Some unknown volume of oil (SG = 0.918) has been dumped into a vat of sea water (SG= 1.028) forming a stratified (layered) fluid column. The vat is known to have a diameter of 3 m. We know a 20 cm diameter, 15 cm tall piece of wood floats with 3.75 cm above the surface in pure water.
Find:
a) Develop an equation for the volume of the oil as a function of the height from the surface of the oil to the top of the wooden cylinder when it is placed in this stratified fluid column and
b) the volume of the oil when the height above the oil surface is 3.5 cm.