04-BS-7 · May 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
04-BS-7 Mechanics of Fluids — National Examination, 2013-May. Three (3) hours duration, closed book. Section A (Calculative, 9 questions, do 7) and Section B (Analytical, 4 questions, do 3); every question is answered below regardless of the exam's "do N of M" instruction, so the set is a complete study resource.
Reference texts: Crowe, C.T., Elger, D.F. & Roberson, J.A., Engineering Fluid Mechanics (the exam's own Moody chart and drag-coefficient chart are reproduced from this text); Douglas, J.F., Gasiorek, J.M., Swaffield, J.A. & Jack, L.B., Fluid Mechanics; White, F.M., Fluid Mechanics.
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.
The popular belief that quicksand swallows people whole is, physically, backwards: the deciding factor for whether a body floats or sinks in any fluid is buoyancy, governed by Archimedes' principle, and buoyancy depends on the density of the fluid relative to the density of the human body — not on how ominous the fluid looks.
An average human body, with lungs reasonably inflated, has a density close to that of fresh water, roughly 985 kg/m³ (slightly below 1000 kg/m³, which is why most people float, or very nearly float, in a swimming pool). Light oil is markedly less dense than water — typically around 850 kg/m³ for a light mineral or vegetable oil. Quicksand, by contrast, is not simply water: it is a suspension of fine sand grains (solid density around 2650 kg/m³) in water, and once it has liquefied ("gone quick") it typically still carries a large solid fraction, giving the bulk slurry a density well above that of water — often 1.6–2.0 times water's density.
Comparing the ratio of body density to fluid density tells the story directly: in light oil, $\rho_{human}/\rho_{oil}\approx985/850\approx1.16$ — a ratio greater than 1 means the body is denser than the fluid, so it cannot displace enough oil to support its own weight and will sink essentially completely, submerging just below the surface (much like a stone sinks in water, though more slowly because oil is more viscous). In the quicksand slurry, $\rho_{human}/\rho_{quicksand}\approx985/1900\approx0.52$ — a ratio well below 1 means the body is considerably less dense than the surrounding slurry, so it floats readily, submerging only to roughly half its volume before buoyant equilibrium is reached — qualitatively similar to how a person floats unusually high in the very dense water of the Dead Sea.
The real hazard of quicksand is therefore not sinking to the bottom but becoming stuck: quicksand is a thixotropic material whose apparent viscosity rises sharply once disturbed, and pulling a limb out quickly creates a transient low-pressure (near-vacuum) suction beneath it that can require a surprisingly large force to overcome — a kinetic problem, not a buoyancy one. A person who stays still and lets the slurry settle can usually float; a person who thrashes works the sand into a denser, stickier state and can become trapped, though even then, full submersion is unlikely given the density argument above.
Conclusion: a human is far more likely to sink fully in the light oil (denser than the oil) than in the quicksand slurry (much less dense than the slurry, and buoyed accordingly).
