Read section 17.4 in the textbook. The drag coefficient for spheres, such as sporting balls, is known to vary as a function of the Reynolds number Re, a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces:

Re = ?VD/?

where ? = the fluids density (kg/m^3), V = its velocity (m/s), D = diameter (m) of the ball, and ? = dynamic viscosity (Ns/m^2) of the fluid. The following table provides values for a smooth spherical ball:

Re (10^-4) 2 5.8 16.8 27.2 29.9 33.9

C_D 0.52 0.51 0.505 0.5 0.49 0.44

Re (10^-4) 36.3 40 46 60 100 200 400

C_D 0.18 0.074 0.067 0.038 0.012 0.01 0.005

Develop a MATLAB function that employs piecewise cubic spline interpolation with not-a-knot end conditions to return the value of the Reynolds number for which C_D is a specified value from input. Note: here you are given C_D and you are tasked to find Re, the opposite of Chapra Prob 18.13.

Note: Simply switching the Re and C_D data will not solve the problem correctly. You must recast it as a root-finding problem, and find the value of Re that makes the function y = spline(ReNo,C_D,x)-CD evaluate to zero, where CD is the input drag coefficient value.

Given Code need Matlab function

function Re = Chapra_18p13(CD)

%% Input

% CD: Drag Coeff Value (vector)

%

%% Output

% Re: Corresponding Reynolds Number (vector)

%% Write your code here.

end