Kinematic viscosity v of water varies with the temperature T in the following manner: T (C) 21.1 37.8 54.4 71.1 87.8 100 v (10-3 m2/s) 1.79 1.13 0.696 0.519 0.338 0.321 0.296 a. Fit the data using a cubic spline and generate a labeled plot of the data and fit. b. Using cubic spline, interpolate v for T = [10 30 60 90] C. c. Using a 2nd order Newton Interpolating polynomial, interpolate v for same temperatures. d. Using a 2nd order Lagrange interpolating polynomial, interpolate v for same temperatures. e. If the dynamic viscosity u (kg/m-s) is related to the kinematic viscosity by: v = /p Calculate the dynamic viscosity for p = [999.7, 999.6, 983.3, 965.3] kg/m3. The values of density of water correspond for T= [10 30 60 90] C, respectively. Use the values obtained from the cubic spline for the calculations. a. Calculate the shear stress (Pa) for a flat plate if the shear stress for a Newtonian fluid is: 1 = H(V/h) where V= 30 m/s and h = 0.05m