04-BS-7 · December 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
04-BS-7 Mechanics of Fluids — December 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. Constants used throughout (from the paper's own Constants page): g = 9.81 m/s², ρwater = 1000 kg/m³, ρair = 1.19 kg/m³ (20°C) / 1.21 kg/m³ (15°C), μair = 1.8×10⁻⁵ N·s/m², Rair = 287 J/kg·K, Rhelium = 2077 J/kg·K, patm = 100 kPa.
Reference texts: F. M. White, Fluid Mechanics, 8th ed. (McGraw-Hill) — fluid statics and manometry (Ch. 2), control-volume momentum/energy and propulsion (Ch. 3), potential/inviscid flow around cylinders (Ch. 8), viscosity and Newtonian shear (Ch. 1), 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.
Dam B will be the more likely of the two to slide. Both dams have the same vertical wall retaining the same head of water and (by the sketch) similar concrete cross-sectional areas, so the destabilizing horizontal hydrostatic thrust pushing each wall downstream is essentially the same for both. The difference lies entirely in where each dam's horizontal footing (heel) sits relative to the water.
Dam A's heel projects UPSTREAM, underneath the retained water. That means the full weight of the water column standing directly on top of the heel presses down on the foundation as an additional vertical load, over and above the concrete's own weight. Since sliding resistance along a "no seepage, but sliding possible" interface is governed by Coulomb friction, Fresist = μN, this extra water weight increases the normal force N transmitted to the foundation, and therefore increases the maximum available frictional resistance to sliding — without adding anything to the destabilizing horizontal thrust, since that thrust depends only on the water depth against the vertical face, not on the footing's shape.
Dam B's heel projects DOWNSTREAM instead, on the dry side of the wall. There is no water sitting on top of that footing, so the normal force at the base comes only from the concrete's own weight — a smaller N than Dam A enjoys for the same wall geometry and water depth. With less normal force, Dam B has less frictional resistance available to resist the same horizontal thrust, so it is more likely to slide.
In short: for two structurally similar L-shaped gravity walls retaining the same water level, orienting the heel to extend UNDER the reservoir (as in Dam A) uses the weight of the retained water itself as a stabilizing force, which is precisely why real gravity dam and retaining-wall heels are commonly designed to extend into the retained fluid/soil side wherever practical.
| Quantity | Result |
|---|---|
| More likely to slide | Dam B (heel on the dry/downstream side — less normal force, less friction resistance) |
| Less likely to slide | Dam A (heel under the water — extra water weight increases normal force and friction resistance) |
