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The height of a liquid metal column in a cylindrical vessel is 3.2 m. At time t=0, liquid metal is drained out from the vessel through a small nozzle located at the base of the vessel. Neglecting frictional losses, the initial mass flow rate (in kg.s-1) through the nozzle is ________________
Given data:
Density of liquid metal = 7000 kg.m-3
Nozzle diameter = 30 mm
Nozzle discharge coefficient = 0.80
Density of liquid metal = 7000 kg.m-3
Nozzle diameter = 30 mm
Nozzle discharge coefficient = 0.80
Correct answer is between '31.0,32.0'. Can you explain this answer?
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The height of a liquid metal column in a cylindrical vessel is 3.2 m. ...
Given data:
Density of liquid metal = 7000 kg/m³
Height of liquid metal column = 3.2 m
Nozzle diameter = 30 mm
Nozzle discharge coefficient = 0.80
Formula:
Mass flow rate (ṁ) = Area of nozzle (A) × Velocity of fluid (V) × Density of fluid (ρ)
Calculations:
1. Convert the nozzle diameter from millimeters to meters:
Nozzle diameter = 30 mm = 0.03 m
2. Calculate the area of the nozzle using the formula for the area of a circle:
A = π * (d/2)², where d is the diameter of the nozzle
A = π * (0.03/2)²
A = 0.000706858 m²
3. Calculate the velocity of the fluid using the equation of motion:
v = √(2 * g * h), where g is the acceleration due to gravity and h is the height of the liquid column
g = 9.8 m/s²
v = √(2 * 9.8 * 3.2)
v = √(62.72)
v = 7.92 m/s
4. Substitute the values into the formula for mass flow rate:
ṁ = A * v * ρ
ṁ = 0.000706858 * 7.92 * 7000
ṁ = 39.979 kg/s
5. Apply the nozzle discharge coefficient:
Mass flow rate through the nozzle = Nozzle discharge coefficient * Mass flow rate
Mass flow rate through the nozzle = 0.80 * 39.979
Mass flow rate through the nozzle = 31.9832 kg/s
Answer:
The initial mass flow rate through the nozzle is approximately 31.98 kg/s. This value falls within the range of 31.0 to 32.0 kg/s as specified.
Density of liquid metal = 7000 kg/m³
Height of liquid metal column = 3.2 m
Nozzle diameter = 30 mm
Nozzle discharge coefficient = 0.80
Formula:
Mass flow rate (ṁ) = Area of nozzle (A) × Velocity of fluid (V) × Density of fluid (ρ)
Calculations:
1. Convert the nozzle diameter from millimeters to meters:
Nozzle diameter = 30 mm = 0.03 m
2. Calculate the area of the nozzle using the formula for the area of a circle:
A = π * (d/2)², where d is the diameter of the nozzle
A = π * (0.03/2)²
A = 0.000706858 m²
3. Calculate the velocity of the fluid using the equation of motion:
v = √(2 * g * h), where g is the acceleration due to gravity and h is the height of the liquid column
g = 9.8 m/s²
v = √(2 * 9.8 * 3.2)
v = √(62.72)
v = 7.92 m/s
4. Substitute the values into the formula for mass flow rate:
ṁ = A * v * ρ
ṁ = 0.000706858 * 7.92 * 7000
ṁ = 39.979 kg/s
5. Apply the nozzle discharge coefficient:
Mass flow rate through the nozzle = Nozzle discharge coefficient * Mass flow rate
Mass flow rate through the nozzle = 0.80 * 39.979
Mass flow rate through the nozzle = 31.9832 kg/s
Answer:
The initial mass flow rate through the nozzle is approximately 31.98 kg/s. This value falls within the range of 31.0 to 32.0 kg/s as specified.
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The height of a liquid metal column in a cylindrical vessel is 3.2 m. At time t=0, liquid metal is drained out from the vessel through a small nozzle located at the base of the vessel. Neglecting frictional losses, the initial mass flow rate (in kg.s-1) through the nozzle is ________________Given data:Density of liquid metal = 7000 kg.m-3Nozzle diameter = 30 mmNozzle discharge coefficient = 0.80Correct answer is between '31.0,32.0'. Can you explain this answer?
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The height of a liquid metal column in a cylindrical vessel is 3.2 m. At time t=0, liquid metal is drained out from the vessel through a small nozzle located at the base of the vessel. Neglecting frictional losses, the initial mass flow rate (in kg.s-1) through the nozzle is ________________Given data:Density of liquid metal = 7000 kg.m-3Nozzle diameter = 30 mmNozzle discharge coefficient = 0.80Correct answer is between '31.0,32.0'. 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 The height of a liquid metal column in a cylindrical vessel is 3.2 m. At time t=0, liquid metal is drained out from the vessel through a small nozzle located at the base of the vessel. Neglecting frictional losses, the initial mass flow rate (in kg.s-1) through the nozzle is ________________Given data:Density of liquid metal = 7000 kg.m-3Nozzle diameter = 30 mmNozzle discharge coefficient = 0.80Correct answer is between '31.0,32.0'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The height of a liquid metal column in a cylindrical vessel is 3.2 m. At time t=0, liquid metal is drained out from the vessel through a small nozzle located at the base of the vessel. Neglecting frictional losses, the initial mass flow rate (in kg.s-1) through the nozzle is ________________Given data:Density of liquid metal = 7000 kg.m-3Nozzle diameter = 30 mmNozzle discharge coefficient = 0.80Correct answer is between '31.0,32.0'. Can you explain this answer?.
The height of a liquid metal column in a cylindrical vessel is 3.2 m. At time t=0, liquid metal is drained out from the vessel through a small nozzle located at the base of the vessel. Neglecting frictional losses, the initial mass flow rate (in kg.s-1) through the nozzle is ________________Given data:Density of liquid metal = 7000 kg.m-3Nozzle diameter = 30 mmNozzle discharge coefficient = 0.80Correct answer is between '31.0,32.0'. 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 The height of a liquid metal column in a cylindrical vessel is 3.2 m. At time t=0, liquid metal is drained out from the vessel through a small nozzle located at the base of the vessel. Neglecting frictional losses, the initial mass flow rate (in kg.s-1) through the nozzle is ________________Given data:Density of liquid metal = 7000 kg.m-3Nozzle diameter = 30 mmNozzle discharge coefficient = 0.80Correct answer is between '31.0,32.0'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The height of a liquid metal column in a cylindrical vessel is 3.2 m. At time t=0, liquid metal is drained out from the vessel through a small nozzle located at the base of the vessel. Neglecting frictional losses, the initial mass flow rate (in kg.s-1) through the nozzle is ________________Given data:Density of liquid metal = 7000 kg.m-3Nozzle diameter = 30 mmNozzle discharge coefficient = 0.80Correct answer is between '31.0,32.0'. Can you explain this answer?.
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