For an open channel of substantial width with a flow depth 'x', the hydraulic radius is equal to________________?
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Answer: A. x
Explanation
Hydraulic radius equals cross sectional flow area divided by the wetted perimeter. For a very wide open channel, wetted perimeter approximates the channel width closely. Width terms cancel out in the division, leaving hydraulic radius equal to flow depth x. Open channel flow occurs when a liquid flows with a free surface exposed to atmosphere. Hydraulic radius is a characteristic length scale used in non-circular conduit calculations. Manning equation relies heavily on hydraulic radius to predict open channel flow velocities.
Civil engineers apply this geometric simplification when designing large irrigation drainage canals. River flow models use hydraulic radius approximations to estimate flood discharge capacities. Stormwater management systems rely on open channel formulas to prevent urban flooding. Option B represents circular conduits running half full rather than wide open channels. Option C introduces an arbitrary fraction not derived from wide channel geometry. Option D incorrectly scales flow depth by a two-thirds factor found in Manning resistance formulas.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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