Question

A 5 kN external load is applied to a square hydrodynamic bearing. The journal speed and diameter are 1000 rpm and 50 mm respectively. Sommerfeld number correspoding to following data is

Diameter clearance = $50\mu m$

Viscosity = 11.62 centipoise

• A. 1.096833
• B. 3.292103
• C. 2.106833
• D. 0.096833

Answer 1

The correct option is D 0.096833

Sommerfeld number, S = ${\left(\frac{D}{C}\right)}^2\frac{Zn}{P}$

Pressure, P = $\frac{W}{LD}=\frac{5\times {10}^3}{0.05\times 0.05}=2\times {10}^{6}Pa$

$Z=\frac{11.62}{100}\times \frac{1}{10}=0.01162Ns/m^2$

So, $S={\left(\frac{0.05}{50\times {10}^{-6}}\right)}^2\times \frac{0.01162\times 1000}{60\times 2\times {10}^6}$

S = 0.096833