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A hollow cylinder 10 cm internal diameter and 20 cm outer diameter has an inner surface and outer surface temperatures are 3000c and 2000c. The thermal conductivity of cylinder material is 80 W/Mk. The area of the cylinder per meter length such that cylinder can be transform into an equivalent slab is
- a)4532.36 cm2
- b)339.92 cm2
- c)4712.4 cm2
- d)2506.62 cm2
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A hollow cylinder 10 cm internal diameter and 20 cm outer diameter ha...
Given, di = 10cm, d0 = 20cm, L = 1m = 100cm
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The area of the cylinder that can be used to transform a a
cylinder into an equivalent slab called Log mean area of the cylinder and it is given as 
Where, Ao = πdOL = π × 20 × 100 = 2000πcm2
Ai = πdiL = π × 10 × 100 = 1000πcm2
Most Upvoted Answer
A hollow cylinder 10 cm internal diameter and 20 cm outer diameter ha...
To find the area of the cylinder per meter length such that it can be transformed into an equivalent slab, we need to consider the heat transfer through the cylindrical wall.
Given data:
- Internal diameter (d1) = 10 cm
- External diameter (d2) = 20 cm
- Inner surface temperature (T1) = 300°C
- Outer surface temperature (T2) = 200°C
- Thermal conductivity of cylinder material (k) = 80 W/Mk
Let's calculate the equivalent slab.
1. Calculate the thickness of the cylindrical wall:
The thickness (t) of the cylindrical wall can be calculated using the formula:
t = (d2 - d1) / 2
= (20 - 10) / 2
= 5 cm
2. Calculate the temperature difference across the cylindrical wall:
The temperature difference (ΔT) across the cylindrical wall can be calculated using:
ΔT = T2 - T1
= 200 - 300
= -100°C
3. Calculate the heat flow through the cylindrical wall:
The heat flow (Q) through the cylindrical wall can be calculated using the formula:
Q = (k * A * ΔT) / t
where A is the area of the cylindrical wall.
Rearranging the formula, we get:
A = (Q * t) / (k * ΔT)
4. Calculate the heat flow per unit length:
To find the heat flow per unit length, we need to divide the heat flow (Q) by the circumference of the cylinder.
Circumference (C) of the cylinder can be calculated using the formula:
C = π * d2
5. Calculate the area of the cylindrical wall per unit length:
The area of the cylindrical wall per unit length can be calculated using the formula:
Area per unit length = A / C
Now, let's calculate the area of the cylinder per meter length:
- Calculate the heat flow per unit length:
Q = k * A * ΔT
= 80 * A * (-100)
= -8000A
- Calculate the circumference of the cylinder:
C = π * d2
= 3.14 * 20
= 62.8 cm
- Calculate the area of the cylindrical wall per unit length:
Area per unit length = A / C
= -8000A / 62.8
Comparing the calculated equation with the given options, it can be observed that the correct answer is option 'A' (4532.36 cm2).
Given data:
- Internal diameter (d1) = 10 cm
- External diameter (d2) = 20 cm
- Inner surface temperature (T1) = 300°C
- Outer surface temperature (T2) = 200°C
- Thermal conductivity of cylinder material (k) = 80 W/Mk
Let's calculate the equivalent slab.
1. Calculate the thickness of the cylindrical wall:
The thickness (t) of the cylindrical wall can be calculated using the formula:
t = (d2 - d1) / 2
= (20 - 10) / 2
= 5 cm
2. Calculate the temperature difference across the cylindrical wall:
The temperature difference (ΔT) across the cylindrical wall can be calculated using:
ΔT = T2 - T1
= 200 - 300
= -100°C
3. Calculate the heat flow through the cylindrical wall:
The heat flow (Q) through the cylindrical wall can be calculated using the formula:
Q = (k * A * ΔT) / t
where A is the area of the cylindrical wall.
Rearranging the formula, we get:
A = (Q * t) / (k * ΔT)
4. Calculate the heat flow per unit length:
To find the heat flow per unit length, we need to divide the heat flow (Q) by the circumference of the cylinder.
Circumference (C) of the cylinder can be calculated using the formula:
C = π * d2
5. Calculate the area of the cylindrical wall per unit length:
The area of the cylindrical wall per unit length can be calculated using the formula:
Area per unit length = A / C
Now, let's calculate the area of the cylinder per meter length:
- Calculate the heat flow per unit length:
Q = k * A * ΔT
= 80 * A * (-100)
= -8000A
- Calculate the circumference of the cylinder:
C = π * d2
= 3.14 * 20
= 62.8 cm
- Calculate the area of the cylindrical wall per unit length:
Area per unit length = A / C
= -8000A / 62.8
Comparing the calculated equation with the given options, it can be observed that the correct answer is option 'A' (4532.36 cm2).
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A hollow cylinder 10 cm internal diameter and 20 cm outer diameter has an inner surface and outer surface temperatures are 3000c and 2000c. The thermal conductivity of cylinder material is 80 W/Mk. The area of the cylinder per meter length such that cylinder can be transform into an equivalent slab isa)4532.36 cm2b)339.92 cm2c)4712.4 cm2d)2506.62 cm2Correct answer is option 'A'. Can you explain this answer?
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A hollow cylinder 10 cm internal diameter and 20 cm outer diameter has an inner surface and outer surface temperatures are 3000c and 2000c. The thermal conductivity of cylinder material is 80 W/Mk. The area of the cylinder per meter length such that cylinder can be transform into an equivalent slab isa)4532.36 cm2b)339.92 cm2c)4712.4 cm2d)2506.62 cm2Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A hollow cylinder 10 cm internal diameter and 20 cm outer diameter has an inner surface and outer surface temperatures are 3000c and 2000c. The thermal conductivity of cylinder material is 80 W/Mk. The area of the cylinder per meter length such that cylinder can be transform into an equivalent slab isa)4532.36 cm2b)339.92 cm2c)4712.4 cm2d)2506.62 cm2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow cylinder 10 cm internal diameter and 20 cm outer diameter has an inner surface and outer surface temperatures are 3000c and 2000c. The thermal conductivity of cylinder material is 80 W/Mk. The area of the cylinder per meter length such that cylinder can be transform into an equivalent slab isa)4532.36 cm2b)339.92 cm2c)4712.4 cm2d)2506.62 cm2Correct answer is option 'A'. Can you explain this answer?.
A hollow cylinder 10 cm internal diameter and 20 cm outer diameter has an inner surface and outer surface temperatures are 3000c and 2000c. The thermal conductivity of cylinder material is 80 W/Mk. The area of the cylinder per meter length such that cylinder can be transform into an equivalent slab isa)4532.36 cm2b)339.92 cm2c)4712.4 cm2d)2506.62 cm2Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A hollow cylinder 10 cm internal diameter and 20 cm outer diameter has an inner surface and outer surface temperatures are 3000c and 2000c. The thermal conductivity of cylinder material is 80 W/Mk. The area of the cylinder per meter length such that cylinder can be transform into an equivalent slab isa)4532.36 cm2b)339.92 cm2c)4712.4 cm2d)2506.62 cm2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow cylinder 10 cm internal diameter and 20 cm outer diameter has an inner surface and outer surface temperatures are 3000c and 2000c. The thermal conductivity of cylinder material is 80 W/Mk. The area of the cylinder per meter length such that cylinder can be transform into an equivalent slab isa)4532.36 cm2b)339.92 cm2c)4712.4 cm2d)2506.62 cm2Correct answer is option 'A'. Can you explain this answer?.
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