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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 0.75m respectively. What is the total pressure (approximately) onone face of the plate?
- a)12kN
- b)16kN
- c)24kN
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
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A circular plate 1.5 m diameter is submerged in water with its greates...
Ans. (c)
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A circular plate 1.5 m diameter is submerged in water with its greates...
Given data:
Diameter of circular plate = 1.5 m
Greatest depth of plate below the surface = 2 m
Least depth of plate below the surface = 0.75 m
Concept:
The total pressure on one face of the plate can be calculated using the formula:
Total pressure = Pressure at the greatest depth - Pressure at the least depth
Calculating pressure at the greatest depth:
The pressure at a depth in a fluid can be calculated using the formula:
Pressure = Density × g × Depth
Calculating pressure at the least depth:
Using the same formula as above, we can calculate the pressure at the least depth.
Calculating total pressure:
Total pressure = Pressure at the greatest depth - Pressure at the least depth
Calculation:
Given that the diameter of the circular plate is 1.5 m, we can calculate the radius:
Radius = Diameter / 2 = 1.5 / 2 = 0.75 m
Calculating pressure at the greatest depth:
Density of water = 1000 kg/m³ (approximate value)
Acceleration due to gravity, g = 9.8 m/s² (approximate value)
Pressure at the greatest depth = Density × g × Depth
= 1000 × 9.8 × 2
= 19600 Pa
Calculating pressure at the least depth:
Pressure at the least depth = Density × g × Depth
= 1000 × 9.8 × 0.75
= 7350 Pa
Calculating total pressure:
Total pressure = Pressure at the greatest depth - Pressure at the least depth
= 19600 - 7350
= 12250 Pa
Converting the pressure from Pascal to kiloNewton:
1 kN = 1000 N
1 Pa = 1 N/m²
Total pressure = 12250 Pa
= 12250 / 1000 kN
= 12.25 kN
Therefore, the total pressure on one face of the plate is approximately 12.25 kN.
Diameter of circular plate = 1.5 m
Greatest depth of plate below the surface = 2 m
Least depth of plate below the surface = 0.75 m
Concept:
The total pressure on one face of the plate can be calculated using the formula:
Total pressure = Pressure at the greatest depth - Pressure at the least depth
Calculating pressure at the greatest depth:
The pressure at a depth in a fluid can be calculated using the formula:
Pressure = Density × g × Depth
Calculating pressure at the least depth:
Using the same formula as above, we can calculate the pressure at the least depth.
Calculating total pressure:
Total pressure = Pressure at the greatest depth - Pressure at the least depth
Calculation:
Given that the diameter of the circular plate is 1.5 m, we can calculate the radius:
Radius = Diameter / 2 = 1.5 / 2 = 0.75 m
Calculating pressure at the greatest depth:
Density of water = 1000 kg/m³ (approximate value)
Acceleration due to gravity, g = 9.8 m/s² (approximate value)
Pressure at the greatest depth = Density × g × Depth
= 1000 × 9.8 × 2
= 19600 Pa
Calculating pressure at the least depth:
Pressure at the least depth = Density × g × Depth
= 1000 × 9.8 × 0.75
= 7350 Pa
Calculating total pressure:
Total pressure = Pressure at the greatest depth - Pressure at the least depth
= 19600 - 7350
= 12250 Pa
Converting the pressure from Pascal to kiloNewton:
1 kN = 1000 N
1 Pa = 1 N/m²
Total pressure = 12250 Pa
= 12250 / 1000 kN
= 12.25 kN
Therefore, the total pressure on one face of the plate is approximately 12.25 kN.
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