A scale model of a reservoir empties in 4 minutes upon opening its sluice gate. Given a model scale of 1:225, how long should the full-scale prototype take to drain?
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Answer: E. 4 x V225 minutes
Explanation
Drainage time scales with the square root of the length scale under Froude similitude. Multiplying the model drainage time by the square root of 225 yields the prototype time. Froude number scaling laws preserve gravitational and inertial force ratios between model and prototype. Hydraulic scale models allow engineers to study complex reservoir drainage before building full systems. Froude similitude governs open channel flows where gravity forces dominate fluid motion. Length scale ratios dictate how time, velocity, and discharge parameters translate to prototypes.
Civil engineers test spillway designs using scaled laboratory models to predict flood discharge behavior. Accurate time scaling ensures that simulated reservoir emptying matches real-world operational timelines. Physical modeling prevents costly design errors in large-scale dam and sluice gate construction. Unscaled multiplication ignores dimensional analysis laws required for physical hydraulic modeling. Cubic root scaling applies to volumetric parameters rather than time intervals in Froude models. Leaving drainage time unchanged defies basic fluid mechanics scaling and gravitational physics.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
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