What is the depth of the center of pressure on a vertical rectangular gate (8 m wide, 6 m high) when the water level aligns with its top edge____________________?
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Answer: B. 3.0 m
Explanation
For a vertical rectangular gate with its top edge at the water surface, the depth of the center of pressure is two-thirds of its height. Multiplying the total gate height of six meters by two-thirds yields a center of pressure depth of four meters. Hydrostatic pressure increases linearly with depth, causing the resultant center of pressure to act below the geometric centroid. Center of pressure is the point where the total equivalent hydrostatic force acts on a submerged surface. The depth of the center of pressure for a submerged vertical rectangle with its top edge exposed is calculated as two-thirds of the height. Hydrostatic force calculations integrate fluid pressure distributions across the entire submerged area of the gate.
A depth of 2.4 meters incorrectly places the center of pressure above the true hydrostatic distribution centroid. A depth of 3.0 meters corresponds to the geometric center of the gate rather than the lower center of pressure. A depth of 5.0 meters overestimates the resultant force location for a six-meter-high rectangular gate under surface water.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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