Question

A piece of corroded steel plate was found in a submerged ocean vessel. It was estimated that the original area of the plate was 11 in.2 and that approximately 2.3 kg had corroded away during the submersion. Assuming a corrosion penetration rate of 200 mpy for this alloy in seawater, estimate the time of submersion in years. The density of steel is 7.9 g/cm3.

Answer 1

Answer:

The time of the submersion is $t_{years} = 9 years$

Explanation:

From the question we are told that

   The area of the plate is  $A = 11 in^2$

    The mass of the corroded plate $m = 2.3 \ kg = 2.3 * 1*10^{6}= 2.3 *10^{6} mg$

    The corrosion penetration rate is $R = 200 mpy$

     The density of steel is  $\rho = 7.9 g/cm^3$

Generally the corrosion penetration rate   can be mathematically represented as

             $R = \frac{K m}{A \rho t}$

Where K is the corrosion imperial unit constant   whose value is  K = 534 mpy

           t is the exposure time of the plate

   Making t the subject of the formula

              $t = \frac{K m}{R \rho A}$      

      Substituting value

             $t = \frac{534 *2.3*10^{6}}{200 * 7.9 * 10 }$

             $t = 77734 hrs$

Converting to years

              $t_{years} = \frac{77734}{365 * 24}$

             $t_{years} = 9 years$