04-BS-7 · December 2019
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
04-BS-7 Mechanics of Fluids — December 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.” Every question is answered below (13 of 13), so students can use the full paper as a study resource. Constants used throughout (from the paper's own Constants page): g = 9.81 m/s², patm = 100 kPa, ρwater = 1000 kg/m³, SGglycerine = 1.26, SGmercury = 13.56, ρconcrete = 2400 kg/m³, ρair = 1.19 kg/m³ (20°C) / 1.21 kg/m³ (15°C), μwater = 1.0×10⁻³ N·s/m², μair = 1.8×10⁻⁵ N·s/m², Rair = 287 J/kg·K.
Reference texts: F. M. White, Fluid Mechanics, 8th ed. (McGraw-Hill) — fluid statics and manometry (Ch. 2), hydrostatic forces and the middle-third rule (Ch. 2), buoyancy and equilibrium (Ch. 2), dimensional analysis and drag (Ch. 5, 7), pipe friction and the Moody/Colebrook relation (Ch. 6), control-volume momentum and propeller/actuator-disk theory (Ch. 3, 11); J. D. Anderson, Fundamentals of Aerodynamics — wave/compressibility drag divergence (Ch. 5) for the Boeing 747 wind-tunnel chart used in Question 9.
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.
Given. Identical hose/nozzle geometry and identical volumetric flow rate in both the suction (Configuration A) and blowing (Configuration B) modes.
Find. Why the effective range differs so much between the two modes for the same flow rate and geometry.
In Configuration A (suction), air is drawn INTO the nozzle from every direction — effectively from an entire hemisphere of surrounding space. Because the same total flow rate must pass through progressively LARGER imaginary hemispherical surfaces as one moves away from the nozzle (surface area growing with the square of the distance), the local air velocity falls off very rapidly with distance from the inlet — roughly as $1/r^2$ near the opening. Sawdust sitting even a short distance away experiences only a weak, rapidly-decaying induced velocity and a correspondingly weak drag force, so the nozzle must be held very close to the floor for the induced velocity (and hence the aerodynamic drag on the sawdust) to be strong enough to lift and entrain it.
In Configuration B (blowing), the SAME flow rate leaves the nozzle as a coherent, directed JET rather than being drawn in from all directions. A free jet does not spread out nearly as fast as suction converges — it entrains some surrounding air and gradually widens, but its centreline velocity decays much more slowly with distance (the jet stays coherent over many nozzle diameters) because momentum is being carried forward in one dominant direction rather than converging from a whole hemisphere. The streamlines in the diagram above show this directly: the suction streamlines fan out over a wide angle very close to the inlet (rapid velocity decay), while the blowing streamlines remain tightly bundled along the jet axis over a much longer distance (slow velocity decay) — so the same volumetric flow rate remains effective at dislodging sawdust much farther from the nozzle when blowing than when vacuuming.
