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A full journal bearing have clearance to radius ratio of 1/200. The lubricant with μ = 40 X 10-3 Pa-s supports the shaft journal running at 3000 rpm. If the bearing pressure is 1.5 MPa, the Sommerfeld’s number is
  • a)
    5.3 x 106
  • b)
    0.053
  • c)
    3.33 x 10-11
  • d)
    0.53
Correct answer is option 'B'. Can you explain this answer?
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A full journal bearing have clearance to radius ratio of 1/200. The l...
= 0.053
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A full journal bearing have clearance to radius ratio of 1/200. The l...
Given data:

Clearance to radius ratio: ε = 1/200

Viscosity of lubricant: μ = 40 x 10^-3 Pa-s

Shaft speed: N = 3000 rpm

Bearing pressure: P = 1.5 MPa

To find: Sommerfeld’s number

Formula used:

Sommerfeld’s number, S = (Pd)/(μN)

Where d is the diameter of the bearing

Solution:

Radius of the bearing, R = d/2

Clearance, c = εR

= (1/200) x R

= R/200

Therefore, the diameter of the bearing, d = 2R = 400c

Speed of the bearing, ω = 2πN/60

= 2π x 3000/60

= 314.16 rad/s

Using the formula for Sommerfeld’s number,

S = (Pd)/(μN)

= (1.5 x 10^6) x (400c) / (40 x 10^-3) x 314.16

= 0.053

Therefore, the Sommerfeld’s number is 0.053, which is option B.

Conclusion:

The Sommerfeld’s number is a dimensionless parameter that is used to characterize the performance of journal bearings. In this question, we have used the formula for Sommerfeld’s number to find the value of S for a full journal bearing. The correct answer is option B, 0.053.
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A full journal bearing have clearance to radius ratio of 1/200. The lubricant with μ = 40 X 10-3 Pa-s supports the shaft journal running at 3000 rpm. If the bearing pressure is 1.5 MPa, the Sommerfeld’s number isa) 5.3 x 106b) 0.053c) 3.33 x 10-11d) 0.53Correct answer is option 'B'. Can you explain this answer?
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A full journal bearing have clearance to radius ratio of 1/200. The lubricant with μ = 40 X 10-3 Pa-s supports the shaft journal running at 3000 rpm. If the bearing pressure is 1.5 MPa, the Sommerfeld’s number isa) 5.3 x 106b) 0.053c) 3.33 x 10-11d) 0.53Correct answer is option 'B'. 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 full journal bearing have clearance to radius ratio of 1/200. The lubricant with μ = 40 X 10-3 Pa-s supports the shaft journal running at 3000 rpm. If the bearing pressure is 1.5 MPa, the Sommerfeld’s number isa) 5.3 x 106b) 0.053c) 3.33 x 10-11d) 0.53Correct answer is option 'B'. 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 full journal bearing have clearance to radius ratio of 1/200. The lubricant with μ = 40 X 10-3 Pa-s supports the shaft journal running at 3000 rpm. If the bearing pressure is 1.5 MPa, the Sommerfeld’s number isa) 5.3 x 106b) 0.053c) 3.33 x 10-11d) 0.53Correct answer is option 'B'. Can you explain this answer?.
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