Question

A drum 60 cm in diameter and 1 metre long has mass 30 kg when empty. If this drum is filled with oil of relative density 0.8, and is floating in fresh water, find the percentage reserve buoyancy.

Answer 1

For this question we have to assume the density of fresh water to be 1g/cc (1g/mL) which is 1kg/L or 1000kg/m³.

Volume V of the cylindrical drum of radius r=30cm=0.3m is given by V=πr²h where h=1m, making V=0.09π m³, and the mass of oil of density 0.8(0.09π)(1000)kg=72πkg. Total mass of drum=72π+30 kg. This is equal to the mass of fresh water displaced, which can be converted to a volume, knowing the density of fresh water: mass/volume=1000, so volume v of water=mass/1000=(72π+30)/1000=0.072π+0.03 m³. Compare this with the volume of the drum: (0.072π+0.03)/0.09π=0.9061 or 90.61%. The reserve buoyancy is therefore about 9.39%.