In an open channel with an economical trapezoidal cross-section, what is the ratio of flow depth to hydraulic radius_____________________?
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Answer: D. 2
Explanation
For an economical trapezoidal open channel the ratio of flow depth to hydraulic radius equals two. Economic channel design minimizes excavation and lining costs by optimizing cross-sectional geometry. Mathematical minimization of wetted perimeter yields this specific depth to hydraulic radius proportion. Hydraulic radius is defined as the flow cross-sectional area divided by the wetted perimeter. Trapezoidal channels feature a bottom base and sloping sides designed for efficient water conveyance. Open channel flow hydraulics govern the design of large artificial water transport networks.
Civil engineers design municipal drainage canals using economical cross-sectional shapes to reduce expenses. Agricultural irrigation networks utilize trapezoidal channels to maximize water flow efficiency. Optimizing channel geometry prevents excessive sediment deposition and minimizes construction costs. A ratio of zero point five fails to satisfy the minimum wetted perimeter economic criteria. A ratio of one represents a different geometric cross-section rather than an economical trapezoid. A ratio of one point five does not match the optimized trapezoidal hydraulic radius formula.
- Subject
- Engineering
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- Chemical Engineering
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- —
- Difficulty
- medium
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