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A cylinder vessel of 35 cm internal diameter is required to withstand 0.8 N/mm pressure. If the cylinder cover is held by 8 studs, find the size of the studs. The tensile stress of the material of the studs is 30N/mm?
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A cylinder vessel of 35 cm internal diameter is required to withstand ...
Problem Statement:
A cylinder vessel with a 35 cm internal diameter needs to withstand a pressure of 0.8 N/mm. The cylinder cover is held by 8 studs. The tensile stress of the stud material is 30 N/mm. Determine the size of the studs.
Solution:
To find the size of the studs, we need to calculate the force exerted on each stud and then determine the diameter of the studs required to withstand this force.
Step 1: Calculate the Force Exerted on each Stud
The force exerted on each stud can be calculated by considering the pressure acting on the cylinder cover.
Given:
Internal diameter of the cylinder (D) = 35 cm = 350 mm
Pressure acting on the cylinder (P) = 0.8 N/mm
The force exerted on the cylinder cover (F) can be calculated using the formula:
F = P * A
where A is the area of the cylinder cover.
The area of the cylinder cover (A) can be calculated using the formula:
A = π * r^2
where r is the radius of the cylinder cover.
The radius of the cylinder cover (r) can be calculated as half of the internal diameter:
r = D/2
Substituting the values, we get:
r = 350/2 = 175 mm
Therefore, the area of the cylinder cover (A) is:
A = π * (175)^2 = 96246.842 mm^2
Now, substituting the values into the formula for force (F), we get:
F = 0.8 * 96246.842 = 76997.474 N
The force exerted on each stud is equal to the total force divided by the number of studs:
Force on each stud = F/8 = 76997.474/8 = 9624.684 N
Step 2: Determine the Diameter of the Studs
The diameter of the studs required to withstand the force can be calculated using the tensile stress of the stud material.
Given:
Tensile stress of the stud material (σ) = 30 N/mm
The formula for tensile stress is:
σ = F/A
where A is the cross-sectional area of the stud.
The cross-sectional area of the stud (A) can be calculated using the formula:
A = π * (d/2)^2
where d is the diameter of the stud.
Rearranging the formula for tensile stress and substituting the values, we get:
d = √(4F/(πσ))
Substituting the values, we get:
d = √(4 * 9624.684/(π * 30)) = √102.496 = 10.123 mm
Therefore, the required size of the studs to withstand the given pressure is approximately 10.123 mm in diameter.
A cylinder vessel with a 35 cm internal diameter needs to withstand a pressure of 0.8 N/mm. The cylinder cover is held by 8 studs. The tensile stress of the stud material is 30 N/mm. Determine the size of the studs.
Solution:
To find the size of the studs, we need to calculate the force exerted on each stud and then determine the diameter of the studs required to withstand this force.
Step 1: Calculate the Force Exerted on each Stud
The force exerted on each stud can be calculated by considering the pressure acting on the cylinder cover.
Given:
Internal diameter of the cylinder (D) = 35 cm = 350 mm
Pressure acting on the cylinder (P) = 0.8 N/mm
The force exerted on the cylinder cover (F) can be calculated using the formula:
F = P * A
where A is the area of the cylinder cover.
The area of the cylinder cover (A) can be calculated using the formula:
A = π * r^2
where r is the radius of the cylinder cover.
The radius of the cylinder cover (r) can be calculated as half of the internal diameter:
r = D/2
Substituting the values, we get:
r = 350/2 = 175 mm
Therefore, the area of the cylinder cover (A) is:
A = π * (175)^2 = 96246.842 mm^2
Now, substituting the values into the formula for force (F), we get:
F = 0.8 * 96246.842 = 76997.474 N
The force exerted on each stud is equal to the total force divided by the number of studs:
Force on each stud = F/8 = 76997.474/8 = 9624.684 N
Step 2: Determine the Diameter of the Studs
The diameter of the studs required to withstand the force can be calculated using the tensile stress of the stud material.
Given:
Tensile stress of the stud material (σ) = 30 N/mm
The formula for tensile stress is:
σ = F/A
where A is the cross-sectional area of the stud.
The cross-sectional area of the stud (A) can be calculated using the formula:
A = π * (d/2)^2
where d is the diameter of the stud.
Rearranging the formula for tensile stress and substituting the values, we get:
d = √(4F/(πσ))
Substituting the values, we get:
d = √(4 * 9624.684/(π * 30)) = √102.496 = 10.123 mm
Therefore, the required size of the studs to withstand the given pressure is approximately 10.123 mm in diameter.
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A cylinder vessel of 35 cm internal diameter is required to withstand 0.8 N/mm pressure. If the cylinder cover is held by 8 studs, find the size of the studs. The tensile stress of the material of the studs is 30N/mm?
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A cylinder vessel of 35 cm internal diameter is required to withstand 0.8 N/mm pressure. If the cylinder cover is held by 8 studs, find the size of the studs. The tensile stress of the material of the studs is 30N/mm? 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 A cylinder vessel of 35 cm internal diameter is required to withstand 0.8 N/mm pressure. If the cylinder cover is held by 8 studs, find the size of the studs. The tensile stress of the material of the studs is 30N/mm? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylinder vessel of 35 cm internal diameter is required to withstand 0.8 N/mm pressure. If the cylinder cover is held by 8 studs, find the size of the studs. The tensile stress of the material of the studs is 30N/mm?.
A cylinder vessel of 35 cm internal diameter is required to withstand 0.8 N/mm pressure. If the cylinder cover is held by 8 studs, find the size of the studs. The tensile stress of the material of the studs is 30N/mm? 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 A cylinder vessel of 35 cm internal diameter is required to withstand 0.8 N/mm pressure. If the cylinder cover is held by 8 studs, find the size of the studs. The tensile stress of the material of the studs is 30N/mm? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylinder vessel of 35 cm internal diameter is required to withstand 0.8 N/mm pressure. If the cylinder cover is held by 8 studs, find the size of the studs. The tensile stress of the material of the studs is 30N/mm?.
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