CODo jul pgall to be certain that it is working properly. To this end, input a simple function to which the roots are known analytically and make certain that the program gives the proper value of the root. Substitute the root into the function to check that f(xr0 Engineering Problem In fluid mechanics, a non-dimensional friction factor z is used to compute the head loss due to fluid friction (viscosity) within the flow. It depends on two non-dimensional parameters: the flow Reynolds' number Re and the relative surface roughness of the pipe e/D. The Colebrook expression is commonly used to relate a to Re and e/D =-2.0 log 2.0 log (37 e/D 2.51 3.7 Revx + 2.51 ) This expression is valid for approximately 0 r 0.05, 2300 Perform the following: Re s 1x 108, and 0 Se/D s o.05. 1. Use the intrinsic MATLAB command logspace to create a vector of values for Re that spans the range 1 10's Re 1x 108 and minimally contains 100 values. The logspace command is analogous to the linspace command used for linear spacing and is necessary because Re varies by several orders-of-magnitude (i.e., decades). You can obtain more information about this command by typing help logspace at the MATLAB command prompt