: Algebra, Physics, Problem Solving, Reasoning and Proof, Science and Technology
Summary
At this point in the unit, students have learned about Pascal's law, Archimedes' principle, Bernoulli's principle, and why aboveground storage tanks are of major concern in the Houston Ship Channel and other coastal areas. In this culminating activity, student groups act as engineering design teams to derive equations to determine the stability of specific aboveground storage tank scenarios with given tank specifications and liquid contents. With their flotation analyses completed and the stability determined, students analyze the tank stability in specific storm conditions. Then, teams are challenged to come up with improved storage tank designs to make them less vulnerable to uplift, displacement and buckling in storm conditions. Teams present their analyses and design ideas in short class presentations.Engineering Connection
The 4,200 aboveground storage tanks located along the 50mile Houston Ship Channel are at high risk for failure during storm events. Because many of these facilities are only protected to 1415 feet above mean sea level, they are very likely to uplift, displace and buckle during major flood surges. With no existing provisions for shell buckling of uplift due to flooding, it is engineers' responsibility to assess these vulnerabilities and improve the code manual to include these important provisions.
Learning Objectives
After this activity, students should be able to:
 Explain what aboveground storage tanks are, where and why they are used, and the associated environmental issues.
 Explain how Pascal's law and Archimedes' principle relate to the use of aboveground storage tanks and the types of failure associated with these tanks.
 Research and apply new scientific knowledge in conjunction with content previously learned in the classroom to answer questions regarding the stability of storage tanks.
 Use critical thinking and the engineering design process to design a solution to an engineering problem.
 Effectively communicate and present unique ideas to an audience.
Educational Standards
Each TeachEngineering lesson or activity is correlated to one or more K12 science,
technology, engineering or math (STEM) educational standards.
All 100,000+ K12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN),
a project of D2L (www.achievementstandards.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics;
within type by subtype, then by grade, etc.
Each TeachEngineering lesson or activity is correlated to one or more K12 science, technology, engineering or math (STEM) educational standards.
All 100,000+ K12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.
NGSS: Next Generation Science Standards  Science
By engaging in the science and engineering practices of using models, constructing explanations and designing solutions, analyzing and interpreting data and using mathematics and computational thinking, students make sense of Archimedes’ principle and Pascal’s law in the engineering design of aboveground storage tanks. Students explore the disciplinary core idea of engineering design while applying the crosscutting concept of systems and system models.
NGSS Performance Expectation  

HSETS12. Design a solution to a complex realworld problem by breaking it down into smaller, more manageable problems that can be solved through engineering. (Grades 9  12) Do you agree with this alignment? 

Click to view other curriculum aligned to this Performance Expectation  
This activity focuses on the following Three Dimensional Learning aspects of NGSS:  
Science & Engineering Practices  Disciplinary Core Ideas  Crosscutting Concepts 
Design a solution to a complex realworld problem, based on scientific knowledge, studentgenerated sources of evidence, prioritized criteria, and tradeoff considerations. Alignment agreement: Analyze complex realworld problems by specifying criteria and constraints for successful solutions.Alignment agreement:  Criteria may need to be broken down into simpler ones that can be approached systematically, and decisions about the priority of certain criteria over others (tradeoffs) may be needed. Alignment agreement:  Investigating or designing new systems or structures requires a detailed examination of the properties of different materials, the structures of different components, and connections of components to reveal its function and/or solve a problem. Alignment agreement: Models (e.g., physical, mathematical, computer models) can be used to simulate systems and interactions—including energy, matter, and information flows—within and between systems at different scales.Alignment agreement: 
NGSS Performance Expectation  

HSETS13. Evaluate a solution to a complex realworld problem based on prioritized criteria and tradeoffs that account for a range of constraints, including cost, safety, reliability, and aesthetics, as well as possible social, cultural, and environmental impacts. (Grades 9  12) Do you agree with this alignment? 

Click to view other curriculum aligned to this Performance Expectation  
This activity focuses on the following Three Dimensional Learning aspects of NGSS:  
Science & Engineering Practices  Disciplinary Core Ideas  Crosscutting Concepts 
Evaluate a solution to a complex realworld problem, based on scientific knowledge, studentgenerated sources of evidence, prioritized criteria, and tradeoff considerations. Alignment agreement: Analyze data using tools, technologies, and/or models (e.g., computational, mathematical) in order to make valid and reliable scientific claims or determine an optimal design solution.Alignment agreement: Use mathematical representations of phenomena or design solutions to describe and/or support claims and/or explanations.Alignment agreement:  When evaluating solutions it is important to take into account a range of constraints including cost, safety, reliability and aesthetics and to consider social, cultural and environmental impacts. Alignment agreement:  New technologies can have deep impacts on society and the environment, including some that were not anticipated. Analysis of costs and benefits is a critical aspect of decisions about technology. Alignment agreement: 
Common Core State Standards  Math

Reason abstractly and quantitatively.
(Grades
K 
12)
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Model with mathematics.
(Grades
K 
12)
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Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
(Grades
9 
12)
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Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
(Grades
9 
12)
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Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
(Grades
9 
12)
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Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
(Grades
9 
12)
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Reason quantitatively and use units to solve problems.
(Grades
9 
12)
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International Technology and Engineering Educators Association  Technology

Students will develop an understanding of the attributes of design.
(Grades
K 
12)
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Students will develop an understanding of engineering design.
(Grades
K 
12)
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Students will develop abilities to apply the design process.
(Grades
K 
12)
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Research and development is a specific problemsolving approach that is used intensively in business and industry to prepare devices and systems for the marketplace.
(Grades
9 
12)
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The design process includes defining a problem, brainstorming, researching and generating ideas, identifying criteria and specifying constraints, exploring possibilities, selecting an approach, developing a design proposal, making a model or prototype, testing and evaluating the design using specifications, refining the design, creating or making it, and communicating processes and results.
(Grades
9 
12)
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The process of engineering design takes into account a number of factors.
(Grades
9 
12)
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State Standards
Texas  Math

solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides;
(Grade
9)
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apply the formulas for the volume of threedimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure.
(Grades
9 
12)
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Texas  Science

communicate valid conclusions supported by the data through various methods such as lab reports, labeled drawings, graphic organizers, journals, summaries, oral reports, and technologybased reports; and
(Grades
9 
12)
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express and manipulate relationships among physical variables quantitatively, including the use of graphs, charts, and equations.
(Grades
9 
12)
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research and describe the connections between physics and future careers; and
(Grades
9 
12)
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demonstrate basic principles of fluid dynamics, including hydrostatic pressure, density, salinity, and buoyancy;
(Grades
10 
12)
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Materials List
Each group needs:
 computer with access to the Internet, Microsoft PowerPoint® and Excel® (or equivalent programs)
 Design Project Worksheet, one per person, a different version for each group; see the Attachment section for five different versions
 (optional) any materials students require to construct or draw models or prototypes
Worksheets and Attachments
Visit [www.teachengineering.org/activities/view/uoh_fluidmechanics_lesson02_activity1] to print or download.More Curriculum Like This
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PreReq Knowledge
Students should have a basic understanding of Pascal's law, Archimedes' principle; the relationship between mass, volume, density and weight; and basic algebra and simple geometry in order to solve and manipulate equations; as well as be familiar with aboveground storage tanks and their associated environmental issues. As prerequisites for this activity, conduct The Physics of Fluid Mechanics and AboveGround Storage Tanks in the Houston Ship Channel lessons.
Introduction/Motivation
Professional code manuals contain provisions for external pressure and floatation, anchorage due to seismic activity, and anchorage due to internal pressure for aboveground storage tanks. However, no provisions exist for shell buckling or uplift caused by flooding, despite the fact that these are ongoing issues with extreme consequences.
For example, the 4,200 aboveground storage tanks in the Houston Ship Channel contain explosive materials, toxic gases and petrochemicals and are vulnerable to the frequent highforce storms and hurricanes common in the region. The lack of relevant code provisions is the motivation for your engineering design challenge project this week.
Now, it is your turn to analyze an aboveground storage tank in given storm conditions to see if your tank will displace. In addition, your team challenge is to use steps of the engineering design process to come up with an engineering design for a new and/or improved tank, perhaps by an addition or change to an existing tank design that prevents it from buckling or displacing.
Procedure
Time Planning
Schedule this activity to take about five 45minute class periods spread over a week. The first day of the project includes an introduction and assignment of the design project, and the last day is for student presentations. The three periods between are class time for student groups to work on the project. If the class time for students to work on the project is instead assigned as homework, the class time required for this activity can be significantly reduced to ~12 class periods.
Background
Archimedes' principle states that the buoyant force is equal to the weight of the water displaced by the aboveground storage tank. If the weight of the water around the storage tank (due to surge) is greater than the weight of the tank, the tank will displace. Pascal's law states that a pressure applied at any point on a confined incompressible fluid is transmitted equally throughout the fluid. The surge creates an increased hydrostatic pressure gradient on the aboveground storage tank that pressurizes the entire tank and can lead to buckling (rupture).
The surge height and liquid level inside ASTs vary daily. For this activity, the diameter range for the aboveground storage tanks were assumed to be 20300 feet and the height range for the tanks were assumed to be 1030 feet, based on information presented at the SSPEED Center Conference: Hurricane Ike 5 Years Later at Rice University on September 24, 2013. Shell materials were extracted from Section 4.2.2 ASTM Specifications in the API Standard 650: Welded Tanks for Oil Storage, and petrochemicals were chosen randomly. For additional background information about ASTs, refer to the associated lesson.
Before the Activity
 Assuming a group size of four students, determine how many engineering design groups you will have in each class. Then make copies of the AboveGround Storage Tank Design Worksheets, one per person; see the Attachments section for five different versions (unique storage tank specifications, tank contents and storm conditions). Each group gets a different worksheet with each person in a group having a copy. If your class has more than five groups, make additional unique worksheet versions, as needed.
 Become familiar with the types of failure that aboveground storage tanks experience as well as the equations that students will be asked to derive.
With the Students
 After having presented to students the AboveGround Storage Tanks Presentation (a PowerPoint® file) as part of conducting the associated lesson, guide students to engage in conversation about the environmental issues associated with aboveground storage tanks along the Houston Ship Channel.
 Divide the class into engineering design groups of four students each and explain that their challenge this week is to design a solution to this realworld problem—the vulnerability of aboveground storage tanks in storm conditions.
 Hand out the worksheets to each group and either allot class time to fill out the packet or assign it as a takehome project. The worksheet engages students by asking them to recall definitions learned in class and presenting a few introductory questions about hurricanes, types of failure associated with aboveground storage tanks and how Archimedes' principle and Pascal's law apply to these tanks.
 Then, students are asked to derive equations to determine the weight of the aboveground storage tank, the weight of the liquid inside the tank, and the weight of the water displaced by the tank. They use these equations in a floatation analysis to determine whether their groups' given aboveground storage tank will displace in their given storm conditions.
 Then students answer some questions about their aboveground storage tanks based on their floatation analysis results. Each engineering team is challenged to come up with at least one design idea to prevent displacement and/or buckling of aboveground storage tanks.
 Direct the design teams to follow the instructions in question #8 on the worksheet to create 58 minute presentations. In this presentation, expect students to reiterate their given storm conditions, state whether their aboveground storage tanks displace and explain why or why not, present and explain their graphs, and present their design ideas to the class.
 Have the engineering design teams make their presentations with the rest of the class as the audience. Encourage the student audience to ask questions about the structural integrity, efficiency, cost, etc., of the presented design ideas. Refer to Figures 1 and 2 and Example Student Designs for examples of student teamgenerated design ideas for improved aboveground storage tanks to combat displacement and buckling.
 Present the AboveGround Storage Tank Conclusions Presentation.
Vocabulary/Definitions
aboveground storage tank: A storage tank that is unburied (above ground) and used to contain fluids such as petrochemicals and petroleum. These tanks are more susceptible to damage and failure from flooding, displacement and buckling since they do not have much storm protection, if any.
buoyancy: The ability of an object to float in a liquid.
density: A measurement of the compactness of an object.
mass: A measurement of the amount of matter in an object.
mass density: Mass per unit volume of a substance.
pressure: A measurement of force per unit area.
volume: A measurement of the amount of space an object occupies.
weight: A measurement of force on an object due to gravity.
Assessment
PreActivity Assessment
Definitions and Presentation: Ask questions to review what was learned in the AboveGround Storage Tanks in the Houston Ship Channel associated lesson. Example questions: What are aboveground storage tanks? Where are they used? Why are they used? Why are they a problem? Who is responsible for cleaning up ruptured aboveground storage tanks after a storm? Also ask students to recap terminology learned in the lesson by discussing the definitions to the vocabulary words.
Activity Embedded Assessment
Floatation Analysis: Direct students to work in their engineering design teams to derive the necessary equations to determine whether their aboveground storage tanks will displace under the given storm conditions. Observe and review student work to gauge their level of comprehension. Refer to the AST Design Worksheet Answer Key and AST Design Equation Answer Key.
Midway CheckIn: It is helpful if the instructor holds midweek "checkpoint" meetings with each team to check students' work and catch derivation mistakes and floatation analysis errors early. Also use this as a chance to ensure teams are making progress on their design ideas and models as well as preparation of the final presentations.
PostActivity Assessment
Student Presentations: Direct the teams to prepare and present short class presentations, as described in question #8 on the worksheet. Expect the presentations to reiterate the groups' given storm conditions, state whether their aboveground storage tanks displace and explain why or why not, present and explain their graphs, and present their design ideas to the class. Direct the student audience to ask questions about the structural integrity, efficiency, cost, etc., of the design ideas. Award points for each complete and accurate section of the presentation; deduct points for missing (storm conditions, graph) or incorrect scientific or mathematical information and logic (incorrect derivations or final floatation analysis).
Safety Issues
If providing class time to construct models or prototypes, make sure tools and fabrication equipment are being used in a safe manner.
Troubleshooting Tips
If students are struggling to derive the equations, supply helpful hints such as, "begin with the surface area of a cylinder." Once students have derived that equation, tell them to convert that equation to volume, and then convert that equation to mass, etc. Provide hints following the guided derivations supplied in the AST Design Worksheet Answer Key.
Activity Extensions
To give this activity more of an engineering design project context, have groups divide up responsibilities and assign roles to each group member such as project manager, project engineer, cost engineer, design engineer, etc. Guide them through the engineering design process and have students compose a formal report to turn in for grading.
Activity Scaling
 For lower grades, or for students who struggle with math, provide the equations needed for the floatation analysis so students only need to plug in their unique numbers.
 For upper grades, incorporate a wind and/or wave analysis to see if the aboveground storage tank will buckle. Add in extra storm conditions such as wind speed, duration, etc., and wave height, etc., and supply students with the equations needed to determine whether the aboveground storage tank will buckle, or guide students to derive those equations as well.
Additional Multimedia Support
At some point during the activity, point out to students that in their engineering design teams they are performing many of the steps of the engineering design process, just like engineers do. The basic steps of the engineering design process are: understand the need (including doing research and analysis to define the problem), generate multiple solutions, analyze and select a design solution, make a plan, create a model or prototype, test and improve the design until achieving satisfactory solution to the design challenge. For more information, see https://www.teachengineering.org/engrdesignprocess.php.
References
Material Property Data (searchable database of material properties) MatWeb, LLC. Accessed March 13, 2014. http://www.matweb.com/
Moore, Sarah. Responders Tour Southeast Texas Looking for Oil Spills. Published September 17, 2008. The Beaumont Enterprise. Accessed March 13, 2014. http://www.beaumontenterprise.com/news/article/ResponderstourSoutheastTexaslookingforoil776445.php#photo399495
Padgett, Jamie E. Structural Integrity of Storage Tanks. September 24, 2013. SSPEED Center Conference: Hurricane Ike 5 Years Later, Severe Storm Prediction, Education and Evacuation from Disasters, Civil and Environmental Engineering Department, Rice University, Houston, TX. Accessed March 13, 2014. (Inspiration for design project.) http://sspeed.rice.edu/sspeed/downloads/September_2013/Day1/1_5_PADGETT_SSPEED.pdf
September 17: Assessing the Damage. Published September 17, 2008. The Beaumont Enterprise. Accessed March 13, 2014. (Pictures of aboveground storage tanks after Hurricane Ike) http://www.beaumontenterprise.com/news/article/Sept17Assessingthedamage962922.php#photo525151
Steel Construction Manual. American Institute of Steel Construction. 13th edition. 2005. Fifth printing. 2010. USA.
Welded Tanks for Oil Storage. API Standard 650. American Petroleum Institute. 12th edition, March 2013, 514 pages. Washington DC: API Publishing Services, 2013. Accessed March 13, 2014. https://docs.google.com/file/d/0Bw8MfqmgWLS4cC1DSlByaFlLXzQ/edit
Copyright
© 2014 by Regents of the University of Colorado; original © 2013 University of HoustonContributors
Emily Sappington, Mila TaylorSupporting Program
National Science Foundation GK12 and Research Experience for Teachers (RET) Programs, University of HoustonAcknowledgements
This digital library content was developed by the University of Houston's College of Engineering, based upon work supported by the National Science Foundation under GK12 grant no. DGE 0840889. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Last modified: October 23, 2020
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