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Modeling of Pipe Flow and Observation of Laminar-Turbulent Transition in Smooth Pipes

Abstract

An undergraduate experiment has been developed to measure the mass flow rate of water exiting a constant-head tank through a tube. There are three tubes that can be investigated independently, with each tube having different entrance geometry. The scenario is a common problem found in undergraduate fluid mechanics textbooks, and loosely based on a classic experiment by Osborne Reynolds. The design of the experiment, and the pedagogical structure, provide a diverse set of educational objectives to be attained. Students are directed not only to develop a model to predict the mass flow rate of the exiting water, but also to predict the accuracy of the resulting model using uncertainty analysis. The experiment is designed to obtain laminar-turbulent transition, and the students use their model to measure the upper-limit transition Reynolds number. The result is an experiment that demonstrates a fundamental application of fluid mechanic – pipe flow theory. Further, the experiment promotes the role and importance of uncertainty analysis in engineering experimentation, and provides an avenue for students to conceptualize laminar and turbulent flow and the physical significance of the Reynolds number. A detailed description of the experiment is presented, along with the development of the pipe flow model and associated uncertainty analysis. The turbulence-based model compares well to the experimental data in the turbulent regime, and the data predictably deviates during transition. The Reynolds number of transition was demonstrated to vary from the accepted value of 2300, depending on tube inlet geometry. Finally, experimentally determined values of pipe friction factor were plotted against Reynolds number, and found to closely match the classic Moody Diagram. A pedagogical approach is developed along with the experiment facility, and is also described in detail.

Introduction

The development of an undergraduate engineering laboratory is challenging, because a laboratory serves two sometimes distinct sets of goals. The first are generally classroom-specific goals: to demonstrate physical phenomena developed in the classroom, to compare theoretical models to experimental data, and to develop an approach to analyzing and designing complex engineering systems. The second goals are laboratory-specific: to introduce methods of measurement and instrumentation, to collect, organize, analyze, and interpret data, and to develop an approach to engineering experimentation. Woven into these goals is the objective of promoting teamwork, communication skills (written and oral), and at the same time achieving learning objectives like those of Bloom’s Taxonomy1.

The difficulty of attaining such a diverse set of objectives can lead to some goals being underemphasized – often, ironically, the laboratory-specific goals. Frequently, the complexity of an experiment, and the sheer amount of data collected, focuses student attention on “crunching data.” As a result, the goal of the students often becomes the mere completion of the assignment, instead of any thoughtful analysis of the results. Furthermore, some aspects of experimentation are neglected; an example of this is the topic of uncertainty analysis, which is of fundamental importance to engineering experimentation and well-suited to the laboratory. Numerous studies,

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Thorncroft, G., & Patton, J. (2006, June), Modeling Of Pipe Flows And Observation Of Laminar Turbulent Transition In Smooth Pipes Paper presented at 2006 Annual Conference & Exposition, Chicago, Illinois. 10.18260/1-2--255