1. Qs. 1 on VI
The coefficient of dynamic viscosity values for a high grade oil and a low grade oil at 40 oC are 15 cp and 60 cp respectively. It is required to determine the viscosity index (VI) of an oil having a viscosity value of 25 cp (centipoise) at 40 oC. The test and reference oils have the same viscosity values at 100 oC. Determine the VI of the test oil using the Dean Davis method.
Step 1. Check whether the viscosity of the test oil at 40 oC (U) is in between those of the high grade oil (H) and low grade oil (L) or not.
We see that L = 60 cp, H = 15 cp, and U = 25 cp, H < U < L
Therefore we can use the formula,
=[(60-25)/(60-15)]x100 = 77.77

2. Practise qs. 2 on tilting pad brg.
The following figure shows a bearing undergoing hydrodynamic lubrication. Reynold’s equation in 1 dimension gives the pressure (p) drop in the x-direction as
Find the pressure drop in the x direction when the height of separation “h” is 0.5 mm. Calculate the flow rate in the x direction given its formula per unit width as
Given: U = 20 cm/s, coefficient of dynamic viscosity h = 40 cp. The distance of separation at maximum pressure ho is 0.4 mm. There is negligible flow in other directions.
Upper surface is stationary h
Bottom surface moves with velocity U x
Oil wedge

3. Soln. The coefficient of dynamic viscosity = 40 cp = 40 x 0.001 Pa.s
Therefore
= 3.84 x 104 Pa/m
Rate of flow
=4.0016x10-8 m3/s = cm3/s

4. Width of bearing B = 50 mm
L/B = 1
Sliding velocity = 5 m/s
Min. film thickness = 0.02 mm
Viscosity = 0.02 Pa.s
Attitude K = 2.0
Find load, friction and coefficient of friction

5. Solution
Coefficient of friction = F/W = 8.861/4.5x10-3 =

6. Prob. Temperature rise in tilting pad brg.
-What is the temperature rise in the oil for the previous problem. Density of the oil = 880 kg/m3, specific heat capacity = 1900 J/kg.K
Mechanical equivalent of heat = 1 J heat per 1 joule of friction energy since we are using SI units throughout

7. Journal dia. = 100 mm
L/D = 1
Radial clearance = mm
Journal speed = 3000 rpm
Eccentricity ratio = 0.6
Viscosity = 0.02 Pa.s
Find attitude angle, load, friction and coefficient of friction for Sommerfeld’s half condition and narrow brg. theory

8. Sommerfelds half condition
Narrow brg.

9. Sommerfeld’s half condition
Friction coefficient

10. Narrow bearing
Therefore

11. Prob. Viscosity and friction for tilting pad brg.
A tilting pad slider bearing has the following operation parameters
Angle of inclination = 0.4o
Leading edge height = 0.75 mm
Trailing edge ht. = 0.25 mm
Load to be carried = 6000 N
Sliding speed = 2.5 m/s
Bearing length L = 8 cm
Bearing width B = 7.5 cm
Calculate the viscosity of the oil required to operate under these conditions and friction at the two surfaces =

12. K=2, W* =
h = 0.055/ = Pa.s