### Summary

At this point in the unit, students have learned about Pascal's law, Archimedes' principle, Bernoulli's principle, and why above-ground 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 above-ground storage tank scenarios with given tank specifications and liquid contents. With their floatation 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 above-ground storage tanks located along the 50-mile Houston Ship Channel are at high risk for failure during storm events. Because many of these facilities are only protected to 14-15 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.

### Pre-Req 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 above-ground storage tanks and their associated environmental issues. As prerequisites for this activity, conduct The Physics of Fluid Mechanics and Above-Ground Storage Tanks in the Houston Ship Channel lessons.

### Learning Objectives

After this activity, students should be able to:

- Explain what above-ground 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 above-ground 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 to design a solution to an engineering problem.
- Effectively communicate and present unique ideas to an audience.

### More Curriculum Like This

**Above-Ground Storage Tanks in the Houston Ship Channel**

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**The Physics of Fluid Mechanics**

From drinking fountains at playgrounds, water systems in homes, and working bathrooms at schools to hydraulic bridges and levee systems, fluid mechanics are an essential part of daily life. Fluid mechanics, the study of how forces are applied to fluids, is outlined in this unit as a sequence of two ...

**Archimedes' Principle, Pascal's Law and Bernoulli's Principle**

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###
Educational Standards
Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 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 K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 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*.

###### Next Generation Science Standards: Science

- Design a solution to a complex real-world problem by breaking it down into smaller, more manageable problems that can be solved through engineering. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Evaluate a solution to a complex real-world problem based on prioritized criteria and trade-offs 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) Details... View more aligned curriculum... Do you agree with this alignment?
- Analyze complex real-world problems by specifying criteria and constraints for successful solutions. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?

###### Common Core State Standards: Math

- Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?

###### International Technology and Engineering Educators Association: Technology

- Research and development is a specific problem-solving approach that is used intensively in business and industry to prepare devices and systems for the marketplace. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- 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) Details... View more aligned curriculum... Do you agree with this alignment?
- The process of engineering design takes into account a number of factors. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?

###### Texas: Science

- demonstrate safe practices during laboratory and field investigations; and (Grades 9 - 10) Details... View more aligned curriculum... Do you agree with this alignment?
- communicate valid conclusions supported by the data through various methods such as lab reports, labeled drawings, graphic organizers, journals, summaries, oral reports, and technology-based reports; and (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- express and manipulate relationships among physical variables quantitatively, including the use of graphs, charts, and equations. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- research and describe the connections between physics and future careers; and (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- demonstrate basic principles of fluid dynamics, including hydrostatic pressure, density, salinity, and buoyancy; (Grades 10 - 12) Details... View more aligned curriculum... Do you agree with this alignment?

### 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

### Introduction/Motivation

Professional code manuals contain provisions for external pressure and floatation, anchorage due to seismic activity, and anchorage due to internal pressure for above-ground 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 above-ground storage tanks in the Houston Ship Channel contain explosive materials, toxic gases and petrochemicals and are vulnerable to the frequent high-force 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 above-ground storage tank in given storm conditions to see if your tank will displace. In addition, your team challenge is 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.

### Vocabulary/Definitions

above-ground 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.

### Procedure

Time Planning

Schedule this activity to take about five 45-minute 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 ~1-2 class periods.

Background

Archimedes' principle states that the buoyant force is equal to the weight of the water displaced by the above-ground 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 above-ground 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 above-ground storage tanks were assumed to be 20-300 feet and the height range for the tanks were assumed to be 10-30 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 Above-Ground 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 above-ground storage tanks experience as well as the equations that students will be asked to derive.

With the Students

- After having presented to students the
*Above-Ground 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 above-ground 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 real-world problem—the vulnerability of above-ground 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 take-home 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 above-ground 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 above-ground 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 above-ground storage tank will displace in their given storm conditions. - Then students answer some questions about their above-ground 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 above-ground storage tanks.
- Direct the design teams to follow the instructions in question #8 on the worksheet to create 5-8 minute presentations. In this presentation, expect students to reiterate their given storm conditions, state whether their above-ground 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 team-generated design ideas for improved above-ground storage tanks to combat displacement and buckling.
- Present the Above-Ground Storage Tank Conclusions Presentation.

### Attachments

### 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.

### Assessment

Pre-Activity Assessment

*Definitions and Presentation:* Ask questions to review what was learned in the Above-Ground Storage Tanks in the Houston Ship Channel associated lesson. Example questions: What are above-ground storage tanks? Where are they used? Why are they used? Why are they a problem? Who is responsible for cleaning up ruptured above-ground 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 above-ground 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 Check-In: *It is helpful if the instructor holds mid-week "check-point" 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.

Post-Activity 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 above-ground 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).

### 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 above-ground 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 above-ground 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/

*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/Responders-tour-Southeast-Texas-looking-for-oil-776445.php#photo-399495

*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 above-ground storage tanks after Hurricane Ike) http://www.beaumontenterprise.com/news/article/Sept-17-Assessing-the-damage-962922.php#photo-525151

*Steel Construction Manua*l. 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

### Contributors

Emily Sappington, Mila Taylor### Copyright

© 2014 by Regents of the University of Colorado; original © 2013 University of Houston### Supporting Program

National Science Foundation GK-12 and Research Experience for Teachers (RET) Programs, University of Houston### Acknowledgements

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 GK-12 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.

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