04-BS-7 · Undated paper
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
04-BS-7 Mechanics of Fluids — undated sitting, identified as May 2019 (National Examinations, three hours, closed book). Section A (Calculative) offers 9 questions and instructs “do seven”; Section B (Analytical) offers 4 questions and instructs “do three.” A complete paper is any 10 of the 13, each worth 5 marks. Every question is answered below (13 of 13) so the set can be used as a full study resource. Constants used throughout (from the paper's own Constants page, p.12): g = 9.81 m/s², patm = 100 kPa, ρwater = 1000 kg/m³, SGbenzene = 0.90, SGmercury = 13.56, SGcarbon tetrachloride = 1.59, ρair = 1.19 kg/m³ (20°C), μwater = 1.0×10⁻³ N·s/m², μair = 1.8×10⁻⁵ N·s/m².
Reference texts: F. M. White, Fluid Mechanics, 8th ed. (McGraw-Hill) — fluid statics and manometry (Ch. 2), hydrostatic forces on plane surfaces (Ch. 2), the Bernoulli/continuity pair and orifice flow (Ch. 3), the linear-momentum equation for moving vanes (Ch. 3), pipe friction and the Moody/Colebrook relation (Ch. 6), boundary layers and drag (Ch. 7), capillary rise (Ch. 1), high-lift devices and aircraft wing aerodynamics (J. D. Anderson, Fundamentals of Aerodynamics, Ch. 4–5).
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.
A person sinks more deeply in the pond of light oil. Sinking depth (for a floating or partially submerged body) is governed entirely by buoyancy, and buoyancy in turn is governed by the density of the surrounding fluid: Archimedes' principle requires that the submerged volume displace a weight of fluid equal to the person's own weight, so ρfluidgVsubmerged = mg. Light oils have a specific gravity of roughly 0.80–0.90, well below the average density of the human body (roughly 0.98, close to that of fresh water); a body floating in light oil must therefore submerge a much larger fraction of itself — and, at these density ratios, may not float at all, sinking to a much greater depth or all the way to the bottom.
Quicksand, by contrast, is a slurry of sand suspended in water and typically has a bulk density in the range of 1.6–2.0 (roughly 1600–2000 kg/m³), substantially denser than either fresh water or the human body. A denser fluid displaces the required buoyant weight with a much smaller submerged volume, so a person actually floats higher in quicksand than in water, contrary to the popular belief that quicksand "sucks people under." The genuine danger of quicksand is not sinking depth but immobilisation: its high apparent viscosity and the suction created by trying to withdraw a limb quickly (which must draw water back in through the surrounding sand to fill the void, a slow process) make escape difficult, and panic-driven struggling can work a person deeper by temporarily liquefying the sand around them — but at rest, buoyancy alone keeps a person floating relatively high in quicksand and low (or fully submerged) in light oil.
| Fluid | Approx. relative density | Sinking behaviour |
|---|---|---|
| Light oil | ≈ 0.80–0.90 | sinks deeply / may not float |
| Quicksand (sand-water slurry) | ≈ 1.6–2.0 | floats comparatively high |
