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18 February, 01:11

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 cm2 and that approximately 7.6 kg had corroded away during the submersion. Assuming a corrosion penetration rate of 4 mm/yr for this alloy in seawater, estimate the time of submersion in years. The density of the alloy is 4.5 g/cm3.

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  1. 18 February, 01:23
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    t = 5.27 years

    Explanation:

    First of all, the formula for corrosion penetration rate is given as;

    CPR = (KW) / (ρAt)

    Where;

    K = Constant dependent on exposed area A.

    W - weight lost after time

    t - time

    ρ - density

    A - exposed area

    From the question;

    W = 7.6kg or 7.6 x 10^ (6) mg

    CPR = 4 mm/yr

    ρ = 4.5 g/cm³

    Area = 800 cm²

    K is a constant of 87.6cm

    Making t the subject of the formula from the CPR equation, we obtain;

    t = KW / (ρA (CPR))

    t = (87.6 x 7.6 x 10^ (6)) / (4.5 x 800 x 4) = 46233.3 hours

    The question wants the time in years.

    So let's convert;

    There are 8760 hours in a year.

    Thus;

    t = 46233.3/8760 = 5.27 years.
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