04-BS-7 · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
04-BS-7 Mechanics of Fluids — May 2015 (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.
Reference texts: F. M. White, Fluid Mechanics, 8th ed. (McGraw-Hill) — fluid statics (Ch. 2), the linear-momentum and energy equations (Ch. 3), pipe friction and the Moody chart (Ch. 6), and drag on immersed bodies (Ch. 7).
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 shower spray is a fast-moving jet of hot water droplets falling through the cubicle; by viscous shear and droplet drag it entrains the surrounding air and drags it downward with it, setting up a persistent internal downward air current inside the enclosed cubicle (an effect reinforced by the buoyant rise of the hot, humid air near the ceiling being replaced by cooler makeup air drawn in near the floor gap under the curtain). Along the curtain's inside face this entrained flow behaves like a jet moving parallel to the curtain: by Bernoulli's principle, a region of locally higher velocity has locally lower static pressure than the surrounding still air (here, the still room air on the OUTSIDE of the curtain, which is close to atmospheric). This pressure difference — lower on the inside face where the air is moving, higher (near-atmospheric) on the outside face where the air is essentially still — produces a net inward pressure force on the flexible curtain, bowing it in toward the shower.
The two governing principles are therefore (i) viscous entrainment/momentum transfer from the falling spray to the surrounding air (what sets up the internal flow in the first place) and (ii) the Bernoulli relation between local velocity and local static pressure (what converts that internal flow into a pressure imbalance across the thin curtain). To estimate the equilibrium curtain angle θ, one would need: the entrained internal air velocity profile along the curtain (from the spray's momentum and flow rate, and the cubicle geometry), the resulting internal static pressure distribution pin(y) from Bernoulli relative to the known outside (room) pressure patm, and the curtain's own mechanical properties (mass per unit area and any tension/stiffness) so that a force balance — net pressure force per unit height on one side, weight and tension/stiffness resisting deflection on the other — can be solved for the equilibrium deflected shape and hence the bulge angle θ at any height.
