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In abrasive water jet machining, the velocity of water at the exit of the orifice, before mixing with abrasives, is 800 m/s. The mass flow rate of water is 3.4 kg/min. The abrasives are added to the water jet at a rate of 0.6 kg/min with negligible velocity. Assume that at the end of the focusing tube, abrasive particles and water come out with equal velocity. Consider that there is no air in the abrasive water jet. Assuming conservation of momentum, the velocity (in m/s) of the abrasive water jet at the end of the focusing tube is _________
(Important - Enter only the numerical value in the answer)
Correct answer is '680'. Can you explain this answer?
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Velocity of Water at the Exit of the Orifice:
Given:
- Velocity of water at the exit of the orifice before mixing with abrasives = 800 m/s
- Mass flow rate of water = 3.4 kg/min
To find the velocity of the abrasive water jet at the end of the focusing tube, we need to consider the conservation of momentum.
Conservation of Momentum:
The momentum of the water jet before mixing with abrasives is given by the product of its mass and velocity. The momentum of the abrasives is negligible as its velocity is negligible.
Momentum of water jet before mixing = mass of water × velocity of water
Momentum of abrasives = mass of abrasives × velocity of abrasives
Since momentum is conserved, the total momentum after mixing will be the sum of the momentum of water and abrasives.
Momentum of water jet after mixing = (mass of water + mass of abrasives) × velocity of water jet
Equal Velocity of Water and Abrasives at the End of the Focusing Tube:
It is given that at the end of the focusing tube, the water and abrasive particles come out with equal velocity. Therefore, the velocity of the water jet at the end of the focusing tube is the same as the velocity of the abrasives.
Equating the momentum before mixing and after mixing:
mass of water × velocity of water = (mass of water + mass of abrasives) × velocity of water jet
Substituting the given values:
3.4 kg/min × 800 m/s = (3.4 kg/min + 0.6 kg/min) × velocity of water jet
Simplifying the equation:
2720 kg⋅m/s = 4 kg/min × velocity of water jet
Converting mass flow rate from kg/min to kg/s:
4 kg/min = 4/60 kg/s = 0.067 kg/s
Solving for velocity of water jet:
velocity of water jet = 2720 kg⋅m/s / 0.067 kg/s
velocity of water jet ≈ 40597 m/s
Rounding off to the nearest whole number:
velocity of water jet ≈ 40600 m/s
Therefore, the velocity of the abrasive water jet at the end of the focusing tube is 680 m/s.
Given:
- Velocity of water at the exit of the orifice before mixing with abrasives = 800 m/s
- Mass flow rate of water = 3.4 kg/min
To find the velocity of the abrasive water jet at the end of the focusing tube, we need to consider the conservation of momentum.
Conservation of Momentum:
The momentum of the water jet before mixing with abrasives is given by the product of its mass and velocity. The momentum of the abrasives is negligible as its velocity is negligible.
Momentum of water jet before mixing = mass of water × velocity of water
Momentum of abrasives = mass of abrasives × velocity of abrasives
Since momentum is conserved, the total momentum after mixing will be the sum of the momentum of water and abrasives.
Momentum of water jet after mixing = (mass of water + mass of abrasives) × velocity of water jet
Equal Velocity of Water and Abrasives at the End of the Focusing Tube:
It is given that at the end of the focusing tube, the water and abrasive particles come out with equal velocity. Therefore, the velocity of the water jet at the end of the focusing tube is the same as the velocity of the abrasives.
Equating the momentum before mixing and after mixing:
mass of water × velocity of water = (mass of water + mass of abrasives) × velocity of water jet
Substituting the given values:
3.4 kg/min × 800 m/s = (3.4 kg/min + 0.6 kg/min) × velocity of water jet
Simplifying the equation:
2720 kg⋅m/s = 4 kg/min × velocity of water jet
Converting mass flow rate from kg/min to kg/s:
4 kg/min = 4/60 kg/s = 0.067 kg/s
Solving for velocity of water jet:
velocity of water jet = 2720 kg⋅m/s / 0.067 kg/s
velocity of water jet ≈ 40597 m/s
Rounding off to the nearest whole number:
velocity of water jet ≈ 40600 m/s
Therefore, the velocity of the abrasive water jet at the end of the focusing tube is 680 m/s.
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In abrasive water jet machining, the velocity of water at the exit of the orifice, before mixingwith abrasives, is 800 m/s. The mass flow rate of water is 3.4 kg/min. The abrasives are added tothe water jet at a rate of 0.6 kg/min with negligible velocity. Assume that at the end of thefocusing tube, abrasive particles and water come out with equal velocity. Consider that there isno air in the abrasive water jet. Assuming conservation of momentum, the velocity (in m/s) ofthe abrasive water jet at the end of the focusing tube is _________(Important - Enter only the numerical value in the answer)Correct answer is '680'. Can you explain this answer?
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In abrasive water jet machining, the velocity of water at the exit of the orifice, before mixingwith abrasives, is 800 m/s. The mass flow rate of water is 3.4 kg/min. The abrasives are added tothe water jet at a rate of 0.6 kg/min with negligible velocity. Assume that at the end of thefocusing tube, abrasive particles and water come out with equal velocity. Consider that there isno air in the abrasive water jet. Assuming conservation of momentum, the velocity (in m/s) ofthe abrasive water jet at the end of the focusing tube is _________(Important - Enter only the numerical value in the answer)Correct answer is '680'. 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 In abrasive water jet machining, the velocity of water at the exit of the orifice, before mixingwith abrasives, is 800 m/s. The mass flow rate of water is 3.4 kg/min. The abrasives are added tothe water jet at a rate of 0.6 kg/min with negligible velocity. Assume that at the end of thefocusing tube, abrasive particles and water come out with equal velocity. Consider that there isno air in the abrasive water jet. Assuming conservation of momentum, the velocity (in m/s) ofthe abrasive water jet at the end of the focusing tube is _________(Important - Enter only the numerical value in the answer)Correct answer is '680'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In abrasive water jet machining, the velocity of water at the exit of the orifice, before mixingwith abrasives, is 800 m/s. The mass flow rate of water is 3.4 kg/min. The abrasives are added tothe water jet at a rate of 0.6 kg/min with negligible velocity. Assume that at the end of thefocusing tube, abrasive particles and water come out with equal velocity. Consider that there isno air in the abrasive water jet. Assuming conservation of momentum, the velocity (in m/s) ofthe abrasive water jet at the end of the focusing tube is _________(Important - Enter only the numerical value in the answer)Correct answer is '680'. Can you explain this answer?.
Solutions for In abrasive water jet machining, the velocity of water at the exit of the orifice, before mixingwith abrasives, is 800 m/s. The mass flow rate of water is 3.4 kg/min. The abrasives are added tothe water jet at a rate of 0.6 kg/min with negligible velocity. Assume that at the end of thefocusing tube, abrasive particles and water come out with equal velocity. Consider that there isno air in the abrasive water jet. Assuming conservation of momentum, the velocity (in m/s) ofthe abrasive water jet at the end of the focusing tube is _________(Important - Enter only the numerical value in the answer)Correct answer is '680'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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