1) An important fluid property is the kinematic viscosity which determines the viscous, or frictional, forces acting in a flow. The kinematic viscosity of air multiplied by 10^6 is given at 350, 450, 500, 550, and 650 K as 20.92,32.39, 38.79, 45.57, and 60.21 m^2/s, respectively. Using any suitable interpolation method, compute the intermediate values at 400 and 600 K. Compare the results obtained with the values given in the literature as 26.41 x 10^-6 m^2/s and 52.69 x 10^6 m^2/s, respectfully. Also, solve the problem using the interpl command in MATLAB and compare the results with those obtained earlier. Use the cubic spline method as well.
2)The acceleration of certain objects is studied in an experimental test track for automobiles. The distance traveled by an object L is measured as a function of time t to yield the following:
|
t(s) |
0.1 |
0.2 |
0.5 |
1.0 |
1.5 |
1.8 |
2.0 |
3.0 |
|
L(m) |
0.26 |
0.55 |
1.56 |
3.90 |
7.41 |
10.28 |
12.6 |
30.9 |
Obtain a best fit to this data, considering first-,second, and third-order polynomials. Using these polynomials, calculate the values of the dependent variable L at the time intervals employed for the given data to evaluate the accuracy of the polynomial representations. Discuss the results obtained.
3) The temperature T of a small copper sphere cooling in air is measured as a function of time t to yield the following:
|
t(s) |
0.2 |
0.6 |
1.0 |
1.8 |
2.0 |
3.0 |
5.0 |
6,0 |
8.0 |
|
T(C) |
146.0 |
129.5 |
114.8 |
90.3 |
85.1 |
63.0 |
34.6 |
25.6 |
14.1 |
An exponential temperature decrease is expected from theoretical considerations. Using linear regression, obtain the exponent c and the constant C, where
T=Ce^(-ct) represents the variation. Also, solve this problem using the polyfit function in MATLAB.
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