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Vertical true centrifugal casting is used to cast aluminum tubing that is 40cm in long with outside diameter = 22cm. density of aluminum = 2.7 g/cm^3. if the speed of rotation during solidfication is 900 rev/min, determine (a) the inside diameters at the top and bottom of the tubing if the total weight of the final casting = 15kg?
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Vertical true centrifugal casting is used to cast aluminum tubing that...
Vertical True Centrifugal Casting Process
Vertical true centrifugal casting is a casting process used to produce cylindrical-shaped objects, such as aluminum tubing, with high density and strength. The process involves rotating a mold at a high speed while pouring the molten metal into the mold. The centrifugal force generated by the rotation ensures that the molten metal is distributed evenly along the mold's walls, resulting in a uniform casting.
Given Data:
- Length of the tubing (L) = 40 cm
- Outside diameter of the tubing (OD) = 22 cm
- Density of aluminum (ρ) = 2.7 g/cm^3
- Speed of rotation during solidification (N) = 900 rev/min
- Total weight of the final casting (W) = 15 kg
Calculating Inside Diameters
To calculate the inside diameters at the top and bottom of the tubing, we need to consider the weight distribution and the density of aluminum.
1. Calculate the volume of the casting:
Volume (V) = Weight (W) / Density (ρ)
V = 15000 g / 2.7 g/cm^3
V = 5555.56 cm^3
2. Calculate the cross-sectional area of the casting:
Cross-sectional Area (A) = π * (OD/2)^2
A = π * (11 cm)^2
A = 381.97 cm^2
3. Calculate the average inside diameter:
Average Inside Diameter (ID_avg) = 2 * √(A/π)
ID_avg = 2 * √(381.97 cm^2 / π)
ID_avg = 24.72 cm
4. Calculate the angular velocity:
Angular Velocity (ω) = (2π * N) / 60
ω = (2π * 900 rev/min) / 60
ω = 94.25 rad/s
5. Calculate the acceleration due to centrifugal force:
Centrifugal Force (F) = W * ω^2 * R
F = 15 kg * (94.25 rad/s)^2 * (22 cm / 2)
F = 60,536.25 N
6. Calculate the height of the casting:
Height (H) = F / (ρ * g * A)
H = 60,536.25 N / (2.7 g/cm^3 * 9.8 m/s^2 * 381.97 cm^2)
H = 6.19 cm
7. Calculate the inside diameters at the top and bottom:
ID_top = ID_avg + 2 * H
ID_bottom = ID_avg - 2 * H
ID_top = 24.72 cm + 2 * 6.19 cm
ID_top = 36.10 cm
ID_bottom = 24.72 cm - 2 * 6.19 cm
ID_bottom = 12.34 cm
Conclusion
The inside diameter of the aluminum tubing at the top and bottom are calculated to be 36.10 cm and 12.34 cm, respectively, based on the given parameters and the principles of vertical true centrifugal casting.
Vertical true centrifugal casting is a casting process used to produce cylindrical-shaped objects, such as aluminum tubing, with high density and strength. The process involves rotating a mold at a high speed while pouring the molten metal into the mold. The centrifugal force generated by the rotation ensures that the molten metal is distributed evenly along the mold's walls, resulting in a uniform casting.
Given Data:
- Length of the tubing (L) = 40 cm
- Outside diameter of the tubing (OD) = 22 cm
- Density of aluminum (ρ) = 2.7 g/cm^3
- Speed of rotation during solidification (N) = 900 rev/min
- Total weight of the final casting (W) = 15 kg
Calculating Inside Diameters
To calculate the inside diameters at the top and bottom of the tubing, we need to consider the weight distribution and the density of aluminum.
1. Calculate the volume of the casting:
Volume (V) = Weight (W) / Density (ρ)
V = 15000 g / 2.7 g/cm^3
V = 5555.56 cm^3
2. Calculate the cross-sectional area of the casting:
Cross-sectional Area (A) = π * (OD/2)^2
A = π * (11 cm)^2
A = 381.97 cm^2
3. Calculate the average inside diameter:
Average Inside Diameter (ID_avg) = 2 * √(A/π)
ID_avg = 2 * √(381.97 cm^2 / π)
ID_avg = 24.72 cm
4. Calculate the angular velocity:
Angular Velocity (ω) = (2π * N) / 60
ω = (2π * 900 rev/min) / 60
ω = 94.25 rad/s
5. Calculate the acceleration due to centrifugal force:
Centrifugal Force (F) = W * ω^2 * R
F = 15 kg * (94.25 rad/s)^2 * (22 cm / 2)
F = 60,536.25 N
6. Calculate the height of the casting:
Height (H) = F / (ρ * g * A)
H = 60,536.25 N / (2.7 g/cm^3 * 9.8 m/s^2 * 381.97 cm^2)
H = 6.19 cm
7. Calculate the inside diameters at the top and bottom:
ID_top = ID_avg + 2 * H
ID_bottom = ID_avg - 2 * H
ID_top = 24.72 cm + 2 * 6.19 cm
ID_top = 36.10 cm
ID_bottom = 24.72 cm - 2 * 6.19 cm
ID_bottom = 12.34 cm
Conclusion
The inside diameter of the aluminum tubing at the top and bottom are calculated to be 36.10 cm and 12.34 cm, respectively, based on the given parameters and the principles of vertical true centrifugal casting.
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Vertical true centrifugal casting is used to cast aluminum tubing that is 40cm in long with outside diameter = 22cm. density of aluminum = 2.7 g/cm^3. if the speed of rotation during solidfication is 900 rev/min, determine (a) the inside diameters at the top and bottom of the tubing if the total weight of the final casting = 15kg?
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Vertical true centrifugal casting is used to cast aluminum tubing that is 40cm in long with outside diameter = 22cm. density of aluminum = 2.7 g/cm^3. if the speed of rotation during solidfication is 900 rev/min, determine (a) the inside diameters at the top and bottom of the tubing if the total weight of the final casting = 15kg? 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 Vertical true centrifugal casting is used to cast aluminum tubing that is 40cm in long with outside diameter = 22cm. density of aluminum = 2.7 g/cm^3. if the speed of rotation during solidfication is 900 rev/min, determine (a) the inside diameters at the top and bottom of the tubing if the total weight of the final casting = 15kg? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Vertical true centrifugal casting is used to cast aluminum tubing that is 40cm in long with outside diameter = 22cm. density of aluminum = 2.7 g/cm^3. if the speed of rotation during solidfication is 900 rev/min, determine (a) the inside diameters at the top and bottom of the tubing if the total weight of the final casting = 15kg?.
Vertical true centrifugal casting is used to cast aluminum tubing that is 40cm in long with outside diameter = 22cm. density of aluminum = 2.7 g/cm^3. if the speed of rotation during solidfication is 900 rev/min, determine (a) the inside diameters at the top and bottom of the tubing if the total weight of the final casting = 15kg? 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 Vertical true centrifugal casting is used to cast aluminum tubing that is 40cm in long with outside diameter = 22cm. density of aluminum = 2.7 g/cm^3. if the speed of rotation during solidfication is 900 rev/min, determine (a) the inside diameters at the top and bottom of the tubing if the total weight of the final casting = 15kg? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Vertical true centrifugal casting is used to cast aluminum tubing that is 40cm in long with outside diameter = 22cm. density of aluminum = 2.7 g/cm^3. if the speed of rotation during solidfication is 900 rev/min, determine (a) the inside diameters at the top and bottom of the tubing if the total weight of the final casting = 15kg?.
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Vertical true centrifugal casting is used to cast aluminum tubing that is 40cm in long with outside diameter = 22cm. density of aluminum = 2.7 g/cm^3. if the speed of rotation during solidfication is 900 rev/min, determine (a) the inside diameters at the top and bottom of the tubing if the total weight of the final casting = 15kg?, a detailed solution for Vertical true centrifugal casting is used to cast aluminum tubing that is 40cm in long with outside diameter = 22cm. density of aluminum = 2.7 g/cm^3. if the speed of rotation during solidfication is 900 rev/min, determine (a) the inside diameters at the top and bottom of the tubing if the total weight of the final casting = 15kg? has been provided alongside types of Vertical true centrifugal casting is used to cast aluminum tubing that is 40cm in long with outside diameter = 22cm. density of aluminum = 2.7 g/cm^3. if the speed of rotation during solidfication is 900 rev/min, determine (a) the inside diameters at the top and bottom of the tubing if the total weight of the final casting = 15kg? theory, EduRev gives you an
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