CAEE 203 - System Balances and Design in CAEE Assigned: Week 3 in lab Buoyant forces on underwater structures Buoyancy is defined as the upward force exerted by a fluid

on an immersed object that opposes the downward forces of the object. Examples of buoyant forces are a helium-filled balloon floating in the atmosphere, a boat floating on a lake, or as in the case of this lab, a cylindrical vessel totally submerged in seawater, that is filled to different volumes with freshwater. A structure will tend to float if the upward buoyant force exceeds the sum of the vertical downward forces due to gravity. This lab considers the design needed to ensure the underwater tank in Figure 1 will remain fixed in its desired location. You are tasked to design the size of two concrete blocks and ten steel cables needed to prevent the structure from floating upward, given a certain tank size, filled capacity, and other given. Note that the structural dimensions shown in Figure 1 are for the outer elements of the tank, and it is 1-inch thick steel. Ignore cable weight. T 10 ft. ● Design Lab #1 20 ft. Problem information Considering the weight of the structure, the various filled capacity of the tank, and the probable tensile stress resistance of steel cabling, develop a technical report that conveys the following: • A free-body diagram of all relevant forces on both the tank and the concrete blocks Given information air-water interface • Plot and table of the magnitude of the forces acting on the tank and how those forces change with the fraction (0 to 1) of the tank filled with freshwater (forces: buoyancy, weight of tank, weight of water in tank, total weight = tank + filled water, resultant = buoyancy - total weight) Figure 1. Schematic of underwater storage tank. • At worst case scenario considering a factor of safety (FS = 1.5) for the upward force to resist, size (volume and dimensions) of two concrete prisms to prevent the vessel from floating upwards (con- sider 20 ft long rectangular prisms and square ends for prisms). • At worst case scenario considering a factor of safety (FS = 1.5) for the upward force to resist, size (diameter) of ten tie down cables, considering the size of each cable needed for: • Mean UTS of steel, for the given normal distribution for steel UTS ● UTS of steel at 1% worst case, for the given normal distribution UTS of steel at 0.1% worst case, for the given normal distribution Factor of safety (FS = 2) with mean UTS of steel, for the given normal distribution 64.2 lb/ft³ 150 lb/ft³ Your report should have the different sections outlined on the next page. Your report should be typed, with a maximum of 3 pages, 1" margins, Times New Roman 11pt, single-spaced font. Any figures and tables should be neat and made with software (e.g. Excel). Presentation and style matters in the final grade, as does the quality of the written components. Equations must be made with equation editor. Weight density of freshwater = 62.4 lb/ft³ Weight density of seawater = Weight density of concrete = Weight density of steel = 500 lb/ft³ Ultimate tensile stress (UTS) for steel = X ~ N(mean = 29000 lb/in², std. dev. = 4000 lb/in²) CAEE 203 - System Balances and Design in CAEE Technical Report Design Lab #1 1. Introduction: Describe the problem to be solved, in general terms. (You are free to reproduce Figure 1 from above.) Your report should have the sections herein. You should use Times New Roman, font size 11 pt., single-spaced as the text in each section, while leaving the formatting of the nine section headings alone. The report should be a discussion supplemented by tables and graphs describing the results. It should be 3 pages maximum. Your written technical language should be economical and avoid unnecessary words. Tables and graphs should be generated (and calculations performed) with a program such as MS Excel. 2. Free body diagrams on tank and concrete blocks: Using software drawn figures (e.g. MS PowerPoint), show the FBDs and describe their forces. Using the shapes and features (boxes, circles, lines, text boxes, etc.) in MS PowerPoint, you can easily construct schematics of the FBDs. Once you have these drawn, you can select and copy all the elements and then paste them into this document as a PDF or other figure file format type of your choosing. 3. Method to calculate forces acting on tank: Using a mix of textual discussion supplement by equations made with Equation Editor in MS Word, describe the solution procedure. Here is an example of the equation tool to get you started: The buoyant force due to seawater displacement, FÅ (N), can be described in Equation 1: FB = Psw Vtankg (Eq. 1) where psw (kg/m³) is the density of seawater; Vtank (m³) is the tank volume; and g (m/s²) is the gravitational constant. In technical writing, you should always introduce an equation in the text, as occurred in this example. It works well if you put the equation in a table inserted into the document, so you can list an equation number, e.g. (Eq. 1), next to it. After the equation occurs, you should describe any variables in the equation, e.g. psw (kg/m³) or Vtank (m³), the first time they appear in your technical report. 4. Result (table, plot, and discussion) of forces acting on tank for volume filled: Describe the results of the calculations made with method of the previous section. Include a table and plot similar to in the Lab 1 Introduction presentation. It works well to make the tables and figures, and format them appropriately, in Excel. Then you can paste the table and figure into this file as a PDF. If you want, you can also wrap text around the PDF graphic to save space. Table 1 is an example. When you use a table or graph in technical writing, you should always introduce it in the text before it or next to where it occurs in the document. Tables should have a caption above the table, while figures should have a caption below. Table 1. Magnitude of forces as a function of volume filled. Fraction Forces (lb) filled Buoyancy Wt. struc. Wt. water Tot wt. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 5. Method to size concrete blocks: Using equations made with Equation Editor in MS Word, describe the solution procedure. Buoy-Tot wt. CAEE 203 - System Balances and Design in CAEE Design Lab #1 6. Result (dimensions and discussion) of size of concrete blocks: Describe the results of the calculations made with method of the previous section. You should state with text the dimensions of the concrete blocks (you are not required to, but providing a schematic drawing of them is a good way to convey information; again, PowerPoint works well for this task). 7. Method to determine size of cables for different cases: Using equations made with Equation Editor in MS Word, describe the solution procedure. 8. Result (table, plot, and discussion) of size of cables for different cases: Describe the results of the calculations made with method of the previous section. 9. General conclusions: Summarize and offer general conclusions about this design problem. Describe any apparent relationship between factor of safety design and probability of failure design.