To Predict Frictional Pressure-Drop of Turbulent Flow of Water Through a Uniform Cross-Section Pipe Using an Artificial Neural Network

Vaibhav Srivastava, Ankit Prakash, Anubhav Rawat

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


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.

Original languageEnglish
Title of host publicationRecent Advances in Applied Mechanics - Proceedings of Virtual Seminar on Applied Mechanics, VSAM 2021
EditorsTezeswi Tadepalli, Vijayabaskar Narayanamurthy
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages16
ISBN (Print)9789811695384
StatePublished - 1 Jan 2022
Externally publishedYes
EventVirtual Seminar on Applied Mechanics, VSAM 2021 - Virtual, Online
Duration: 28 May 202129 May 2021

Publication series

NameLecture Notes in Mechanical Engineering
ISSN (Print)2195-4356
ISSN (Electronic)2195-4364


ConferenceVirtual Seminar on Applied Mechanics, VSAM 2021
CityVirtual, Online


  • Artificial Neural Networks
  • Colebrook equation
  • Friction factor

ASJC Scopus subject areas

  • Automotive Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


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