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To calculate the maximum allowable stresses in pressure vessels, compute the minimum allowable thickness of pressure vessels to meet certain constraints, and observe and compare properties of different pressure vessel shapes. Engineers are considering two possible vessel shapes for storing fuel. One shape is cylindrical and the other is spherical. Each vessel would be constructed out of the same material such that its hoop stresses and longitudinal stresses would be no greater than 15.0 ksi. The cylindrical pressure vessel has an inside diameter of de = 30.0 in and a thickness of te = 1.00 in . The spherical pressure vessel has an inside diameter of d, = 30.0 in and a thickness of t, = 0.750 in .

To calculate the maximum allowable stresses in pressure vessels, compute the minimum allowable thickness of pressure vessels to meet certain constraints, and observe and compare properties of different pressure vessel shapes. Engineers are considering two possible vessel shapes for storing fuel. One shape is cylindrical and the other is spherical. Each vessel would be constructed out of the same material such that its hoop stresses and longitudinal stresses would be no greater than 15.0 ksi. The cylindrical pressure vessel has an inside diameter of de = 30.0 in and a thickness of te = 1.00 in . The spherical pressure vessel has an inside diameter of d, = 30.0 in and a thickness of t, = 0.750 in .

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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### Learning Goal: To calculate the maximum allowable stresses in pressure vessels, compute the minimum allowable thickness of pressure vessels to meet certain constraints, and observe and compare properties of different pressure vessel shapes. Engineers are considering two possible vessel shapes for storing fuel. One shape is cylindrical and the other is spherical. Each vessel would be constructed out of the same material such that its hoop stresses and longitudinal stresses would be no greater than 15.0 ksi. The cylindrical pressure vessel has an inside diameter of \( d_c = 30.0 \, \text{in} \) and a thickness of \( t_c = 1.00 \, \text{in} \). The spherical pressure vessel has an inside diameter of \( d_s = 30.0 \, \text{in} \) and a thickness of \( t_s = 0.750 \, \text{in} \). ### Part A - Maximum allowable pressure in the cylindrical pressure vessel Determine the maximum allowable pressure, \( p_{c,\text{max}} \), in the cylindrical pressure vessel. Express your answer in psi to three significant figures. <div style="background-color: #f9f9f9; padding: 10px; border-radius: 5px;"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mrow> <msub> <mi>p</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> </mrow> </mstyle> </math> <span> psi</span> <button type="button">Submit</button> </div> ### Part B - Maximum allowable pressure in the spherical pressure vessel Determine the maximum allowable pressure, \( p_{s,\text{max}} \), in the spherical pressure vessel. Express your answer in psi to three significant figures. <div style="background-color: #f9f9f9; padding: 10px; border-radius: 5px;"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mrow> <
Transcribed Image Text:### Learning Goal: To calculate the maximum allowable stresses in pressure vessels, compute the minimum allowable thickness of pressure vessels to meet certain constraints, and observe and compare properties of different pressure vessel shapes. Engineers are considering two possible vessel shapes for storing fuel. One shape is cylindrical and the other is spherical. Each vessel would be constructed out of the same material such that its hoop stresses and longitudinal stresses would be no greater than 15.0 ksi. The cylindrical pressure vessel has an inside diameter of \( d_c = 30.0 \, \text{in} \) and a thickness of \( t_c = 1.00 \, \text{in} \). The spherical pressure vessel has an inside diameter of \( d_s = 30.0 \, \text{in} \) and a thickness of \( t_s = 0.750 \, \text{in} \). ### Part A - Maximum allowable pressure in the cylindrical pressure vessel Determine the maximum allowable pressure, \( p_{c,\text{max}} \), in the cylindrical pressure vessel. Express your answer in psi to three significant figures. <div style="background-color: #f9f9f9; padding: 10px; border-radius: 5px;"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mrow> <msub> <mi>p</mi> <mrow> <mi>c</mi> <mo>,</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> </mrow> </mstyle> </math> <span> psi</span> <button type="button">Submit</button> </div> ### Part B - Maximum allowable pressure in the spherical pressure vessel Determine the maximum allowable pressure, \( p_{s,\text{max}} \), in the spherical pressure vessel. Express your answer in psi to three significant figures. <div style="background-color: #f9f9f9; padding: 10px; border-radius: 5px;"> <math xmlns="http://www.w3.org/1998/Math/MathML"> <mstyle displaystyle="true"> <mrow> <
### Part C - Required thickness of the cylindrical pressure vessel for maximum pressure equivalency Determine the required thickness of the cylindrical pressure vessel, \( t_r \), if it is subjected to the maximum allowable pressure of the spherical pressure vessel that was calculated in Part B. Express your answer to three significant figures and include appropriate units. #### Interface Instructions: 1. **Available Hint(s):** - Click the "View Available Hint(s)" link if you need assistance in solving the problem. 2. **Input Section:** - An input box is provided where you will enter your answer. - Next to the input box, there are dropdown options for selecting the units. 3. **Submission:** - Once your answer is input correctly, click the "Submit" button. #### Diagram Explanation: There is an equation box present with the placeholder for thickness \( t_r \) and units to be entered after calculation. The detailed graphical icons show standard editing and help options which include: - Save - Undo - Redo - Clear - Hints Clicking these icons will help you manipulate the input effectively.
Transcribed Image Text:### Part C - Required thickness of the cylindrical pressure vessel for maximum pressure equivalency Determine the required thickness of the cylindrical pressure vessel, \( t_r \), if it is subjected to the maximum allowable pressure of the spherical pressure vessel that was calculated in Part B. Express your answer to three significant figures and include appropriate units. #### Interface Instructions: 1. **Available Hint(s):** - Click the "View Available Hint(s)" link if you need assistance in solving the problem. 2. **Input Section:** - An input box is provided where you will enter your answer. - Next to the input box, there are dropdown options for selecting the units. 3. **Submission:** - Once your answer is input correctly, click the "Submit" button. #### Diagram Explanation: There is an equation box present with the placeholder for thickness \( t_r \) and units to be entered after calculation. The detailed graphical icons show standard editing and help options which include: - Save - Undo - Redo - Clear - Hints Clicking these icons will help you manipulate the input effectively.
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