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Cylindrical tank of 1.0 m diameter and 5 m total length has hemispherical ends. It contains liquid oxygen which has boiling point and heat of vapourisation -1800C and 210 kJ/kg respectively. It is required to insulate the tank so as to reduce the boit off rate of oxygen is steady state to 14 kg/h. Assume room temperature outside the insulation as 250C. If the maximum thickness of the insulating material is limited to 70 mm, the thermal conductivity(W/m0C) is
- a)0.0272
- b)0.053
- c)0.0164
- d)0.042
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Cylindrical tank of 1.0 m diameter and 5 m total length has hemispheri...
r1 = 0.5 m
r2 = 0.57 m
ti = - 180°C, t0 = 25°C
Boil off rate = 14 kg/hr
r2 = 0.57 m
ti = - 180°C, t0 = 25°C
Boil off rate = 14 kg/hr
hfg = 210 kJ/kg
= 14 × 210 = 2940
Also L + 2r1 = 5
L = 4 m
Qcyl = 644.69 watt
So, K = 0.0164 W /m0C
Also L + 2r1 = 5
L = 4 m
Qcyl = 644.69 watt
So, K = 0.0164 W /m0C
Most Upvoted Answer
Cylindrical tank of 1.0 m diameter and 5 m total length has hemispheri...
To reduce the boil-off rate of liquid oxygen in a cylindrical tank with hemispherical ends, insulation needs to be added to the tank. The maximum thickness of the insulation material is limited to 70 mm. We need to determine the thermal conductivity of the insulation material.
Given data:
- Diameter of the tank (D) = 1.0 m
- Total length of the tank (L) = 5 m
- Boiling point of liquid oxygen (T_boil) = -180°C
- Heat of vaporization of liquid oxygen (H_vap) = 210 kJ/kg
- Boil-off rate of oxygen in steady state (m_dot) = 14 kg/h
- Room temperature outside the insulation (T_room) = 25°C
To determine the thermal conductivity of the insulation material, we can use the concept of heat transfer through a cylindrical wall.
Heat Transfer Equation:
The heat transfer rate (Q) through a cylindrical wall is given by the equation:
Q = (2πkL(T_inside - T_outside)) / ln(r2/r1)
where:
- Q is the heat transfer rate (W)
- k is the thermal conductivity of the insulation material (W/m°C)
- L is the length of the cylindrical wall (m)
- T_inside is the temperature inside the tank (°C)
- T_outside is the temperature outside the insulation (°C)
- r1 and r2 are the inner and outer radii of the cylindrical wall (m)
Calculating the Inner and Outer Radii:
The inner radius of the cylindrical wall (r1) is half of the diameter (D/2), and the outer radius (r2) is the sum of r1 and the insulation thickness (70 mm converted to meters):
r1 = D/2 = 1.0/2 = 0.5 m
r2 = r1 + insulation thickness = 0.5 + 0.07 = 0.57 m
Calculating the Temperature Inside the Tank:
The temperature inside the tank (T_inside) can be calculated using the boiling point and the heat of vaporization:
T_inside = T_boil + (Q/m_dot * H_vap)
Q is the heat transfer rate, which can be calculated using the boil-off rate:
Q = m_dot * H_vap
Q = 14 * 210 = 2940 kJ/h
Converting Q to W:
Q = 2940 * 1000 / 3600 = 816.6667 W
T_inside = -180 + (816.6667 / 14 * 210) = -180 + 1080 = 900 °C
Calculating the Thermal Conductivity:
Using the heat transfer equation, we can rearrange it to solve for the thermal conductivity (k):
k = (Q * ln(r2/r1)) / (2πL(T_inside - T_outside))
k = (816.6667 * ln(0.57/0.5)) / (2π * 5 * (900 - 25))
k ≈ 0.053 W/m°C
Therefore, the thermal conductivity of the insulation material is approximately 0.053 W/m°C, which corresponds to option B.
Given data:
- Diameter of the tank (D) = 1.0 m
- Total length of the tank (L) = 5 m
- Boiling point of liquid oxygen (T_boil) = -180°C
- Heat of vaporization of liquid oxygen (H_vap) = 210 kJ/kg
- Boil-off rate of oxygen in steady state (m_dot) = 14 kg/h
- Room temperature outside the insulation (T_room) = 25°C
To determine the thermal conductivity of the insulation material, we can use the concept of heat transfer through a cylindrical wall.
Heat Transfer Equation:
The heat transfer rate (Q) through a cylindrical wall is given by the equation:
Q = (2πkL(T_inside - T_outside)) / ln(r2/r1)
where:
- Q is the heat transfer rate (W)
- k is the thermal conductivity of the insulation material (W/m°C)
- L is the length of the cylindrical wall (m)
- T_inside is the temperature inside the tank (°C)
- T_outside is the temperature outside the insulation (°C)
- r1 and r2 are the inner and outer radii of the cylindrical wall (m)
Calculating the Inner and Outer Radii:
The inner radius of the cylindrical wall (r1) is half of the diameter (D/2), and the outer radius (r2) is the sum of r1 and the insulation thickness (70 mm converted to meters):
r1 = D/2 = 1.0/2 = 0.5 m
r2 = r1 + insulation thickness = 0.5 + 0.07 = 0.57 m
Calculating the Temperature Inside the Tank:
The temperature inside the tank (T_inside) can be calculated using the boiling point and the heat of vaporization:
T_inside = T_boil + (Q/m_dot * H_vap)
Q is the heat transfer rate, which can be calculated using the boil-off rate:
Q = m_dot * H_vap
Q = 14 * 210 = 2940 kJ/h
Converting Q to W:
Q = 2940 * 1000 / 3600 = 816.6667 W
T_inside = -180 + (816.6667 / 14 * 210) = -180 + 1080 = 900 °C
Calculating the Thermal Conductivity:
Using the heat transfer equation, we can rearrange it to solve for the thermal conductivity (k):
k = (Q * ln(r2/r1)) / (2πL(T_inside - T_outside))
k = (816.6667 * ln(0.57/0.5)) / (2π * 5 * (900 - 25))
k ≈ 0.053 W/m°C
Therefore, the thermal conductivity of the insulation material is approximately 0.053 W/m°C, which corresponds to option B.
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Cylindrical tank of 1.0 m diameter and 5 m total length has hemispherical ends. It contains liquid oxygen which has boiling point and heat of vapourisation -1800C and 210 kJ/kg respectively. It is required to insulate the tank so as to reduce the boit off rate of oxygen is steady state to 14 kg/h. Assume room temperature outside the insulation as 250C. If the maximum thickness of the insulating material is limited to 70 mm, the thermal conductivity(W/m0C) isa)0.0272b)0.053c)0.0164d)0.042Correct answer is option 'B'. Can you explain this answer?
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Cylindrical tank of 1.0 m diameter and 5 m total length has hemispherical ends. It contains liquid oxygen which has boiling point and heat of vapourisation -1800C and 210 kJ/kg respectively. It is required to insulate the tank so as to reduce the boit off rate of oxygen is steady state to 14 kg/h. Assume room temperature outside the insulation as 250C. If the maximum thickness of the insulating material is limited to 70 mm, the thermal conductivity(W/m0C) isa)0.0272b)0.053c)0.0164d)0.042Correct 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 Cylindrical tank of 1.0 m diameter and 5 m total length has hemispherical ends. It contains liquid oxygen which has boiling point and heat of vapourisation -1800C and 210 kJ/kg respectively. It is required to insulate the tank so as to reduce the boit off rate of oxygen is steady state to 14 kg/h. Assume room temperature outside the insulation as 250C. If the maximum thickness of the insulating material is limited to 70 mm, the thermal conductivity(W/m0C) isa)0.0272b)0.053c)0.0164d)0.042Correct 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 Cylindrical tank of 1.0 m diameter and 5 m total length has hemispherical ends. It contains liquid oxygen which has boiling point and heat of vapourisation -1800C and 210 kJ/kg respectively. It is required to insulate the tank so as to reduce the boit off rate of oxygen is steady state to 14 kg/h. Assume room temperature outside the insulation as 250C. If the maximum thickness of the insulating material is limited to 70 mm, the thermal conductivity(W/m0C) isa)0.0272b)0.053c)0.0164d)0.042Correct answer is option 'B'. Can you explain this answer?.
Cylindrical tank of 1.0 m diameter and 5 m total length has hemispherical ends. It contains liquid oxygen which has boiling point and heat of vapourisation -1800C and 210 kJ/kg respectively. It is required to insulate the tank so as to reduce the boit off rate of oxygen is steady state to 14 kg/h. Assume room temperature outside the insulation as 250C. If the maximum thickness of the insulating material is limited to 70 mm, the thermal conductivity(W/m0C) isa)0.0272b)0.053c)0.0164d)0.042Correct 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 Cylindrical tank of 1.0 m diameter and 5 m total length has hemispherical ends. It contains liquid oxygen which has boiling point and heat of vapourisation -1800C and 210 kJ/kg respectively. It is required to insulate the tank so as to reduce the boit off rate of oxygen is steady state to 14 kg/h. Assume room temperature outside the insulation as 250C. If the maximum thickness of the insulating material is limited to 70 mm, the thermal conductivity(W/m0C) isa)0.0272b)0.053c)0.0164d)0.042Correct 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 Cylindrical tank of 1.0 m diameter and 5 m total length has hemispherical ends. It contains liquid oxygen which has boiling point and heat of vapourisation -1800C and 210 kJ/kg respectively. It is required to insulate the tank so as to reduce the boit off rate of oxygen is steady state to 14 kg/h. Assume room temperature outside the insulation as 250C. If the maximum thickness of the insulating material is limited to 70 mm, the thermal conductivity(W/m0C) isa)0.0272b)0.053c)0.0164d)0.042Correct answer is option 'B'. Can you explain this answer?.
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