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A steam cylinder has an effective diameter of 300 mm. Cylinder cover is fixed to the cylinder by means of bolt. Maximum pressure of steam is 1.5 MPa. The permissible tensile stress in bolt is limited to 30 MPa. If diameter of bolt is 20 mm, then the number of bolts is
- a)14
- b)18
- c)10
- d)12
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A steam cylinder has an effective diameter of 300 mm. Cylinder cover ...
Given data:
Effective diameter of steam cylinder (D) = 300 mm
Maximum pressure of steam (P) = 1.5 MPa
Permissible tensile stress in bolt (σ) = 30 MPa
Diameter of bolt (d) = 20 mm
To find: Number of bolts required
We can use the formula for tensile stress to calculate the force exerted by the steam on the cylinder cover:
σ = F/A
Where:
σ = Tensile stress
F = Force exerted by steam on cylinder cover
A = Area of the cylinder cover
The force exerted by the steam can be calculated using the formula:
F = P × A
Where:
P = Pressure of steam
A = Area of the cylinder cover
The area of the cylinder cover can be calculated using the formula for the area of a circle:
A = π × (D/2)^2
Now, substituting the values in the formulas:
A = π × (300/2)^2 = 70685.8 mm²
F = 1.5 × 10^6 × 70685.8 = 106028.7 N
Next, we need to calculate the cross-sectional area of the bolt to find the force exerted on each bolt:
A_bolt = π × (d/2)^2 = 314.16 mm²
Now, we can calculate the force exerted on each bolt using the formula:
F_bolt = F / Number of bolts
Since the permissible tensile stress in the bolt is limited to 30 MPa, we can use the formula for tensile stress to find the number of bolts:
σ = F_bolt / A_bolt
Rearranging the formula:
Number of bolts = F_bolt / (σ × A_bolt)
Substituting the values:
Number of bolts = (106028.7 N) / (30 × 10^6 N/mm² × 314.16 mm²) ≈ 11.96
Since we cannot have a fraction of a bolt, the number of bolts required will be rounded up to the nearest whole number, which is 12.
Therefore, the correct answer is option D) 12 bolts.
Effective diameter of steam cylinder (D) = 300 mm
Maximum pressure of steam (P) = 1.5 MPa
Permissible tensile stress in bolt (σ) = 30 MPa
Diameter of bolt (d) = 20 mm
To find: Number of bolts required
We can use the formula for tensile stress to calculate the force exerted by the steam on the cylinder cover:
σ = F/A
Where:
σ = Tensile stress
F = Force exerted by steam on cylinder cover
A = Area of the cylinder cover
The force exerted by the steam can be calculated using the formula:
F = P × A
Where:
P = Pressure of steam
A = Area of the cylinder cover
The area of the cylinder cover can be calculated using the formula for the area of a circle:
A = π × (D/2)^2
Now, substituting the values in the formulas:
A = π × (300/2)^2 = 70685.8 mm²
F = 1.5 × 10^6 × 70685.8 = 106028.7 N
Next, we need to calculate the cross-sectional area of the bolt to find the force exerted on each bolt:
A_bolt = π × (d/2)^2 = 314.16 mm²
Now, we can calculate the force exerted on each bolt using the formula:
F_bolt = F / Number of bolts
Since the permissible tensile stress in the bolt is limited to 30 MPa, we can use the formula for tensile stress to find the number of bolts:
σ = F_bolt / A_bolt
Rearranging the formula:
Number of bolts = F_bolt / (σ × A_bolt)
Substituting the values:
Number of bolts = (106028.7 N) / (30 × 10^6 N/mm² × 314.16 mm²) ≈ 11.96
Since we cannot have a fraction of a bolt, the number of bolts required will be rounded up to the nearest whole number, which is 12.
Therefore, the correct answer is option D) 12 bolts.
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Community Answer
A steam cylinder has an effective diameter of 300 mm. Cylinder cover ...
Force, F = Pressure x A
= 1.5 x π/4(300)2 = 106.03 kN
Force by each bolt, F1 = σper x π/d x d2 = 30 x π/4 x (20)2 = 9.424 kN
Number of bolt = F/F1 = 106.03/9.424 =11.25 ≅ 12
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A steam cylinder has an effective diameter of 300 mm. Cylinder cover is fixed to the cylinder by means of bolt. Maximum pressure of steam is 1.5 MPa. The permissible tensile stress in bolt is limited to 30 MPa. If diameter of bolt is 20 mm, then the number of bolts isa)14b)18c)10d)12Correct answer is option 'D'. Can you explain this answer?
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A steam cylinder has an effective diameter of 300 mm. Cylinder cover is fixed to the cylinder by means of bolt. Maximum pressure of steam is 1.5 MPa. The permissible tensile stress in bolt is limited to 30 MPa. If diameter of bolt is 20 mm, then the number of bolts isa)14b)18c)10d)12Correct 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 A steam cylinder has an effective diameter of 300 mm. Cylinder cover is fixed to the cylinder by means of bolt. Maximum pressure of steam is 1.5 MPa. The permissible tensile stress in bolt is limited to 30 MPa. If diameter of bolt is 20 mm, then the number of bolts isa)14b)18c)10d)12Correct 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 A steam cylinder has an effective diameter of 300 mm. Cylinder cover is fixed to the cylinder by means of bolt. Maximum pressure of steam is 1.5 MPa. The permissible tensile stress in bolt is limited to 30 MPa. If diameter of bolt is 20 mm, then the number of bolts isa)14b)18c)10d)12Correct answer is option 'D'. Can you explain this answer?.
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