Sustainable Drink Bottle Design for Energy: Revisit the carbonated drink bottle
ID: 1841965 • Letter: S
Question
Sustainable Drink Bottle Design for Energy: Revisit the carbonated drink bottle – Bottles for bottled water are used only once and then recycled or combusted. The largest contribution of the lifeenergy and CO2 release is from the material of the bottle itself, thus to have the most impact, the material selection of the bottle to minimize life-energy is considered in this case study. An example bottle in question is shown below. The table below shows the different plastic types that are considered for the bottle design.
The internal pressure p in the bottle creates tensile stresses in its walls. The circumfrenetial stress is c = pr/t and the axial stress is a = pr/2t, where r is the radius of the bottle and t its wall thickness. The wall must be thick enough to support the largest stress without failing thus the wall thickness is t = S*(pr/ y) Where y is the yield strength (use tensile strength in this case) of the wall material and S is a safety factor. The embodied energy of the material of the wall per unit area, HA (which we want to minimize is. HA = tHm = Spr(Hm/ y) Where is the density of the bottle material and Hm is its embodied energy per kg. The best choice of the material is the one with the smallest value of M1. M1 = Hm/ y Cost is also an issue and the cost is determined per unit area similar to energy. The cheapest bottle is that made from the material with the smallest value of the index M2 M2 = Cm/ y .
Task: Determine the metrics M1 and M2 (10 points) for each of the plastic bottles and plot the results (10 points). Analyze the tradeoffs between the cost and embodied energy and determine the best bottle material overall, only for cost, and only for energy (10 points). You will need to find the tensile strengths for PET and PP. Explain why M1 and M2 are viable metrics for this scenario (can show mathematically).
assume the data needed
material density(kg/m^3) tensile strength(Mpa) Emboided energy(MJ/kg) price $/kg high density polythene 960 23 38 4.5 low density polythene 920 20 115 1 ploythene terephthalate 1380 60 1 poly vinyl chloride 1420 52 98 0.1 polypropylene 1040 42 40 2 polystereneExplanation / Answer
material density(kg/m^3) tensile strength(Mpa) Emboided energy(MJ/kg) price $/kg M1 M2 high density polythene 960 23 38 4.5 1586.086957 187.8261 low density polythene 920 20 115 1 5290 46 ploythene terephthalate 1380 65 60 1 1273.846154 21.23077 poly vinyl chloride 1420 52 98 0.1 2676.153846 2.730769 polypropylene 1040 42 40 2 990.4761905 49.52381
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