What can students learn while solving Colebrook's flow friction equation?

Abstract

Even a relatively simple equation such as Colebrook's offers a lot of possibilities to students to increase their computational skills. The Colebrook's equation is implicit in the flow friction factor and, therefore, it needs to be solved iteratively or using explicit approximations, which need to be developed using different approaches. Various procedures can be used for iterative methods, such as single the fixed-point iterative method, Newton-Raphson, and other types of multi-point iterative methods, iterative methods in a combination with Pade polynomials, special functions such as Lambert W, artificial intelligence such as neural networks, etc. In addition, to develop explicit approximations or to improve their accuracy, regression analysis, genetic algorithms, and curve fitting techniques can be used too. In this learning numerical exercise, a few numerical examples will be shown along with the explanation of the estimated pedagogical impact for university students. Students can see what the difference is between the classical vs. floating-point algebra used in computers.