What Can Students Learn While Solving Colebrook’s Flow Friction Equation?
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 approximati...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-06-01
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| Series: | Fluids |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2311-5521/4/3/114 |
| _version_ | 1818302053211963392 |
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| author | Dejan Brkić Pavel Praks |
| author_facet | Dejan Brkić Pavel Praks |
| author_sort | Dejan Brkić |
| collection | DOAJ |
| description | 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 Padé 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. |
| first_indexed | 2024-12-13T05:32:47Z |
| format | Article |
| id | doaj.art-8ae21f61565a47a9a06795c263870d73 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-12-13T05:32:47Z |
| publishDate | 2019-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-8ae21f61565a47a9a06795c263870d732022-12-21T23:58:02ZengMDPI AGFluids2311-55212019-06-014311410.3390/fluids4030114fluids4030114What Can Students Learn While Solving Colebrook’s Flow Friction Equation?Dejan Brkić0Pavel Praks1IT4Innovations, VŠB—Technical University of Ostrava, 708 00 Ostrava, Czech RepublicIT4Innovations, VŠB—Technical University of Ostrava, 708 00 Ostrava, Czech RepublicEven 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 Padé 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.https://www.mdpi.com/2311-5521/4/3/114Colebrook equationLambert W functionPadé polynomialsiterative methodsexplicit approximationslearningteaching strategiesfloating-point computations |
| spellingShingle | Dejan Brkić Pavel Praks What Can Students Learn While Solving Colebrook’s Flow Friction Equation? Fluids Colebrook equation Lambert W function Padé polynomials iterative methods explicit approximations learning teaching strategies floating-point computations |
| title | What Can Students Learn While Solving Colebrook’s Flow Friction Equation? |
| title_full | What Can Students Learn While Solving Colebrook’s Flow Friction Equation? |
| title_fullStr | What Can Students Learn While Solving Colebrook’s Flow Friction Equation? |
| title_full_unstemmed | What Can Students Learn While Solving Colebrook’s Flow Friction Equation? |
| title_short | What Can Students Learn While Solving Colebrook’s Flow Friction Equation? |
| title_sort | what can students learn while solving colebrook s flow friction equation |
| topic | Colebrook equation Lambert W function Padé polynomials iterative methods explicit approximations learning teaching strategies floating-point computations |
| url | https://www.mdpi.com/2311-5521/4/3/114 |
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