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Chapter 17: Problem 11

A piece of corroded metal alloy plate was found in a submerged ocean vessel. It was estimated that the original area of the plate was \(800 \mathrm{cm}^{2}\) and that approximately \(7.6 \mathrm{kg}\) had corroded away during the submersion. Assuming a corrosion penetration rate of \(4 \mathrm{mm} / \mathrm{yr}\) for this alloy in seawater, estimate the time of submersion in years. The density of the alloy is \(4.5 \mathrm{g} / \mathrm{cm}^{3}\)

Short Answer

Expert verified
Question: Estimate the time of submersion for a corroded metal plate with an original area of 800 cm², a weight of 7.6 kg, a density of 4.5 g/cm³, and a corrosion penetration rate of 4 mm/year. Answer: The estimated time of submersion is approximately 5.28 years.

Step by step solution

01

Calculate the volume of the corroded part

Given the weight (\(7.6\,\mathrm{kg}\)) and density (\(4.5\, \mathrm{g/cm}^{3}\)) of the corroded part, we can calculate its volume using the formula: Volume = Weight / Density First, convert the weight to grams: \(7.6\, \mathrm{kg} = 7600\, \mathrm{g}\) Now, compute the volume: Volume = \(\frac{7600\, \mathrm{g}}{4.5\, \mathrm{g/cm}^{3}} \approx 1688.89\, \mathrm{cm}^{3}\)
02

Calculate the average thickness of the corroded layer

Next, we will determine the average thickness of the corroded metal by dividing the volume of the corroded part by its original area: Average Thickness = \(\frac{\text{Volume of Corroded Part}}{\text{Original Area}}\) Average Thickness = \( \frac{1688.89\,\mathrm{cm}^{3}}{800\,\mathrm{cm}^{2}} \approx 2.11\,\mathrm{cm}\)
03

Convert the thickness to millimeters

Since the corrosion penetration rate is given in millimeters per year, we need to convert the average thickness from centimeters to millimeters: Average Thickness = \(2.11 \, \mathrm{cm} \times 10\, \mathrm{mm/cm} = 21.1\, \mathrm{mm}\)
04

Calculate the time of submersion

Finally, we can estimate the time of submersion by dividing the average thickness of the corroded layer by the corrosion penetration rate: Submersion Time = \(\frac{\text{Average Thickness}}{\text{Corrosion Penetration Rate}}\) Submersion Time = \(\frac{21.1\,\mathrm{mm}}{4\,\mathrm{mm/yr}} \approx 5.28\,\mathrm{yr}\) Hence, the estimated time of submersion is approximately 5.28 years.

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