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A circular plate 1 m in diameter is submerged vertically in water such its upper edge is 8 m below the free surface of water. The total hydrostatic pressure force on one side of plate is
[1988]
- a)6.7 kN
- b)65.4 kN
- c)45.0 kN
- d)77.0 kN
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A circular plate 1 m in diameter is submerged vertically in water such...
Total hydrostatic pressure force, F = ρghA
F = 1000 × 9.81 × 8.5 × 0.785 = 65458 N
or
F = 65.45 KN
Most Upvoted Answer
A circular plate 1 m in diameter is submerged vertically in water such...
To calculate the total hydrostatic pressure force on one side of the circular plate, we need to consider the pressure exerted by the water column above the plate.
Here's how we can calculate it:
1. Determine the height of the water column:
The upper edge of the plate is 8 m below the free surface of water. Since the plate is submerged vertically, the height of the water column above the plate is 8 m.
2. Calculate the pressure exerted by the water column:
The pressure exerted by a fluid column is given by the formula: pressure = density × gravitational acceleration × height
In this case, the density of water is approximately 1000 kg/m³ and the gravitational acceleration is 9.81 m/s².
Therefore, the pressure exerted by the water column above the plate is: pressure = 1000 kg/m³ × 9.81 m/s² × 8 m = 78,480 N/m² = 78.48 kPa
3. Calculate the area of the plate:
The plate is circular with a diameter of 1 m, so its radius is 0.5 m.
The area of a circle is given by the formula: area = π × radius²
Therefore, the area of the plate is: area = π × (0.5 m)² = 0.7854 m²
4. Calculate the total hydrostatic pressure force:
The total hydrostatic pressure force is given by the formula: force = pressure × area
Therefore, the total hydrostatic pressure force on one side of the plate is: force = 78.48 kPa × 0.7854 m² = 61.4 kN
Hence, the correct answer is option 'B' which is 65.4 kN.
Here's how we can calculate it:
1. Determine the height of the water column:
The upper edge of the plate is 8 m below the free surface of water. Since the plate is submerged vertically, the height of the water column above the plate is 8 m.
2. Calculate the pressure exerted by the water column:
The pressure exerted by a fluid column is given by the formula: pressure = density × gravitational acceleration × height
In this case, the density of water is approximately 1000 kg/m³ and the gravitational acceleration is 9.81 m/s².
Therefore, the pressure exerted by the water column above the plate is: pressure = 1000 kg/m³ × 9.81 m/s² × 8 m = 78,480 N/m² = 78.48 kPa
3. Calculate the area of the plate:
The plate is circular with a diameter of 1 m, so its radius is 0.5 m.
The area of a circle is given by the formula: area = π × radius²
Therefore, the area of the plate is: area = π × (0.5 m)² = 0.7854 m²
4. Calculate the total hydrostatic pressure force:
The total hydrostatic pressure force is given by the formula: force = pressure × area
Therefore, the total hydrostatic pressure force on one side of the plate is: force = 78.48 kPa × 0.7854 m² = 61.4 kN
Hence, the correct answer is option 'B' which is 65.4 kN.
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Community Answer
A circular plate 1 m in diameter is submerged vertically in water such...
Total hydrostatic pressure force, F = ρghA
F = 1000 × 9.81 × 8.5 × 0.785 = 65458 N
or
F = 65.45 KN
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A circular plate 1 m in diameter is submerged vertically in water such its upper edge is 8 m below the free surface of water. The total hydrostatic pressure force on one side of plate is[1988]a)6.7 kNb)65.4 kNc)45.0 kNd)77.0 kNCorrect answer is option 'B'. Can you explain this answer?
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A circular plate 1 m in diameter is submerged vertically in water such its upper edge is 8 m below the free surface of water. The total hydrostatic pressure force on one side of plate is[1988]a)6.7 kNb)65.4 kNc)45.0 kNd)77.0 kNCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A circular plate 1 m in diameter is submerged vertically in water such its upper edge is 8 m below the free surface of water. The total hydrostatic pressure force on one side of plate is[1988]a)6.7 kNb)65.4 kNc)45.0 kNd)77.0 kNCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular plate 1 m in diameter is submerged vertically in water such its upper edge is 8 m below the free surface of water. The total hydrostatic pressure force on one side of plate is[1988]a)6.7 kNb)65.4 kNc)45.0 kNd)77.0 kNCorrect answer is option 'B'. Can you explain this answer?.
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