This topic is under programming (science & engineering) by using MATLAB. Please answer the following question by using MATLAB software. Thank you.

12. As you will soon learn in Engineering Fluid Mechanics, for the fluid flow in a pipe, the frictional resistance is represented by the non-dimensional number called a friction factor. For turbulent flows, this friction factor is obtained by solving the following equation 1 = 0, 2.51 81= + 2.0 log 3.7D Ref where e is the roughness, D is the diamter of the pipe and Re is the Reynolds number given by PVD Re. where p is the density of fluid, V is the velocity of the fluid in the pipe and p is the dynamic viscosity. (a) For the case of air flow in a circular duet with D = 0.005 m, V = 40 m/s, p = 1.23 kg/m, u = 1.79x 10-5 Ns/mande = 0.0015 m, plot g() over 0.01 s f 30.08. To ease what follows next, define g() using an anonymous function. (b) Based on the figure you obtained above for Part (a), suggest values for a and b that are appropriate for a bisection method. (c) Using a and b, compute the root of g(f) within a tolerance of 10-12. (d) (Optional) Save the error in the estimate during each iteration of the while loop in an array. Plot the error vs. the iteration number on a log scale (loglog command would be helpful). What can you conclude about the rate of convergence of the bisection method