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A sprue in a sand mould has top diameter of 20 mm and height of 200 mm. The velocity of the molten metal at the entry of the sprue is 0.5 m/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?
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A sprue in a sand mould has top diameter of 20 mm and height of 200 mm...
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A sprue in a sand mould has top diameter of 20 mm and height of 200 mm...
To find the velocity of the molten metal at the bottom of the sprue, we can use the principle of conservation of energy. The energy at the top of the sprue is equal to the energy at the bottom of the sprue.
The energy at the top of the sprue consists of two components:
1. Potential energy due to height: PE = mgh
2. Kinetic energy due to velocity: KE = 0.5mv^2
The energy at the bottom of the sprue is also the sum of potential energy and kinetic energy:
PE' = mgh'
KE' = 0.5mv'^2
Since the mass of the molten metal remains constant, we can cancel out the mass term from both sides of the equation.
At the top of the sprue:
PE + KE = mgh + 0.5mv^2
At the bottom of the sprue:
PE' + KE' = mgh' + 0.5mv'^2
Since we are neglecting losses, the energy at the top and bottom of the sprue remains the same. Therefore, we can equate the two equations:
mgh + 0.5mv^2 = mgh' + 0.5mv'^2
Rearranging the equation, we get:
0.5mv^2 - 0.5mv'^2 = mgh' - mgh
Dividing both sides by 0.5m and factoring out the mass term, we get:
v^2 - v'^2 = 2g(h' - h)
Now, let's plug in the given values:
- v = 0.5 m/s (velocity at the top of the sprue)
- h = 200 mm = 0.2 m (height at the top of the sprue)
- g = 9.8 m/s^2 (acceleration due to gravity)
Using these values, we can solve for v':
v^2 - v'^2 = 2g(h' - h)
(0.5)^2 - v'^2 = 2(9.8)(h' - 0.2)
0.25 - v'^2 = 19.6(h' - 0.2)
v'^2 = 0.25 - 19.6(h' - 0.2)
v' = sqrt(0.25 - 19.6(h' - 0.2))
To find the velocity at the bottom of the sprue (v'), we need to know the height at the bottom of the sprue (h'). Unfortunately, this information is not provided in the question. Without the value of h', we cannot determine the exact velocity at the bottom of the sprue. Therefore, we cannot provide the correct answer.
Note: The given range of the correct answer, '2.04, 2.07', is not valid without knowing the value of h'.
The energy at the top of the sprue consists of two components:
1. Potential energy due to height: PE = mgh
2. Kinetic energy due to velocity: KE = 0.5mv^2
The energy at the bottom of the sprue is also the sum of potential energy and kinetic energy:
PE' = mgh'
KE' = 0.5mv'^2
Since the mass of the molten metal remains constant, we can cancel out the mass term from both sides of the equation.
At the top of the sprue:
PE + KE = mgh + 0.5mv^2
At the bottom of the sprue:
PE' + KE' = mgh' + 0.5mv'^2
Since we are neglecting losses, the energy at the top and bottom of the sprue remains the same. Therefore, we can equate the two equations:
mgh + 0.5mv^2 = mgh' + 0.5mv'^2
Rearranging the equation, we get:
0.5mv^2 - 0.5mv'^2 = mgh' - mgh
Dividing both sides by 0.5m and factoring out the mass term, we get:
v^2 - v'^2 = 2g(h' - h)
Now, let's plug in the given values:
- v = 0.5 m/s (velocity at the top of the sprue)
- h = 200 mm = 0.2 m (height at the top of the sprue)
- g = 9.8 m/s^2 (acceleration due to gravity)
Using these values, we can solve for v':
v^2 - v'^2 = 2g(h' - h)
(0.5)^2 - v'^2 = 2(9.8)(h' - 0.2)
0.25 - v'^2 = 19.6(h' - 0.2)
v'^2 = 0.25 - 19.6(h' - 0.2)
v' = sqrt(0.25 - 19.6(h' - 0.2))
To find the velocity at the bottom of the sprue (v'), we need to know the height at the bottom of the sprue (h'). Unfortunately, this information is not provided in the question. Without the value of h', we cannot determine the exact velocity at the bottom of the sprue. Therefore, we cannot provide the correct answer.
Note: The given range of the correct answer, '2.04, 2.07', is not valid without knowing the value of h'.
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A sprue in a sand mould has top diameter of 20 mm and height of 200 mm. The velocity of the molten metal at the entry of the sprue is 0.5 m/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/sCorrect answer is between '2.04,2.07'. Can you explain this answer?
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A sprue in a sand mould has top diameter of 20 mm and height of 200 mm. The velocity of the molten metal at the entry of the sprue is 0.5 m/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/sCorrect answer is between '2.04,2.07'. 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 sprue in a sand mould has top diameter of 20 mm and height of 200 mm. The velocity of the molten metal at the entry of the sprue is 0.5 m/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/sCorrect answer is between '2.04,2.07'. 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 sprue in a sand mould has top diameter of 20 mm and height of 200 mm. The velocity of the molten metal at the entry of the sprue is 0.5 m/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/sCorrect answer is between '2.04,2.07'. Can you explain this answer?.
A sprue in a sand mould has top diameter of 20 mm and height of 200 mm. The velocity of the molten metal at the entry of the sprue is 0.5 m/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/sCorrect answer is between '2.04,2.07'. 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 sprue in a sand mould has top diameter of 20 mm and height of 200 mm. The velocity of the molten metal at the entry of the sprue is 0.5 m/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/sCorrect answer is between '2.04,2.07'. 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 sprue in a sand mould has top diameter of 20 mm and height of 200 mm. The velocity of the molten metal at the entry of the sprue is 0.5 m/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/sCorrect answer is between '2.04,2.07'. Can you explain this answer?.
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