Engr Help

Viscosity

Example 1 A 25 mm diameter shaft is pulled through a cylindrical bearing as shown below.

The lubricant that fills the 0.33 mm gap between the shaft and the bearing is an oil having

a kinematic viscosity, ν = 8.0 x 10^-8 m²/sec and a specific gravity, SG = 0.91. Find the force

P required to pull the shaft at a constant speed of 3 m/sec. Assume the velocity distribution

in the gap is linear. Length of the shaft, L, is 0.5 m.

Strategy:

Step 1	Calculate the shear stress in the gap.
Step 2	Calculate the shear force exerted by the lubricant on the shaft
Step 3	For equilibrium the applied force must balance the shear force.

The figure below shows an enlarged view of the gap, b, with the linear velocity distribution.

The velocity distribution is V(y) = V_o (1 – y/b) where b is the gap width and V_o is the

constant velocity of the shaft.