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Aluminium powder having an apparent density of 810 kg.m-3 is compacted in a cylindrical die at 600 MPa. The density of the as-pressed aluminium compact is 1755 kg.m-3. If the height of the as-pressed compact is 12 mm, the fill height (in mm) required is ___________
Correct answer is between '25.5,26.5'. Can you explain this answer?
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Aluminium powder having an apparent density of 810 kg.m-3 is compacted...
Given data:
Apparent density of aluminium powder = 810 kg/m³
Pressure applied to compact the powder = 600 MPa
Density of the as-pressed aluminium compact = 1755 kg/m³
Height of the as-pressed compact = 12 mm
Finding the Fill Height:
To find the fill height, we need to use the equation of density:
ρ = m/V
where ρ is the density, m is the mass, and V is the volume.
Finding the Volume of the As-Pressed Aluminium Compact:
We can find the volume of the as-pressed aluminium compact by using its height and density. The volume can be calculated as:
V = h*A
where h is the height of the compact and A is its area.
A = π*r²
where r is the radius of the compact.
Given that the compact is cylindrical in shape, we can assume that its radius is the same as the die used to compact the powder. Therefore, we can find the radius by using the equation:
P = 4F/πd²
where P is the pressure applied, F is the force applied, and d is the diameter of the die.
Since the die is cylindrical, its diameter can be found using its area:
A = πd²/4
Solving these equations, we get:
d = (4F/P)^(1/2)
A = πd²/4
r = d/2
V = h*A
Finding the Mass of the As-Pressed Aluminium Compact:
The mass of the as-pressed aluminium compact can be found by using its volume and density:
m = ρ*V
Once we have the mass, we can use it to find the fill height by using the equation:
m = ρ*V = ρ*A*h*f
where f is the fill height.
Solving for f, we get:
f = m/(ρ*A*h)
Substituting the given values, we get:
d = (4F/P)^(1/2) = (4*600*10^6)/(π*810*10^3)^(1/2) = 3.34 mm
A = πd²/4 = π*(3.34*10^-3)²/4 = 8.80*10^-6 m²
r = d/2 = 1.67 mm
V = h*A = 12*10^-3*8.80*10^-6 = 1.06*10^-4 m³
m = ρ*V = 1755*1.06*10^-4 = 0.0186 kg
f = m/(ρ*A*h) = 0.0186/(810*8.80*10^-6*12*10^-3) = 25.9 mm
Therefore, the fill height required is between 25.5 mm and 26.5 mm.
Apparent density of aluminium powder = 810 kg/m³
Pressure applied to compact the powder = 600 MPa
Density of the as-pressed aluminium compact = 1755 kg/m³
Height of the as-pressed compact = 12 mm
Finding the Fill Height:
To find the fill height, we need to use the equation of density:
ρ = m/V
where ρ is the density, m is the mass, and V is the volume.
Finding the Volume of the As-Pressed Aluminium Compact:
We can find the volume of the as-pressed aluminium compact by using its height and density. The volume can be calculated as:
V = h*A
where h is the height of the compact and A is its area.
A = π*r²
where r is the radius of the compact.
Given that the compact is cylindrical in shape, we can assume that its radius is the same as the die used to compact the powder. Therefore, we can find the radius by using the equation:
P = 4F/πd²
where P is the pressure applied, F is the force applied, and d is the diameter of the die.
Since the die is cylindrical, its diameter can be found using its area:
A = πd²/4
Solving these equations, we get:
d = (4F/P)^(1/2)
A = πd²/4
r = d/2
V = h*A
Finding the Mass of the As-Pressed Aluminium Compact:
The mass of the as-pressed aluminium compact can be found by using its volume and density:
m = ρ*V
Once we have the mass, we can use it to find the fill height by using the equation:
m = ρ*V = ρ*A*h*f
where f is the fill height.
Solving for f, we get:
f = m/(ρ*A*h)
Substituting the given values, we get:
d = (4F/P)^(1/2) = (4*600*10^6)/(π*810*10^3)^(1/2) = 3.34 mm
A = πd²/4 = π*(3.34*10^-3)²/4 = 8.80*10^-6 m²
r = d/2 = 1.67 mm
V = h*A = 12*10^-3*8.80*10^-6 = 1.06*10^-4 m³
m = ρ*V = 1755*1.06*10^-4 = 0.0186 kg
f = m/(ρ*A*h) = 0.0186/(810*8.80*10^-6*12*10^-3) = 25.9 mm
Therefore, the fill height required is between 25.5 mm and 26.5 mm.
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Aluminium powder having an apparent density of 810 kg.m-3 is compacted in a cylindrical die at 600 MPa. The density of the as-pressed aluminium compact is 1755 kg.m-3. If the height of the as-pressed compact is 12 mm, the fill height (in mm) required is ___________Correct answer is between '25.5,26.5'. Can you explain this answer?
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Aluminium powder having an apparent density of 810 kg.m-3 is compacted in a cylindrical die at 600 MPa. The density of the as-pressed aluminium compact is 1755 kg.m-3. If the height of the as-pressed compact is 12 mm, the fill height (in mm) required is ___________Correct answer is between '25.5,26.5'. 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 Aluminium powder having an apparent density of 810 kg.m-3 is compacted in a cylindrical die at 600 MPa. The density of the as-pressed aluminium compact is 1755 kg.m-3. If the height of the as-pressed compact is 12 mm, the fill height (in mm) required is ___________Correct answer is between '25.5,26.5'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Aluminium powder having an apparent density of 810 kg.m-3 is compacted in a cylindrical die at 600 MPa. The density of the as-pressed aluminium compact is 1755 kg.m-3. If the height of the as-pressed compact is 12 mm, the fill height (in mm) required is ___________Correct answer is between '25.5,26.5'. Can you explain this answer?.
Aluminium powder having an apparent density of 810 kg.m-3 is compacted in a cylindrical die at 600 MPa. The density of the as-pressed aluminium compact is 1755 kg.m-3. If the height of the as-pressed compact is 12 mm, the fill height (in mm) required is ___________Correct answer is between '25.5,26.5'. 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 Aluminium powder having an apparent density of 810 kg.m-3 is compacted in a cylindrical die at 600 MPa. The density of the as-pressed aluminium compact is 1755 kg.m-3. If the height of the as-pressed compact is 12 mm, the fill height (in mm) required is ___________Correct answer is between '25.5,26.5'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Aluminium powder having an apparent density of 810 kg.m-3 is compacted in a cylindrical die at 600 MPa. The density of the as-pressed aluminium compact is 1755 kg.m-3. If the height of the as-pressed compact is 12 mm, the fill height (in mm) required is ___________Correct answer is between '25.5,26.5'. Can you explain this answer?.
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