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Differential Calculus2D

Applications of the Derivative - Theory & Concepts - Canal Optimization

Apply differentiation to solve problems in motion, optimization, geometric analysis, and marginal cost.

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Canal Optimization

Adjust the depth yy of the trapezoidal canal. The total area is held constant at 50 m². Notice how the wetted perimeter PP changes, reaching a minimum when the cross-section approaches a half-hexagon.

Cross-Section Properties:
Area A: 50.0 m² (Constant)
Depth y: 5.37 m
Bottom Width b: 6.21 m
Wetted Perimeter P: 18.61 m
Optimal Design (Minimum P)
b = 6.2my = 5.4m
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