Solution of the Colebrook Equation

Project I Introduce a counter into our m file colebrookplotsolve. m, which finds the number of function evaluations performed in the first 10 lines of the code when trying to find an inclusion interval for the solution / of the Colebrook equation. 

Example 1.1 Solution of the Colebrook Equation by Successive Substitution, Linear Interpolation, and Newton Raph on Methods. Develop MATLAB functions to solve nonlinear equations by the successive substitution method, the linear interpolation, and the Newton-Raphson root-finding techniques. Use these functions to calculate the friction factor from the Colebrook equation [Eq. (1.4)] for flow of a fluid in a pipe with e/Z> =10 and Njf, = 10. Compare these methods with each other. 

The MATLAB program Example ].m finds the friction factor from the Colebrook equation by three different methods of root finding. The program first asks the user to input the values for and e/D. It then asks for the method of solution of the Colebrook equation, name of the m-file that contains the Colebrook equation, and the initial value(s) to start the method. The program then calculates the fiiction factor by the selected method and continues asking for the method of solution until the user enters 0. 

Note that the terra e/D is the relative roughness from Figure 2-11. The solution of the above equation is trial and error. Colebrook [6] also proposed a direct solution equation that is reported [7] to have... 

Values of k and k for various polymer/tube systems are given in Table 5.10. (Values of k and ki can be determined for a given polymer solution from laboratory measurements of pressure drop in smooth tubes at two flow rates in the turbulent range.) These values can be used with the model to predict friction loss for that solution at any Reynolds number in any size pipe. If the Colebrook equation for smooth tubes is used, the appropriate generalized expression for the friction factor is... 

Chen, J. J. J., Systematic Explicit Solutions of the Prandtl and Colebrook-White Equations for Pipe flow, Proc. Instn. Civ. Engrs, 79, 383-389 (1985). 

---