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A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical riser does not contribute as cooling surface. If the diameter of the riser is equal to its height, then the height of the riser (in mm) is
- a)150
- b)200
- c)100
- d)125
Correct answer is option 'A'. Can you explain this answer?
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To determine the height of the riser using the modulus method of riser design, we need to consider the cooling surfaces involved and the dimensions of the cylindrical job and riser.
Given:
Diameter of the cylindrical job = 200 mm
Height of the cylindrical job = 100 mm
1. Cooling Surfaces:
The bottom surface of the cylindrical riser does not contribute as a cooling surface. Therefore, only the lateral surface of the riser will be considered as a cooling surface.
2. Dimensions of the Riser:
Let's assume the diameter and height of the riser as 'D' and 'H', respectively.
3. Calculation of the Modulus:
The modulus method of riser design states that the modulus of the riser should be equal to the modulus of the job. The modulus of a cylindrical job is given by the formula:
Modulus of job = (π/4) * (D^2 - d^2) * H
Where:
D = Diameter of the job
d = Diameter of the riser
H = Height of the job
Since the diameter of the riser is equal to its height (D = H), we can rewrite the formula as:
Modulus of job = (π/4) * (D^2 - d^2) * D
4. Substituting the Given Values:
Substituting the given values into the equation, we have:
(π/4) * (200^2 - d^2) * 100 = (π/4) * (200^2 - d^2) * d
Cancelling out the common terms, the equation simplifies to:
200^2 - d^2 = d
Simplifying further:
d^2 + d - 200^2 = 0
Using the quadratic formula, we can solve for 'd':
d = (-1 ± √(1^2 - 4*1*(-200^2))) / 2*1
Simplifying further:
d = (-1 ± √(1 + 4*200^2)) / 2
d ≈ 199.5 mm (Taking the positive value)
Therefore, the approximate diameter of the riser is 199.5 mm.
Since the height of the riser is equal to its diameter (H = D), the height of the riser is approximately 199.5 mm.
However, none of the given options match this result. Therefore, it seems there may be an error in the options provided.
Given:
Diameter of the cylindrical job = 200 mm
Height of the cylindrical job = 100 mm
1. Cooling Surfaces:
The bottom surface of the cylindrical riser does not contribute as a cooling surface. Therefore, only the lateral surface of the riser will be considered as a cooling surface.
2. Dimensions of the Riser:
Let's assume the diameter and height of the riser as 'D' and 'H', respectively.
3. Calculation of the Modulus:
The modulus method of riser design states that the modulus of the riser should be equal to the modulus of the job. The modulus of a cylindrical job is given by the formula:
Modulus of job = (π/4) * (D^2 - d^2) * H
Where:
D = Diameter of the job
d = Diameter of the riser
H = Height of the job
Since the diameter of the riser is equal to its height (D = H), we can rewrite the formula as:
Modulus of job = (π/4) * (D^2 - d^2) * D
4. Substituting the Given Values:
Substituting the given values into the equation, we have:
(π/4) * (200^2 - d^2) * 100 = (π/4) * (200^2 - d^2) * d
Cancelling out the common terms, the equation simplifies to:
200^2 - d^2 = d
Simplifying further:
d^2 + d - 200^2 = 0
Using the quadratic formula, we can solve for 'd':
d = (-1 ± √(1^2 - 4*1*(-200^2))) / 2*1
Simplifying further:
d = (-1 ± √(1 + 4*200^2)) / 2
d ≈ 199.5 mm (Taking the positive value)
Therefore, the approximate diameter of the riser is 199.5 mm.
Since the height of the riser is equal to its diameter (H = D), the height of the riser is approximately 199.5 mm.
However, none of the given options match this result. Therefore, it seems there may be an error in the options provided.
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A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct answer is option 'A'. Can you explain this answer?
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A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct 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 cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct 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 cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct answer is option 'A'. Can you explain this answer?.
A cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct 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 cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct 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 cylindrical job with diameter of 200 mm and height of 100 mm is to be cast using modulusmethod of riser design. Assume that the bottom surface of cylindrical riser does not contribute ascooling surface. If the diameter of the riser is equal to its height, then the height of the riser (inmm) isa)150b)200c)100d)125Correct answer is option 'A'. Can you explain this answer?.
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