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A cast steel slab of dimension 30 x 20 x 5 cm3 is poured horizontally using a side riser. The riser is cylindrical in shape with diameter and height both equal to 12 cm. The freezing ratio of mould for Caine’s empirical equation is:
- a)0.567
- b)1.764
- c)1.133
- d)2.396
Correct answer is option 'C'. Can you explain this answer?
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A cast steel slab of dimension 30 x 20 x 5 cm3 is poured horizontally...
= 0.567
= 1.134
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A cast steel slab of dimension 30 x 20 x 5 cm3 is poured horizontally...
To solve this problem, we need to understand Caine’s empirical equation and how it relates to the freezing ratio of the mold.
Caine’s empirical equation is used to determine the freezing ratio in solidification processes. It is given by the formula:
Freezing ratio = (Volume of casting / Volume of casting + Volume of riser)
In this case, we have a cast steel slab with dimensions 30 x 20 x 5 cm³ and a cylindrical riser with a diameter and height both equal to 12 cm. Let's calculate the volumes of the casting and the riser and then substitute them into the formula to find the freezing ratio.
- Volume of casting:
The volume of the casting is given by the formula:
Volume of casting = Length x Width x Height
Plugging in the given dimensions, we get:
Volume of casting = 30 cm x 20 cm x 5 cm
= 3000 cm³
- Volume of riser:
The volume of a cylindrical object is given by the formula:
Volume of riser = π x (Radius of riser)² x Height of riser
Since the diameter of the riser is given as 12 cm, the radius is half of that, which is 6 cm. Plugging in this value and the height of the riser, we get:
Volume of riser = π x (6 cm)² x 12 cm
= 432π cm³
- Freezing ratio:
Now, we can substitute the values of the volume of the casting and the volume of the riser into Caine’s empirical equation:
Freezing ratio = (Volume of casting / Volume of casting + Volume of riser)
= (3000 cm³ / 3000 cm³ + 432π cm³)
= (3000 cm³ / 3000 cm³ + 432 x 3.14 cm³)
= (3000 cm³ / 3000 cm³ + 1359.36 cm³)
= (3000 cm³ / 4359.36 cm³)
≈ 0.688
Therefore, the freezing ratio of the mold, according to Caine’s empirical equation, is approximately 0.688.
However, none of the given options match this value. Therefore, the correct answer cannot be determined based on the information provided.
Caine’s empirical equation is used to determine the freezing ratio in solidification processes. It is given by the formula:
Freezing ratio = (Volume of casting / Volume of casting + Volume of riser)
In this case, we have a cast steel slab with dimensions 30 x 20 x 5 cm³ and a cylindrical riser with a diameter and height both equal to 12 cm. Let's calculate the volumes of the casting and the riser and then substitute them into the formula to find the freezing ratio.
- Volume of casting:
The volume of the casting is given by the formula:
Volume of casting = Length x Width x Height
Plugging in the given dimensions, we get:
Volume of casting = 30 cm x 20 cm x 5 cm
= 3000 cm³
- Volume of riser:
The volume of a cylindrical object is given by the formula:
Volume of riser = π x (Radius of riser)² x Height of riser
Since the diameter of the riser is given as 12 cm, the radius is half of that, which is 6 cm. Plugging in this value and the height of the riser, we get:
Volume of riser = π x (6 cm)² x 12 cm
= 432π cm³
- Freezing ratio:
Now, we can substitute the values of the volume of the casting and the volume of the riser into Caine’s empirical equation:
Freezing ratio = (Volume of casting / Volume of casting + Volume of riser)
= (3000 cm³ / 3000 cm³ + 432π cm³)
= (3000 cm³ / 3000 cm³ + 432 x 3.14 cm³)
= (3000 cm³ / 3000 cm³ + 1359.36 cm³)
= (3000 cm³ / 4359.36 cm³)
≈ 0.688
Therefore, the freezing ratio of the mold, according to Caine’s empirical equation, is approximately 0.688.
However, none of the given options match this value. Therefore, the correct answer cannot be determined based on the information provided.
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A cast steel slab of dimension 30 x 20 x 5 cm3 is poured horizontally using a side riser. The riser is cylindrical in shape with diameter and height both equal to 12 cm. The freezing ratio of mould for Caine’s empirical equation is:a) 0.567b) 1.764c) 1.133d) 2.396Correct answer is option 'C'. Can you explain this answer?
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A cast steel slab of dimension 30 x 20 x 5 cm3 is poured horizontally using a side riser. The riser is cylindrical in shape with diameter and height both equal to 12 cm. The freezing ratio of mould for Caine’s empirical equation is:a) 0.567b) 1.764c) 1.133d) 2.396Correct answer is option 'C'. 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 A cast steel slab of dimension 30 x 20 x 5 cm3 is poured horizontally using a side riser. The riser is cylindrical in shape with diameter and height both equal to 12 cm. The freezing ratio of mould for Caine’s empirical equation is:a) 0.567b) 1.764c) 1.133d) 2.396Correct answer is option 'C'. 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 A cast steel slab of dimension 30 x 20 x 5 cm3 is poured horizontally using a side riser. The riser is cylindrical in shape with diameter and height both equal to 12 cm. The freezing ratio of mould for Caine’s empirical equation is:a) 0.567b) 1.764c) 1.133d) 2.396Correct answer is option 'C'. Can you explain this answer?.
A cast steel slab of dimension 30 x 20 x 5 cm3 is poured horizontally using a side riser. The riser is cylindrical in shape with diameter and height both equal to 12 cm. The freezing ratio of mould for Caine’s empirical equation is:a) 0.567b) 1.764c) 1.133d) 2.396Correct answer is option 'C'. 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 A cast steel slab of dimension 30 x 20 x 5 cm3 is poured horizontally using a side riser. The riser is cylindrical in shape with diameter and height both equal to 12 cm. The freezing ratio of mould for Caine’s empirical equation is:a) 0.567b) 1.764c) 1.133d) 2.396Correct answer is option 'C'. 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 A cast steel slab of dimension 30 x 20 x 5 cm3 is poured horizontally using a side riser. The riser is cylindrical in shape with diameter and height both equal to 12 cm. The freezing ratio of mould for Caine’s empirical equation is:a) 0.567b) 1.764c) 1.133d) 2.396Correct answer is option 'C'. Can you explain this answer?.
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