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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...
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Given data:
Diameter of circular plate = 1.5 m
Greatest depth below the surface = 2 m
Least depth below the surface = 0.75 m
To find:
Total pressure on one face of the plate
Solution:
1. Calculate the pressure at the greatest depth:
Pressure = ρgh
Where,
ρ = Density of water = 1000 kg/m³
g = Acceleration due to gravity = 9.81 m/s²
h = Depth below the surface = 2 m
Pressure at the greatest depth = 1000 × 9.81 × 2 = 19620 Pa
2. Calculate the pressure at the least depth:
h = Depth below the surface = 0.75 m
Pressure at the least depth = 1000 × 9.81 × 0.75 = 7357.5 Pa
3. Calculate the average pressure:
Average pressure = (Pressure at greatest depth + Pressure at least depth) / 2
Average pressure = (19620 + 7357.5) / 2 = 13488.75 Pa
4. Calculate the force on the circular plate:
Force = Pressure × Area
Where,
Area = πr²
r = Radius of the circular plate = Diameter/2 = 1.5/2 = 0.75 m
Force = 13488.75 × π × 0.75² = 23961.79 N
5. Convert the force to kilonewtons:
Force in kN = Force / 1000
Force in kN = 23961.79 / 1000 = 23.96179 kN
Therefore, the total pressure on one face of the plate is approximately 24 kN (option C).
Diameter of circular plate = 1.5 m
Greatest depth below the surface = 2 m
Least depth below the surface = 0.75 m
To find:
Total pressure on one face of the plate
Solution:
1. Calculate the pressure at the greatest depth:
Pressure = ρgh
Where,
ρ = Density of water = 1000 kg/m³
g = Acceleration due to gravity = 9.81 m/s²
h = Depth below the surface = 2 m
Pressure at the greatest depth = 1000 × 9.81 × 2 = 19620 Pa
2. Calculate the pressure at the least depth:
h = Depth below the surface = 0.75 m
Pressure at the least depth = 1000 × 9.81 × 0.75 = 7357.5 Pa
3. Calculate the average pressure:
Average pressure = (Pressure at greatest depth + Pressure at least depth) / 2
Average pressure = (19620 + 7357.5) / 2 = 13488.75 Pa
4. Calculate the force on the circular plate:
Force = Pressure × Area
Where,
Area = πr²
r = Radius of the circular plate = Diameter/2 = 1.5/2 = 0.75 m
Force = 13488.75 × π × 0.75² = 23961.79 N
5. Convert the force to kilonewtons:
Force in kN = Force / 1000
Force in kN = 23961.79 / 1000 = 23.96179 kN
Therefore, the total pressure on one face of the plate is approximately 24 kN (option C).
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