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.

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.