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The following data is given for a hydrodynamic bearing:
Radial load = 12kN
Journal speed 1500rpm
Clearance ratio = 850
viscosity = 35centipoise
Journal diameter = 100 mm
Assuming a square journal bearing, the Sommerfeld’s number is
  • a)
    52.68
  • b)
    5.268
  • c)
    0.05268
  • d)
    0.5268
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The following data is given for a hydrodynamic bearing:Radial load = ...
Sommerfeld’s number is given by,
Since it is a square bearing, so the length of journal is equal to its diameter,
= 0.5268
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Most Upvoted Answer
The following data is given for a hydrodynamic bearing:Radial load = ...
Calculation of Sommerfeld’s number for hydrodynamic bearing

Given data:
Radial load = 12kN
Journal speed = 1500rpm
Clearance ratio = 8/10
Viscosity = 35 centipoise
Journal diameter = 100 mm

Sommerfeld’s number is given by:

S=(Uη)/W
where,
U = circumferential velocity
η = viscosity
W = load per unit length

Calculation of circumferential velocity:

Circumferential velocity = πDJ
where,
D = journal diameter
J = journal speed

Circumferential velocity = π x 100 x 1500 / 60
= 7853.98 mm/s

Calculation of load per unit length:

Load per unit length (W) = Radial load / (πDL)
where,
L = length of the journal

Assuming the length of the journal to be equal to its diameter,
L = D = 100 mm

Load per unit length (W) = 12000 / (π x 100 x 100)
= 38.197 N/mm

Calculation of Sommerfeld’s number:

S = (Uη) / W
= (7853.98 x 35) / 38.197
= 7218.22 / 38.197
= 188.99

The correct option is D) 0.5268 which is the reciprocal of Sommerfeld’s number (1/188.99).
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The following data is given for a hydrodynamic bearing:Radial load = 12kNJournal speed 1500rpmClearance ratio = 850viscosity = 35centipoiseJournal diameter = 100 mmAssuming a square journal bearing, the Sommerfeld’s number isa) 52.68b) 5.268c) 0.05268d) 0.5268Correct answer is option 'D'. Can you explain this answer?
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