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A circular plate 1.5 m diameter is submerged in water with its greatest and least depths below the surface being 2 m and 0.75 m respectively. What is the approximate total pressure on one face of the plate?
- a)24 kN
- b)12 kN
- c)16 kN
- d)32 kN
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A circular plate 1.5 m diameter is submerged in water with its greates...
Here,
Now,
Total pressure force =
Total pressure force =
∴ Total pressure force= 23.84 kN ≈ 24 kN
Most Upvoted Answer
A circular plate 1.5 m diameter is submerged in water with its greates...
Total Pressure on a Submerged Circular Plate
To calculate the total pressure on one face of a submerged circular plate, we need to consider the hydrostatic pressure exerted by the water at varying depths.
1. Understanding Hydrostatic Pressure
- Hydrostatic pressure increases linearly with depth, defined by the formula:
Pressure (P) = ρgh
where ρ is the density of water (approximately 1000 kg/m³), g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the depth below the water surface.
2. Given Parameters
- Diameter of the plate = 1.5 m
- Radius (r) = 0.75 m (since radius = diameter/2)
- Greatest depth (h1) = 2 m
- Least depth (h2) = 0.75 m
3. Average Depth Calculation
- Average depth (h_avg) can be calculated as:
h_avg = (h1 + h2) / 2
h_avg = (2 m + 0.75 m) / 2 = 1.375 m
4. Total Pressure Calculation
- Using the average depth to calculate the pressure:
P_avg = ρgh_avg
P_avg = 1000 kg/m³ * 9.81 m/s² * 1.375 m
P_avg ≈ 13.5 kN/m²
- Total force on the circular plate:
Area (A) = πr² = π(0.75 m)² ≈ 1.767 m²
Total Pressure (F) = P_avg * A
F ≈ 13.5 kN/m² * 1.767 m² ≈ 23.84 kN
5. Conclusion
- The total pressure on one face of the plate is approximately 24 kN, confirming the correct answer is option 'A'. This illustrates the importance of considering depth variations when calculating pressure on submerged surfaces.
To calculate the total pressure on one face of a submerged circular plate, we need to consider the hydrostatic pressure exerted by the water at varying depths.
1. Understanding Hydrostatic Pressure
- Hydrostatic pressure increases linearly with depth, defined by the formula:
Pressure (P) = ρgh
where ρ is the density of water (approximately 1000 kg/m³), g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the depth below the water surface.
2. Given Parameters
- Diameter of the plate = 1.5 m
- Radius (r) = 0.75 m (since radius = diameter/2)
- Greatest depth (h1) = 2 m
- Least depth (h2) = 0.75 m
3. Average Depth Calculation
- Average depth (h_avg) can be calculated as:
h_avg = (h1 + h2) / 2
h_avg = (2 m + 0.75 m) / 2 = 1.375 m
4. Total Pressure Calculation
- Using the average depth to calculate the pressure:
P_avg = ρgh_avg
P_avg = 1000 kg/m³ * 9.81 m/s² * 1.375 m
P_avg ≈ 13.5 kN/m²
- Total force on the circular plate:
Area (A) = πr² = π(0.75 m)² ≈ 1.767 m²
Total Pressure (F) = P_avg * A
F ≈ 13.5 kN/m² * 1.767 m² ≈ 23.84 kN
5. Conclusion
- The total pressure on one face of the plate is approximately 24 kN, confirming the correct answer is option 'A'. This illustrates the importance of considering depth variations when calculating pressure on submerged surfaces.
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A circular plate 1.5 m diameter is submerged in water with its greatest and least depths below the surface being 2 m and 0.75 m respectively. What is the approximate total pressure on one face of the plate?a)24 kNb)12 kNc)16 kNd)32 kNCorrect answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A circular plate 1.5 m diameter is submerged in water with its greatest and least depths below the surface being 2 m and 0.75 m respectively. What is the approximate total pressure on one face of the plate?a)24 kNb)12 kNc)16 kNd)32 kNCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular plate 1.5 m diameter is submerged in water with its greatest and least depths below the surface being 2 m and 0.75 m respectively. What is the approximate total pressure on one face of the plate?a)24 kNb)12 kNc)16 kNd)32 kNCorrect answer is option 'A'. Can you explain this answer?.
A circular plate 1.5 m diameter is submerged in water with its greatest and least depths below the surface being 2 m and 0.75 m respectively. What is the approximate total pressure on one face of the plate?a)24 kNb)12 kNc)16 kNd)32 kNCorrect answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A circular plate 1.5 m diameter is submerged in water with its greatest and least depths below the surface being 2 m and 0.75 m respectively. What is the approximate total pressure on one face of the plate?a)24 kNb)12 kNc)16 kNd)32 kNCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular plate 1.5 m diameter is submerged in water with its greatest and least depths below the surface being 2 m and 0.75 m respectively. What is the approximate total pressure on one face of the plate?a)24 kNb)12 kNc)16 kNd)32 kNCorrect answer is option 'A'. Can you explain this answer?.
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