# Numerical - Sommerfeld number, given - journal speed, radial clearance, viscosity & diameter

Q.  Determine the Sommerfeld number considering the following data for hydrodynamic bearing?
1. Diameter of bearing = 120 mm
2. Bearing pressure = 5 N/mm2
3. Oil viscosity = 30 cP
4. Journal speed = 900 rpm
5. Radial clearance = 150 microns

- Published on 19 Oct 15

a. 0.2360
b. 0.0144
c. 0.0115
d. 0.0178

#### Discussion

• Sravanthi   -Posted on 05 Oct 15
Given: Diameter of bearing = 120 mm, Bearing pressure = 5 N/mm2, Oil viscosity = 30 cP = 30 x 10-9 N-s / mm2,
Journal speed = 900 rpm = 900 / 60 = 15, Radial clearance = 150 microns = 0.15 mm

Sommerfeld number is a dimensionless parameter used by Raimondi and Boyd for studying relations of variables.
Sommerfeld number is also called as bearing characteristic number.

Sommerfeld number is given by
S = (r/c)2 (μns / p)

here,
S = Sommerfeld number
p = bearing pressure
ns = speed of rotating shaft (rev/s)
μ = oil viscosity

Substituting the given values we get,

S = (r/c)2 (μns / p)
S = (60 / 0.15)2 ( 30 x 10-9 x 15/ 5)
S = 0.0144

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