Abstract
The current work uses an Artificial Neural Network (ANN) approach to determine the friction factor for turbulent flows of water in a pipe of uniform circular cross-section. The Colebrook equation which is the most fundamental equation in the context of this problem and combines the available data for transition and turbulent flow in pipes is implicit in the friction factor. Also, some approximations of the Colebrook equation, explicit in friction factor developed using an analytical approach, introduce some significant additional errors in the solution. The most popular approach today used by engineers is the Moody Chart, which relates friction factor as a function of Reynolds number and relative roughness. However, referring to the chart repeatedly is a time-consuming activity. Besides these conventional approaches, neural networks (a subset of artificial intelligence) can be applied as they have in recent time matured to a point of offering practical benefits in many of their applications. In this study, the best performance in terms of Mean Absolute Percentage Error and R2 Score was achieved by 2-6-6-6-6-6-1 network with tanh, sigmoid, tanh, tanh, sigmoid functions respectively for hidden layers and ReLU for output layer, which was around 0.59% in terms of Maximum Error and Explained Variance Score. The 2-6-8-6-8-6-1 architecture with sigmoid, tanh, sigmoid, tanh, sigmoid for hidden layers and ReLU output performed slightly better with a Maximum Error of 0.0008 and Explained Variance Score of 0.99985. This study also sought to discover a relationship between the number of data points and the accuracy of Artificial Neural Networks tested.
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References
Yunus AC (2010) Fluid mechanics: fundamentals and applications (SI units). Tata McGraw Hill Education Private Limited, New York
Nikuradse J (1933) Stromungsgesetze in rauhen Rohren [Laws of flow in rough pipes]. Forschung Auf dem Gebiete des Ingenieurwesens. NACA Technical Memorandum 1292 (in German) 361. NAID 10024691252
Colebrook CF, Blench T, Chatley H, Essex EH, Finniecome JR, Lacey G, Williamson J and MacDonald GG(1939) Correspondence. Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws (includes plates). J Inst Civil Eng 12(8):393–422. https://doi.org/10.1680/ijoti.1939.14509
Haaland SE (1983) Simple and explicit formulas for the friction factor in turbulent pipe flow. J Fluids Eng 105:89–90. https://doi.org/10.1115/1.3240948
Fox W, Pritchard P and McDonald A (2010) Introduction to fluid mechanics, 7th edn. Wiley, New York
Moody LF (1944) Friction factors for pipe flow. Trans ASME 66:671–684
Shayya WH and Sablani SS (1998) An artificial neural network for non-iterative calculation of the friction factor in pipeline flow. Comput Electron Agric 21(3):219–228. https://doi.org/10.1016/S0168-1699(98)00032-5
Yazdi M and Bardi A (2011) Estimation of friction factor in pipe flow using artificial neural networks. Can J Autom Control Intell Syst 2(4):52–56
Fadare DA and Ofidhe UI (2009) Artificial neural network model for prediction of friction factor in pipe flow. http://ir.library.ui.edu.ng/handle/123456789/1924. Accessed 25 Nov 2020
Sahai S, Kulkarni T, Tikhe S and Mathpati CS (2017) Use of artificial neural network to predict Pressure-Drop in rough pipes. In: Paper presented at the 2017 international conference on computing methodologies and communication (ICCMC), pp 452–455. IEEE, 18 July 2017
Brkić D and Ćojbašić Ž (2016) Intelligent flow friction estimation. Comput Intell Neurosci 2016:1–10 (2016). https://doi.org/10.1155/2016/5242596
Offor UH and Alabi SB (2016) Artificial neural network model for friction factor prediction. J Mater Sci Chem Eng 4(7):77–83. https://doi.org/10.4236/msce.2016.47011
Ng A, Katanforoosh K and Mourri YB (2020) Neural networks and deep learning [MOOC]. Coursera. https://www.coursera.org/learn/neural-networks-deep-learning/. Accessed 3 July 2020
Newton method for finding roots (2020). http://en.wikipedia.org/wiki/Newton's_method. Accessed 10 Nov 2020
Eremenko K and Ponteves H (2020) SuperDataScience team. Deep learning A–Z™: Hands-on artificial neural networks [MOOC]. Udemy. https://www.udemy.com/course/deeplearning/(2020). Accessed 28 Nov 2020
Ng A, Katanforoosh K and Mourri YB (2020) Improving deep neural networks: hyperparameter tuning, regularization and optimization [MOOC]. Coursera. https://www.coursera.org/learn/neural-networks-deep-learning/. Accessed 28 Aug 2020
Sethi A, Rawat A and Srivastava V (2022) Artificial neural network models for wall parameters on plug-1 flow characteristics through pipelines. J Eng Res (in Press)
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Srivastava, V., Prakash, A., Rawat, A. (2022). To Predict Frictional Pressure-Drop of Turbulent Flow of Water Through a Uniform Cross-Section Pipe Using an Artificial Neural Network. In: Tadepalli, T., Narayanamurthy, V. (eds) Recent Advances in Applied Mechanics. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-16-9539-1_28
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