A temporary vertical barrier holds water 1.20 m deep along each 1.0 m width. Use water density 1000 kg/m³ and g = 9.8 N/kg. The pressure rises linearly from zero gauge pressure at the surface to ρgh at the bottom. Design X uses reusable aluminium panels costing $480 per metre; design Y uses single-use filled polymer bags costing $150 per metre. (a) Calculate bottom gauge pressure and the resultant horizontal water force on each metre of barrier. [5] (b) Explain why the force acts below mid-depth. [2] (c) Evaluate safety, cost, deployment, access and environmental consequences. [7] (d) Give a conditional recommendation. [2]

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Bottom gauge pressure is 11,760 Pa. The triangular pressure distribution gives force 7056 N per metre. Procurement should depend on anchoring, failure tests, deployment time, reuse and the community's flood frequency—not purchase price alone. (a) Bottom gauge pressure is p = ρgh = 1000 × 9.8 × 1.20 = 11,760 Pa. (a) Average gauge pressure over a vertical wall is half the bottom value because the distribution is triangular: 5880 Pa. Area per metre width is 1.20 m². (a) Resultant horizontal force is 5880 × 1.20 = 7056 N per metre of barrier, before adding waves, seepage, impacts or a safety factor. (b) Pressure is larger at greater depth, so the lower part contributes more force. The centre of pressure for an ideal vertical rectangular wall is one-third of the depth above the bottom, not at mid-depth. (c) Aluminium costs more initially but can reduce material use across repeated floods if inspection, storage and transport are feasible. Single-use bags may be faster and cheaper for a rare emergency yet produce waste and need filling material and labour. (c) Residents, emergency teams, taxpayers, waste workers and people with limited mobility have different needs. Failure can endanger lives, so certified anchoring, leakage, overtopping and debris-impact evidence must outweigh a simple cost-per-metre comparison. (d) For a flood-prone community with trained staff and storage, choose a tested reusable system if whole-life cost and safety performance are better. For a rare event, a bag system may be justified only with a credible deployment, collection and disposal plan.

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