Question

Sommerfeld number consists of parameters

• A. Viscosity, speed, load, bearing length and clearance
• B. Viscosity, speed, journal radius, pressure, and clearance
• C. Viscosity, speed, bearing length, clearance and oil temperature
• D. Journal radius, bearing length, pressure, surface roughness, and clearance

Hint:

The Sommerfeld number \( S = \left(\frac{r}{c}\right)^2 \frac{\mu N}{P} \) is used to analyze hydrodynamic bearings, involving viscosity, speed, radius, pressure, and clearance.

Answer 1

The Correct Option is B

Step 1: Understand the Sommerfeld number.
The Sommerfeld number (also called the bearing characteristic number) is a dimensionless quantity used in the design of hydrodynamic journal bearings to characterize the bearing's performance under specific operating conditions. Step 2: Recall the formula for the Sommerfeld number.
The Sommerfeld number \( S \) is defined as: \[ S = \left(\frac{r}{c}\right)^2 \frac{\mu N}{P}, \] where:
\( r \) = journal radius,
\( c \) = radial clearance (\( c = r_{\text{bearing}} - r_{\text{journal}} \)),
\( \mu \) = viscosity of the lubricant,
\( N \) = rotational speed (in revolutions per second),
\( P \) = pressure, defined as the load per unit projected area (\( P = \frac{W}{L \cdot D} \), where \( W \) is the load, \( L \) is the bearing length, and \( D = 2r \) is the diameter).
Thus, the parameters involved are:
Viscosity (\( \mu \)),
Speed (\( N \)),
Journal radius (\( r \)),
Pressure (\( P \), which incorporates the load),
Clearance (\( c \)).
Step 3: Evaluate the options.
(1) Viscosity, speed, load, bearing length, and clearance: Load and bearing length are used to calculate pressure, but pressure is the direct parameter in the Sommerfeld number, not load and length separately. Incorrect.
(2) Viscosity, speed, journal radius, pressure, and clearance: Matches the parameters in the formula. Correct.
(3) Viscosity, speed, bearing length, clearance, and oil temperature: Bearing length is not directly in the Sommerfeld number (it's part of pressure), and oil temperature affects viscosity but is not a direct parameter. Incorrect.
(4) Journal radius, bearing length, pressure, surface roughness, and clearance: Surface roughness is not part of the Sommerfeld number, and bearing length is not a direct parameter. Incorrect. Step 4: Select the correct answer.
The Sommerfeld number consists of viscosity, speed, journal radius, pressure, and clearance, matching option (2).