The total pressure on the surface of a vertical sluice gate 2 m x 1 m with its top 2 m surface being 0.5 m below the water level will be ________________?
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Answer: D. 2000 kg
Explanation
Total hydrostatic pressure on a submerged vertical gate is calculated by multiplying water specific weight, gate area, and centroid depth. The vertical sluice gate has dimensions of two meters by one meter, yielding a total surface area of two square meters. With the top edge located zero point five meters below the water level, the centroid depth is one point five meters, giving two thousand kilograms total force. Hydrostatic pressure force equals the product of fluid density, acceleration due to gravity, submerged centroid depth, and surface area. For fresh water, density is one thousand kilograms per cubic meter, making total pressure calculations straightforward in metric units. The center of pressure acts below the centroid because pressure increases linearly with depth along the vertical submerged surface.
Option A of five hundred kilograms underestimates the pressure by failing to account for the correct centroid depth and area. Option B of one thousand kilograms represents an incomplete calculation that misses the full area and depth integration. Option C of fifteen hundred kilograms and Option E of four thousand kilograms result from arithmetic calculation errors.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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