Implement the pipe friction problem described in Sec 8.4 using MATLAB. Show your implementation of roots or fzero function and the output.

8.4 PIPE FRICTION (MECHANICAL/AEROSPACE ENGINEERING Background. Determining fluid ow through pipes and tubes has great relevance in many areas of engineering and science. In mecharical and aerospace engineering, typical applications include the fow of liquids and gases through cooling systems The resistance to ow in such conduits is parameterized by a dimensionless number fow, the Colebrook equation provides a means called the friction factor. For turbule to calculate the friction factor, 0 2.0 log 8.21) D Rev where -the roughness (m), D-diameter (m), and Re-the Reynolds number Re-VD where -the fluid's density (kg/m3), V-its velocity (ms), and -dynamic viscos- ity (N /m). In addition to appearing in Eq. (821), the Reynods number aso serves as the criterion for whether low is turbulent (Re4000). In the present case study, we will trate how the mumerical methods covered in this part of the book can be employed to determine f for air how through a smooth, hin tube For this case, the parameters are -1.23 kg/m. -1.79 10 5 N , stn, D-0.005 m, V-40 ms, and0.0015 mm. Nole that fricion factors range from about 0.008 o0.08. In addiion, an explicit fomulation called the Swamee-Jain equation provides an approxi- mate estimate 1.325 (8.22) 60 2 3.D Re The Reynolds number can be computed as VD 1.23(40000 13,743 Solution. 1.79 x 10 This value along with the other parameters can be substituted into Eq. (8.21) to give 2.0 logf0.000001S2.51 3.7(0.00s) 13,743V Before deermining the o is advisable to plo the function to estimate initial guesses and to anticipate possible difliculties. This can be done easily with tools such 3H 0.01 0.02 0.03 004 0.05 0.06 007 048