Mechanical Engineering Exam > Mechanical Engineering Questions > A sprue in a sand mould has a top diameter of...
Start Learning for Free
A sprue in a sand mould has a top diameter of 20mm and height of 200mm. The velocity of the molten metal at the entry of the sprue is 0.5m/s. Assume acceleration due to gravity as 9.8 m/s2 and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is ________ m/s.
Correct answer is between '2.04,2.07'. Can you explain this answer?
Verified Answer
A sprue in a sand mould has a top diameter of 20mm and height of 200mm...
Apply Bernoulli's between (1) and (2)
Most Upvoted Answer
A sprue in a sand mould has a top diameter of 20mm and height of 200mm...
Given data:
- Top diameter of sprue (D1) = 20 mm = 0.02 m
- Height of sprue (H) = 200 mm = 0.2 m
- Velocity at entry of sprue (V1) = 0.5 m/s
- Acceleration due to gravity (g) = 9.8 m/s²
Calculating the cross-sectional area at the top:
The cross-sectional area of the sprue at the top can be calculated using the formula for the area of a circle:
A1 = π * (D1/2)²
A1 = π * (0.02/2)²
A1 ≈ 0.000314 m²
Calculating the cross-sectional area at the bottom:
Since the sprue tapers down towards the bottom, the cross-sectional area at the bottom (A2) can be calculated using the formula for the volume of a frustum:
A2 = A1 * (H1 / H2)²
Since the height at the bottom (H2) is 0 (as it is the bottom), we need to find the height at the top (H1).
H1 = H - H2
H1 = 0.2 - 0
H1 = 0.2 m
Therefore, the cross-sectional area at the bottom can be calculated as:
A2 = A1 * (H1 / H2)²
A2 = 0.000314 * (0.2 / 0)²
As the denominator is zero, the cross-sectional area at the bottom is considered to be zero as well.
Calculating the velocity at the bottom:
Using the principle of conservation of energy, we can equate the potential energy at the top to the sum of the potential and kinetic energy at the bottom:
m * g * H = m * g * H2 + (1/2) * m * V2²
Since the mass (m) cancels out, we can simplify the equation to:
g * H = g * H2 + (1/2) * V2²
Substituting the given values:
9.8 * 0.2 = 9.8 * 0 + (1/2) * V2²
1.96 = 0 + (1/2) * V2²
1.96 = (1/2) * V2²
V2² = 1.96 * 2
V2² = 3.92
V2 = √3.92
V2 ≈ 1.98 m/s (rounded to 3 decimal places)
Hence, the velocity of the molten metal at the bottom of the sprue is approximately 1.98 m/s.
- Top diameter of sprue (D1) = 20 mm = 0.02 m
- Height of sprue (H) = 200 mm = 0.2 m
- Velocity at entry of sprue (V1) = 0.5 m/s
- Acceleration due to gravity (g) = 9.8 m/s²
Calculating the cross-sectional area at the top:
The cross-sectional area of the sprue at the top can be calculated using the formula for the area of a circle:
A1 = π * (D1/2)²
A1 = π * (0.02/2)²
A1 ≈ 0.000314 m²
Calculating the cross-sectional area at the bottom:
Since the sprue tapers down towards the bottom, the cross-sectional area at the bottom (A2) can be calculated using the formula for the volume of a frustum:
A2 = A1 * (H1 / H2)²
Since the height at the bottom (H2) is 0 (as it is the bottom), we need to find the height at the top (H1).
H1 = H - H2
H1 = 0.2 - 0
H1 = 0.2 m
Therefore, the cross-sectional area at the bottom can be calculated as:
A2 = A1 * (H1 / H2)²
A2 = 0.000314 * (0.2 / 0)²
As the denominator is zero, the cross-sectional area at the bottom is considered to be zero as well.
Calculating the velocity at the bottom:
Using the principle of conservation of energy, we can equate the potential energy at the top to the sum of the potential and kinetic energy at the bottom:
m * g * H = m * g * H2 + (1/2) * m * V2²
Since the mass (m) cancels out, we can simplify the equation to:
g * H = g * H2 + (1/2) * V2²
Substituting the given values:
9.8 * 0.2 = 9.8 * 0 + (1/2) * V2²
1.96 = 0 + (1/2) * V2²
1.96 = (1/2) * V2²
V2² = 1.96 * 2
V2² = 3.92
V2 = √3.92
V2 ≈ 1.98 m/s (rounded to 3 decimal places)
Hence, the velocity of the molten metal at the bottom of the sprue is approximately 1.98 m/s.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
A sprue in a sand mould has a top diameter of 20mm and height of 200mm. The velocity of the molten metal at the entry of the sprue is 0.5m/s. Assume acceleration due to gravity as 9.8 m/s2and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is ________ m/s.Correct answer is between '2.04,2.07'. Can you explain this answer?
Question Description
A sprue in a sand mould has a top diameter of 20mm and height of 200mm. The velocity of the molten metal at the entry of the sprue is 0.5m/s. Assume acceleration due to gravity as 9.8 m/s2and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is ________ m/s.Correct answer is between '2.04,2.07'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A sprue in a sand mould has a top diameter of 20mm and height of 200mm. The velocity of the molten metal at the entry of the sprue is 0.5m/s. Assume acceleration due to gravity as 9.8 m/s2and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is ________ m/s.Correct answer is between '2.04,2.07'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sprue in a sand mould has a top diameter of 20mm and height of 200mm. The velocity of the molten metal at the entry of the sprue is 0.5m/s. Assume acceleration due to gravity as 9.8 m/s2and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is ________ m/s.Correct answer is between '2.04,2.07'. Can you explain this answer?.
A sprue in a sand mould has a top diameter of 20mm and height of 200mm. The velocity of the molten metal at the entry of the sprue is 0.5m/s. Assume acceleration due to gravity as 9.8 m/s2and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is ________ m/s.Correct answer is between '2.04,2.07'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A sprue in a sand mould has a top diameter of 20mm and height of 200mm. The velocity of the molten metal at the entry of the sprue is 0.5m/s. Assume acceleration due to gravity as 9.8 m/s2and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is ________ m/s.Correct answer is between '2.04,2.07'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sprue in a sand mould has a top diameter of 20mm and height of 200mm. The velocity of the molten metal at the entry of the sprue is 0.5m/s. Assume acceleration due to gravity as 9.8 m/s2and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is ________ m/s.Correct answer is between '2.04,2.07'. Can you explain this answer?.
Solutions for A sprue in a sand mould has a top diameter of 20mm and height of 200mm. The velocity of the molten metal at the entry of the sprue is 0.5m/s. Assume acceleration due to gravity as 9.8 m/s2and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is ________ m/s.Correct answer is between '2.04,2.07'. 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 A sprue in a sand mould has a top diameter of 20mm and height of 200mm. The velocity of the molten metal at the entry of the sprue is 0.5m/s. Assume acceleration due to gravity as 9.8 m/s2and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is ________ m/s.Correct answer is between '2.04,2.07'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A sprue in a sand mould has a top diameter of 20mm and height of 200mm. The velocity of the molten metal at the entry of the sprue is 0.5m/s. Assume acceleration due to gravity as 9.8 m/s2and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is ________ m/s.Correct answer is between '2.04,2.07'. Can you explain this answer?, a detailed solution for A sprue in a sand mould has a top diameter of 20mm and height of 200mm. The velocity of the molten metal at the entry of the sprue is 0.5m/s. Assume acceleration due to gravity as 9.8 m/s2and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is ________ m/s.Correct answer is between '2.04,2.07'. Can you explain this answer? has been provided alongside types of A sprue in a sand mould has a top diameter of 20mm and height of 200mm. The velocity of the molten metal at the entry of the sprue is 0.5m/s. Assume acceleration due to gravity as 9.8 m/s2and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is ________ m/s.Correct answer is between '2.04,2.07'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A sprue in a sand mould has a top diameter of 20mm and height of 200mm. The velocity of the molten metal at the entry of the sprue is 0.5m/s. Assume acceleration due to gravity as 9.8 m/s2and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is ________ m/s.Correct answer is between '2.04,2.07'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup