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A pressure vessel initially empty has an internal volume of 0.5 m3 . It is desired to test the vessel at 300 bar by pumping water into it. The estimated increase in volume of containers during the test is 6%. How much water (in kg) is required to be pumped? Consider the bulk modulus of elasticity for water to be 2 GPa.
Correct answer is 'Range: 537.5 to 538.5'. Can you explain this answer?
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A pressure vessel initially empty has an internal volume of 0.5 m3 . ...
During the test, initial volume of container (when it is empty) is
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V1 = 0.5 m3
The volume increases by 6%, thus final volume is
V2 = V1 + 6% of V1 = 0.5 × 1.06
= 0.53 m3
Let the water pumped into the container have a volume of V3 when it is outside (i.e. under atmospheric conditions). But when it is pumped into the container it’s final volume will be V2 and pressure equal to 300 bar.
∴ for water
K = dp / (−dV / V)
i. e. −dV / V = dp / K
⇒ −(V2 − V3) / V3 = dp / K
⇒ V3 − V2 / V3 = dp / K
⇒ V3 (1 − dp / K) = V2
⇒ V3 = V2 / 1 −dp / K
V3 = 0.53 / 1 −300×105 / 2×109
⇒ V3 = 0.538
Mass of water = ρ × V3 = 1000 × 0.538 = 538 kg
Most Upvoted Answer
A pressure vessel initially empty has an internal volume of 0.5 m3 . ...
Solution:
Given data:
- Internal volume of the pressure vessel = 0.5 m3
- Pressure to be tested = 300 bar
- Estimated increase in volume during test = 6%
- Bulk modulus of elasticity for water = 2 GPa
Calculation:
The increase in volume of the pressure vessel during the test can be calculated as follows:
Increase in volume = (6/100) × 0.5 m3 = 0.03 m3
The total volume of the vessel after the test will be:
Total volume = 0.5 m3 + 0.03 m3 = 0.53 m3
To calculate the amount of water required to be pumped into the vessel, the change in volume due to pressure needs to be calculated. This can be done using the bulk modulus of elasticity formula:
ΔV = -(V/K) × ΔP
Where:
- ΔV = change in volume due to pressure (m3)
- V = initial volume of the vessel (m3)
- K = bulk modulus of elasticity for water (Pa)
- ΔP = change in pressure (Pa)
Substituting the given values, we get:
ΔV = -(0.5 m3 / 2 GPa) × (300 × 105 Pa) = -0.075 m3
Here, the negative sign indicates that the volume of the water decreases when pressure is applied.
Therefore, the total volume of water required to fill the vessel at 300 bar pressure will be:
Total volume of water = 0.53 m3 - (-0.075 m3) = 0.605 m3
The mass of water required can be calculated using the density of water:
Density of water = 1000 kg/m3
Mass of water = Volume of water × Density of water
= 0.605 m3 × 1000 kg/m3
= 605 kg
Therefore, the amount of water required to be pumped into the vessel is 605 kg.
Answer:
The correct answer is in the range of 537.5 to 538.5.
Given data:
- Internal volume of the pressure vessel = 0.5 m3
- Pressure to be tested = 300 bar
- Estimated increase in volume during test = 6%
- Bulk modulus of elasticity for water = 2 GPa
Calculation:
The increase in volume of the pressure vessel during the test can be calculated as follows:
Increase in volume = (6/100) × 0.5 m3 = 0.03 m3
The total volume of the vessel after the test will be:
Total volume = 0.5 m3 + 0.03 m3 = 0.53 m3
To calculate the amount of water required to be pumped into the vessel, the change in volume due to pressure needs to be calculated. This can be done using the bulk modulus of elasticity formula:
ΔV = -(V/K) × ΔP
Where:
- ΔV = change in volume due to pressure (m3)
- V = initial volume of the vessel (m3)
- K = bulk modulus of elasticity for water (Pa)
- ΔP = change in pressure (Pa)
Substituting the given values, we get:
ΔV = -(0.5 m3 / 2 GPa) × (300 × 105 Pa) = -0.075 m3
Here, the negative sign indicates that the volume of the water decreases when pressure is applied.
Therefore, the total volume of water required to fill the vessel at 300 bar pressure will be:
Total volume of water = 0.53 m3 - (-0.075 m3) = 0.605 m3
The mass of water required can be calculated using the density of water:
Density of water = 1000 kg/m3
Mass of water = Volume of water × Density of water
= 0.605 m3 × 1000 kg/m3
= 605 kg
Therefore, the amount of water required to be pumped into the vessel is 605 kg.
Answer:
The correct answer is in the range of 537.5 to 538.5.
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A pressure vessel initially empty has an internal volume of 0.5 m3 . ...
538
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A pressure vessel initially empty has an internal volume of 0.5 m3 . It is desired to test the vessel at 300 bar by pumping water into it. The estimated increase in volume of containers during the test is 6%. How much water (in kg) is required to be pumped? Consider the bulk modulus of elasticity for water to be 2 GPa.Correct answer is 'Range: 537.5 to 538.5'. Can you explain this answer?
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A pressure vessel initially empty has an internal volume of 0.5 m3 . It is desired to test the vessel at 300 bar by pumping water into it. The estimated increase in volume of containers during the test is 6%. How much water (in kg) is required to be pumped? Consider the bulk modulus of elasticity for water to be 2 GPa.Correct answer is 'Range: 537.5 to 538.5'. Can you explain this answer? for Civil Engineering (CE) 2024 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 pressure vessel initially empty has an internal volume of 0.5 m3 . It is desired to test the vessel at 300 bar by pumping water into it. The estimated increase in volume of containers during the test is 6%. How much water (in kg) is required to be pumped? Consider the bulk modulus of elasticity for water to be 2 GPa.Correct answer is 'Range: 537.5 to 538.5'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pressure vessel initially empty has an internal volume of 0.5 m3 . It is desired to test the vessel at 300 bar by pumping water into it. The estimated increase in volume of containers during the test is 6%. How much water (in kg) is required to be pumped? Consider the bulk modulus of elasticity for water to be 2 GPa.Correct answer is 'Range: 537.5 to 538.5'. Can you explain this answer?.
A pressure vessel initially empty has an internal volume of 0.5 m3 . It is desired to test the vessel at 300 bar by pumping water into it. The estimated increase in volume of containers during the test is 6%. How much water (in kg) is required to be pumped? Consider the bulk modulus of elasticity for water to be 2 GPa.Correct answer is 'Range: 537.5 to 538.5'. Can you explain this answer? for Civil Engineering (CE) 2024 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 pressure vessel initially empty has an internal volume of 0.5 m3 . It is desired to test the vessel at 300 bar by pumping water into it. The estimated increase in volume of containers during the test is 6%. How much water (in kg) is required to be pumped? Consider the bulk modulus of elasticity for water to be 2 GPa.Correct answer is 'Range: 537.5 to 538.5'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pressure vessel initially empty has an internal volume of 0.5 m3 . It is desired to test the vessel at 300 bar by pumping water into it. The estimated increase in volume of containers during the test is 6%. How much water (in kg) is required to be pumped? Consider the bulk modulus of elasticity for water to be 2 GPa.Correct answer is 'Range: 537.5 to 538.5'. Can you explain this answer?.
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