Table 1: Kinematic viscosity of SAE 30 oil
temperature, T (C) viscosity, µ (m2 /sec)
1
2.5e-3
20
5.5e-4
40
1e-4
60
5e-5
80
2e-5
100
1.2e-5
120
6e-6
Homework 6
Problem 1
The kinematic viscosity of SAE 30 oil with variation in temperature was found to be as
those in table 1. Find a relationship between the two parameters of the following form:
µ = a exp(b/T ).
Problem 2
Derive linear least-squares regression procedure with multiple variables. Assume the data
points
(x1,i , x2,i , . . . , xn,i , yi )
i = 1, 2, . . . , m given. Apply your result to the following problem.
The efficiency (η) of a gear pump with volumetric flow rate of the fluid v and the pressure
of the fluid p varies as described in table 2. Develop a linear relationship between the variables
p, v and η.
Problem 3
Find Newton interpolating polynomial for the data shown in the table. 3
1
Table 2: The efficiency of a reaction turbine
v (gallons/min) p (psig) η
42
3000
83
53
3000
86
58
3000
88
36
2000
83
46
2000
86
57
2000
88
49
1000
83
65
1000
86
Table 3: Table
x
f(x)
1
3
3/2 13/4
0
3
2
5/3
2