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The velocity of water (before mixing with abrasives) at the orifice of the abrasive water jet machining head is 900 m/s. After complete mixing with the abrasive, the velocity of the water abrasive jet is 787.6 m/s. Discharge coefficients considered to be unity. If the water mass flow rate is 2.8 kg/mm by considering velocity of abrasives at entry as 0, the abrasive mass flow rate is nearest to (in kg /min) is
- a)0.1
- b)0.2
- c)0.6
- d)0.4
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The velocity of water (before mixing with abrasives) at the orifice o...
Given:
- Velocity of water at orifice (before mixing with abrasives): 900 m/s
- Velocity of water abrasive jet (after complete mixing with abrasives): 787.6 m/s
- Discharge coefficient: unity (C = 1)
- Water mass flow rate: 2.8 kg/mm
- Velocity of abrasives at entry: 0 m/s
To find:
The abrasive mass flow rate (in kg/min)
Solution:
1. Calculation of Water Volume Flow Rate:
The water mass flow rate is given as 2.8 kg/mm.
To convert it to a standard unit, we need to convert mm to m.
Since 1 mm = 0.001 m, the water mass flow rate becomes: 2.8 kg/0.001 m = 2800 kg/m.
2. Calculation of Water Volume Flow Rate:
The volume flow rate of water can be calculated using the formula:
Q = A x V
Where Q is the volume flow rate, A is the cross-sectional area, and V is the velocity.
The cross-sectional area can be calculated using the formula:
A = πr^2
Where r is the radius of the orifice.
Assuming the cross-sectional area of the orifice is constant throughout the process, we can equate the water volume flow rate before and after mixing:
Q1 = Q2
3. Calculation of Abrasive Mass Flow Rate:
The volume flow rate of the water abrasive jet can be calculated using the same formula as above:
Q = A x V
Since the velocity of the abrasives at entry is given as 0 m/s, the volume flow rate of the abrasives can be equated to the water volume flow rate:
Q_abrasive = Q_water
4. Calculation of Abrasive Mass Flow Rate:
The mass flow rate of the abrasive can be calculated using the formula:
m = ρ x Q
Where m is the mass flow rate, ρ is the density, and Q is the volume flow rate.
Since the abrasive density is not given, we can assume it to be the same as water (ρ_water = 1000 kg/m^3).
The abrasive mass flow rate can now be calculated as:
m_abrasive = ρ_abrasive x Q_abrasive
5. Conversion to kg/min:
Finally, we need to convert the abrasive mass flow rate from kg/m to kg/min.
Since 1 kg/m = 1000 kg/min, the abrasive mass flow rate becomes:
m_abrasive = m_abrasive x 1000
Answer:
The abrasive mass flow rate is approximately 0.4 kg/min (option D).
- Velocity of water at orifice (before mixing with abrasives): 900 m/s
- Velocity of water abrasive jet (after complete mixing with abrasives): 787.6 m/s
- Discharge coefficient: unity (C = 1)
- Water mass flow rate: 2.8 kg/mm
- Velocity of abrasives at entry: 0 m/s
To find:
The abrasive mass flow rate (in kg/min)
Solution:
1. Calculation of Water Volume Flow Rate:
The water mass flow rate is given as 2.8 kg/mm.
To convert it to a standard unit, we need to convert mm to m.
Since 1 mm = 0.001 m, the water mass flow rate becomes: 2.8 kg/0.001 m = 2800 kg/m.
2. Calculation of Water Volume Flow Rate:
The volume flow rate of water can be calculated using the formula:
Q = A x V
Where Q is the volume flow rate, A is the cross-sectional area, and V is the velocity.
The cross-sectional area can be calculated using the formula:
A = πr^2
Where r is the radius of the orifice.
Assuming the cross-sectional area of the orifice is constant throughout the process, we can equate the water volume flow rate before and after mixing:
Q1 = Q2
3. Calculation of Abrasive Mass Flow Rate:
The volume flow rate of the water abrasive jet can be calculated using the same formula as above:
Q = A x V
Since the velocity of the abrasives at entry is given as 0 m/s, the volume flow rate of the abrasives can be equated to the water volume flow rate:
Q_abrasive = Q_water
4. Calculation of Abrasive Mass Flow Rate:
The mass flow rate of the abrasive can be calculated using the formula:
m = ρ x Q
Where m is the mass flow rate, ρ is the density, and Q is the volume flow rate.
Since the abrasive density is not given, we can assume it to be the same as water (ρ_water = 1000 kg/m^3).
The abrasive mass flow rate can now be calculated as:
m_abrasive = ρ_abrasive x Q_abrasive
5. Conversion to kg/min:
Finally, we need to convert the abrasive mass flow rate from kg/m to kg/min.
Since 1 kg/m = 1000 kg/min, the abrasive mass flow rate becomes:
m_abrasive = m_abrasive x 1000
Answer:
The abrasive mass flow rate is approximately 0.4 kg/min (option D).
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Community Answer
The velocity of water (before mixing with abrasives) at the orifice o...
Given Vw = 900 m/s, V = 787.6 m/s, mw = 2.8 kg/min
∴ maVa + mwVw = V (mw + ma)
mw X Vw = V(mw + ma)
(∵ Va = 0, negligible velocity)
2.8 x 900 = 787.6(2.8 + ma)
⇒ ma = 0.399
≅0.4 kg/min
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The velocity of water (before mixing with abrasives) at the orifice of the abrasive water jet machining head is 900 m/s. After complete mixing with the abrasive, the velocity of the water abrasive jet is 787.6 m/s. Discharge coefficients considered to be unity. If the water mass flow rate is 2.8 kg/mm by considering velocity of abrasives at entry as 0, the abrasive mass flow rate is nearest to (in kg /min) isa)0.1b)0.2c)0.6d)0.4Correct answer is option 'D'. Can you explain this answer?
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The velocity of water (before mixing with abrasives) at the orifice of the abrasive water jet machining head is 900 m/s. After complete mixing with the abrasive, the velocity of the water abrasive jet is 787.6 m/s. Discharge coefficients considered to be unity. If the water mass flow rate is 2.8 kg/mm by considering velocity of abrasives at entry as 0, the abrasive mass flow rate is nearest to (in kg /min) isa)0.1b)0.2c)0.6d)0.4Correct answer is option 'D'. 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 The velocity of water (before mixing with abrasives) at the orifice of the abrasive water jet machining head is 900 m/s. After complete mixing with the abrasive, the velocity of the water abrasive jet is 787.6 m/s. Discharge coefficients considered to be unity. If the water mass flow rate is 2.8 kg/mm by considering velocity of abrasives at entry as 0, the abrasive mass flow rate is nearest to (in kg /min) isa)0.1b)0.2c)0.6d)0.4Correct answer is option 'D'. 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 The velocity of water (before mixing with abrasives) at the orifice of the abrasive water jet machining head is 900 m/s. After complete mixing with the abrasive, the velocity of the water abrasive jet is 787.6 m/s. Discharge coefficients considered to be unity. If the water mass flow rate is 2.8 kg/mm by considering velocity of abrasives at entry as 0, the abrasive mass flow rate is nearest to (in kg /min) isa)0.1b)0.2c)0.6d)0.4Correct answer is option 'D'. Can you explain this answer?.
The velocity of water (before mixing with abrasives) at the orifice of the abrasive water jet machining head is 900 m/s. After complete mixing with the abrasive, the velocity of the water abrasive jet is 787.6 m/s. Discharge coefficients considered to be unity. If the water mass flow rate is 2.8 kg/mm by considering velocity of abrasives at entry as 0, the abrasive mass flow rate is nearest to (in kg /min) isa)0.1b)0.2c)0.6d)0.4Correct answer is option 'D'. 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 The velocity of water (before mixing with abrasives) at the orifice of the abrasive water jet machining head is 900 m/s. After complete mixing with the abrasive, the velocity of the water abrasive jet is 787.6 m/s. Discharge coefficients considered to be unity. If the water mass flow rate is 2.8 kg/mm by considering velocity of abrasives at entry as 0, the abrasive mass flow rate is nearest to (in kg /min) isa)0.1b)0.2c)0.6d)0.4Correct answer is option 'D'. 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 The velocity of water (before mixing with abrasives) at the orifice of the abrasive water jet machining head is 900 m/s. After complete mixing with the abrasive, the velocity of the water abrasive jet is 787.6 m/s. Discharge coefficients considered to be unity. If the water mass flow rate is 2.8 kg/mm by considering velocity of abrasives at entry as 0, the abrasive mass flow rate is nearest to (in kg /min) isa)0.1b)0.2c)0.6d)0.4Correct answer is option 'D'. Can you explain this answer?.
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