Mechanical Engineering Exam > Mechanical Engineering Questions > T he rat io of the solidification time of two...
Start Learning for Free
T he rat io of the solidification time of two cylindrical risers of sizes 30 cm in diameter × 60 cm in height and
60 cm in diameter × 30 cm in height subjected to identical conditions of cooling
60 cm in diameter × 30 cm in height subjected to identical conditions of cooling
Correct answer is between '0.60,0.70'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
T he rat io of the solidification time of two cylindrical risers of si...
Most Upvoted Answer
T he rat io of the solidification time of two cylindrical risers of si...
And 20 cm in diameter can be calculated using the Chvorinov's rule. This rule states that the solidification time is proportional to the square of the volume-to-surface area ratio of the casting. The formula for the solidification time is given as:
t = K(V/A)^n
where t is the solidification time, V is the volume of the casting, A is the surface area of the casting, K is a constant, and n is a constant exponent.
Assuming that the risers have the same height, we can calculate their volumes and surface areas using the formulas:
Volume = πr^2h
Surface area = 2πrh + 2πr^2
where r is the radius of the riser and h is the height of the riser.
For the 30 cm diameter riser, the volume and surface area are:
Volume = π(15)^2h = 225πh
Surface area = 2π(15)h + 2π(15)^2 = 30πh + 450π
For the 20 cm diameter riser, the volume and surface area are:
Volume = π(10)^2h = 100πh
Surface area = 2π(10)h + 2π(10)^2 = 20πh + 200π
The volume-to-surface area ratio for the 30 cm diameter riser is:
V/A = (225πh)/(30πh + 450π) = 225/480 ≈ 0.469
The volume-to-surface area ratio for the 20 cm diameter riser is:
V/A = (100πh)/(20πh + 200π) = 100/220 ≈ 0.455
Using Chvorinov's rule, we can calculate the ratio of the solidification times as:
(t1/t2) = [(V1/A1)^n]/[(V2/A2)^n]
where t1 and t2 are the solidification times for the 30 cm and 20 cm diameter risers, respectively.
Substituting the values, we get:
(t1/t2) = [(0.469)^n]/[(0.455)^n]
Since we do not know the value of n, we cannot calculate the exact ratio of the solidification times. However, we can say that the solidification time for the larger riser (30 cm diameter) will be longer than the solidification time for the smaller riser (20 cm diameter) due to its lower volume-to-surface area ratio.
t = K(V/A)^n
where t is the solidification time, V is the volume of the casting, A is the surface area of the casting, K is a constant, and n is a constant exponent.
Assuming that the risers have the same height, we can calculate their volumes and surface areas using the formulas:
Volume = πr^2h
Surface area = 2πrh + 2πr^2
where r is the radius of the riser and h is the height of the riser.
For the 30 cm diameter riser, the volume and surface area are:
Volume = π(15)^2h = 225πh
Surface area = 2π(15)h + 2π(15)^2 = 30πh + 450π
For the 20 cm diameter riser, the volume and surface area are:
Volume = π(10)^2h = 100πh
Surface area = 2π(10)h + 2π(10)^2 = 20πh + 200π
The volume-to-surface area ratio for the 30 cm diameter riser is:
V/A = (225πh)/(30πh + 450π) = 225/480 ≈ 0.469
The volume-to-surface area ratio for the 20 cm diameter riser is:
V/A = (100πh)/(20πh + 200π) = 100/220 ≈ 0.455
Using Chvorinov's rule, we can calculate the ratio of the solidification times as:
(t1/t2) = [(V1/A1)^n]/[(V2/A2)^n]
where t1 and t2 are the solidification times for the 30 cm and 20 cm diameter risers, respectively.
Substituting the values, we get:
(t1/t2) = [(0.469)^n]/[(0.455)^n]
Since we do not know the value of n, we cannot calculate the exact ratio of the solidification times. However, we can say that the solidification time for the larger riser (30 cm diameter) will be longer than the solidification time for the smaller riser (20 cm diameter) due to its lower volume-to-surface area ratio.
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
T he rat io of the solidification time of two cylindrical risers of sizes 30 cm in diameter × 60 cm in height and60 cm in diameter × 30 cm in height subjected to identical conditions of coolingCorrect answer is between '0.60,0.70'. Can you explain this answer?
Question Description
T he rat io of the solidification time of two cylindrical risers of sizes 30 cm in diameter × 60 cm in height and60 cm in diameter × 30 cm in height subjected to identical conditions of coolingCorrect answer is between '0.60,0.70'. 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 T he rat io of the solidification time of two cylindrical risers of sizes 30 cm in diameter × 60 cm in height and60 cm in diameter × 30 cm in height subjected to identical conditions of coolingCorrect answer is between '0.60,0.70'. 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 T he rat io of the solidification time of two cylindrical risers of sizes 30 cm in diameter × 60 cm in height and60 cm in diameter × 30 cm in height subjected to identical conditions of coolingCorrect answer is between '0.60,0.70'. Can you explain this answer?.
T he rat io of the solidification time of two cylindrical risers of sizes 30 cm in diameter × 60 cm in height and60 cm in diameter × 30 cm in height subjected to identical conditions of coolingCorrect answer is between '0.60,0.70'. 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 T he rat io of the solidification time of two cylindrical risers of sizes 30 cm in diameter × 60 cm in height and60 cm in diameter × 30 cm in height subjected to identical conditions of coolingCorrect answer is between '0.60,0.70'. 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 T he rat io of the solidification time of two cylindrical risers of sizes 30 cm in diameter × 60 cm in height and60 cm in diameter × 30 cm in height subjected to identical conditions of coolingCorrect answer is between '0.60,0.70'. Can you explain this answer?.
Solutions for T he rat io of the solidification time of two cylindrical risers of sizes 30 cm in diameter × 60 cm in height and60 cm in diameter × 30 cm in height subjected to identical conditions of coolingCorrect answer is between '0.60,0.70'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of T he rat io of the solidification time of two cylindrical risers of sizes 30 cm in diameter × 60 cm in height and60 cm in diameter × 30 cm in height subjected to identical conditions of coolingCorrect answer is between '0.60,0.70'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
T he rat io of the solidification time of two cylindrical risers of sizes 30 cm in diameter × 60 cm in height and60 cm in diameter × 30 cm in height subjected to identical conditions of coolingCorrect answer is between '0.60,0.70'. Can you explain this answer?, a detailed solution for T he rat io of the solidification time of two cylindrical risers of sizes 30 cm in diameter × 60 cm in height and60 cm in diameter × 30 cm in height subjected to identical conditions of coolingCorrect answer is between '0.60,0.70'. Can you explain this answer? has been provided alongside types of T he rat io of the solidification time of two cylindrical risers of sizes 30 cm in diameter × 60 cm in height and60 cm in diameter × 30 cm in height subjected to identical conditions of coolingCorrect answer is between '0.60,0.70'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice T he rat io of the solidification time of two cylindrical risers of sizes 30 cm in diameter × 60 cm in height and60 cm in diameter × 30 cm in height subjected to identical conditions of coolingCorrect answer is between '0.60,0.70'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup