Question 13 of 13: Relative Sinking Depth in Light Oil vs Quicksand

Question 13: Relative Sinking Depth in Light Oil vs Quicksand (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Approach/answer. Both fluids exert a buoyant force on a submerged person equal to the weight of fluid displaced (Archimedes' principle); the equilibrium submerged depth is set by how that buoyant force compares with body weight, which in turn depends almost entirely on the fluid's density relative to the human body (specific gravity ≈ 0.98–1.0).

1. Light oil. Typical light oils have specific gravity of roughly 0.85–0.9, i.e. LESS dense than a human body. The buoyant force an oil pond can offer, even at full immersion, is therefore less than the person's own weight — equilibrium can only be reached by sinking until the body is almost, or fully, submerged, so a person floats very low (or not at all) in oil.
2. Quicksand (sand-water slurry). As stated in Question 9's slurry example, agitated sand-water slurries commonly reach bulk specific gravities of 1.3–2.0 — substantially DENSER than the human body. A denser suspending fluid provides MORE buoyant force per unit submerged volume, so equilibrium is reached with a much smaller fraction of the body submerged; in the well-known popular-physics result, a person cannot fully submerge in true fluid quicksand at all, though the slurry's high viscosity can make withdrawing a submerged limb slow.
3. Conclusion. Since the oil pond's density is below body density while the quicksand pond's is above it, a human will sink deeper in the light oil than in the quicksand, even though quicksand has the more intimidating reputation.