Let's break down the task and provide step-by-step guidance to answer Question 2. --- ### **Step 1: Extract Given Data** - **Material 1:** 6061-T6 Aluminium - Yield Stress (\(\sigma_{y}\)): 280 MPa - **Material 2:** Filament-wound E-glass/epoxy - **Safety Factor (SF):** 3 - **Dimensions (from Figure 2):** - **Length (\(L\)):** 120 cm = 1.2 m - **Outer Diameter (\(D_{o}\)):** 15.6 cm = 0.156 m - **Assume wall thickness (\(t\)), if not given, estimate or use thin-wall assumption for calculation.** --- ### **Step 2: Thin-Walled Pressure Vessel Formula** For a thin-walled cylindrical vessel: \[ \sigma_{hoop} = \frac{P \cdot r}{t} \] Where: - \(\sigma_{hoop}\) = Hoop stress (circumferential stress) - \(P\) = Internal pressure - \(r\) = Inner radius - \(t\) = Wall thickness Rearrange to solve for \(P\): \[ P = \frac{\sigma_{allowable} \cdot t}{r} \] Where, \[ \sigma_{allowable} = \frac{\sigma_{y}}{SF} \] --- ### **Step 3: Calculating Allowable Pressure (for Aluminium Vessel)** #### 1. **Calculate Allowable Stress:** \[ \sigma_{allowable\_Al} = \frac{280\, \text{MPa}}{3} \approx 93.33\, \text{MPa} \] #### 2. **If wall thickness (\(t\)) is not given, state it as \(t\):** - Inner radius, \(r = \frac{D_{o}}{2} - t\) For thin-walled assumption, \(r \approx \frac{D_{o}}{2}\). \[ r \approx \frac{0.156\, \text{m}}{2} = 0.078\, \text{m} \] \[ P_{Al} = \frac{93.33 \times 10^6 \cdot t}{0.078} \] --- ### **Step 4: For E-glass/Epoxy Vessel** - You need the yield strength or allowable stress for E-glass/epoxy. **Typical values:** - Tensile strength (fiber dominated): **~1200 MPa** (can vary, check your reference/textbook) - With SF = 3: \(\sigma_{allowable\_composite} = 1200 / 3 = 400\, \text{MPa}\) \[ P_{Composite} = \frac{400 \times 10^6 \cdot t}{0.078} \] --- ### **Step 5: Compare the Two Vessels** - **Aluminium vessel can withstand:** \(93.33 \times t / 0.078\) - **E-glass/epoxy vessel can withstand:** \(400 \times t / 0.078\) **Conclusion:** The E-glass/epoxy vessel can withstand a much higher allowable internal pressure than the aluminium vessel **(by a factor of ~4.3×, assuming the same wall thickness)**. --- ### **Step 6: Example with Assumed Wall Thickness** Assume \(t = 0.005\, \text{m} = 5\, \text{mm}\): - **Aluminium:** \[ P_{Al} = \frac{93.33 \times 10^6 \cdot 0.005}{0.078} \approx 5.98 \times 10^6\, \text{Pa} = 5.98\, \text{MPa} \] - **Composite:** \[ P_{Composite} = \frac{400 \times 10^6 \cdot 0.005}{0.078} \approx 25.64 \times 10^6\, \text{Pa} = 25.64\, \text{MPa} \] --- ## **Summary Table** | Material | Allowable Stress (MPa) | Allowable Pressure (MPa, \(t=5\,mm\)) | |--------------------|-----------------------|----------------------------------------| | 6061-T6 Aluminium | 93.33 | 5.98 | | E-glass/Epoxy | 400 | 25.64 | --- ## **Analysis & Comparison** - The composite vessel can withstand a much higher pressure for the same dimensions and wall thickness, making it more suitable for hydrogen storage (higher pressure = more gas stored). - **Weight savings:** Composites are lighter than aluminium, so the vessel will also be lighter for the same strength. --- ### **Note** - If you have a specific wall thickness for the composite or aluminium vessel, substitute that value for more precise results. - If you have a different allowable strength for E-glass/epoxy, use that value. --- **Let me know if you need calculations for a different wall thickness or more details!**