04-BS-7 · May 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
04-BS-7 Mechanics of Fluids — National Examinations, May 2014. Three (3) hours, closed book. Section A: Calculative (9 questions, do 7); Section B: Analytical/Graphical (4 questions, do 3). Ten questions constitute a complete paper (50 marks). Every printed question is solved below, including the two "extra" questions in each Section beyond the minimum required.
Reference texts: White, Fluid Mechanics, 8th ed. (fluid statics & capillarity Ch.2; Bernoulli/energy equation Ch.3; pipe friction & the Moody chart Ch.6; drag on immersed bodies Ch.7; buoyancy Ch.2; momentum & jet propulsion Ch.3).
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 cyclist moving at racing speed is resisted almost entirely by aerodynamic drag: air is a low-density, low-viscosity fluid, but drag rises with velocity squared (FD=CD½ρV²A), and at 30–50 km/h this term dominates rolling resistance by a wide margin. A trailing cyclist rides inside the leading rider's wake, a region of reduced relative air velocity and lower local dynamic pressure; because the trailing rider's frontal area A and drag coefficient CD are essentially unchanged, the entire benefit comes from a reduced effective V in the drag equation, and a trailing rider typically saves roughly 25–40% of the drag they would face riding alone, at close wheel-to-wheel spacing.
For a swimmer the resisting fluid is water, roughly 800 times denser than air. Total resistance is made up of skin friction, form (pressure) drag and, for a swimmer at the free surface, wave-making drag, which rises steeply with speed. Because every term scales with ρ, drag forces are very large even at the swimmer's low speed of about 1.5–2 m/s. The swimmer in front leaves a wake behind it in which the water is already moving forward with the leader: a wake-velocity deficit relative to the still pool. A follower close behind therefore moves at a lower speed relative to the surrounding water. Since drag scales with the square of relative velocity, even a modest wake velocity cuts the follower's form and wave drag noticeably. The follower also swims through the leader's trough rather than building a full bow wave of their own.
The same wake-shielding principle that helps the cyclist therefore applies to the swimmer. Measurements of passive drag on swimmers towed behind a leader show a drag reduction of roughly 10–20% when following within about 0–50 cm of the leader's feet. The benefit falls off quickly as the gap grows beyond about 1 m, because a water wake decays over a shorter distance than a cyclist's air wake. A smaller benefit is also available alongside the leader at hip level, where the follower rides the leader's bow-wave pressure field. The costs are the leader's turbulent kick-wash, which can disturb stroke timing, and the need to stay very close. In a pool race, lane ropes prevent it altogether. Conclusion: yes, drafting is advantageous for a swimmer, as it is for a cyclist. Following closely, directly behind or just off the leader's hip, reduces the follower's drag and therefore their energy cost. This is why drafting is permitted and widely used in open-water swimming and in the swim leg of triathlon. The benefit is somewhat smaller and far more sensitive to spacing than in cycling.
