The minimum depth of harbor of the oil tank is 2.22 m
The given parameters:
mass of the oil tanker, m = 40,000 tonnes
length of the tanker, l = 500 m
width of the tanker, w = 40 m
To find:
minimum depth of harbor
Note: The specific gravity of oil is approximately 0.9
The density of water ([tex]\rho_w[/tex]) = 1000 kg/m³
Covert the given mass to kilogram
1 tonne = 1000 kg
40,000 tonnes = 40,000,000 kg
The density of the oil tanker is calculated as:
[tex]S.G = \frac{\rho_o}{\rho_w} \\\\\rho_o = S.G \times \rho_w\\\\\rho_o = 0.9 \times 1000\\\\\rho_o = 900 \ kg/m^3[/tex]
The volume of the oil tanker is calculated as:
[tex]Volume = \frac{mass}{density} \\\\Volume = \frac{40,000,000}{900} \\\\Volume = 44,444.44 \ m^3[/tex]
The minimum depth of harbor is calculated as:
[tex]height = \frac{volume}{Length \times width} \\\\height = \frac{44,444.44}{500\times 40} \\\\height = 2.22 \ m[/tex]
The minimum depth of harbor of the oil tank is 2.22 m
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