Conduit Fluid Flow
by
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The text is an original work by the author undertaken to develop reliable engineering solutions to conduit fluid flow problems. The result is the formation of a rational science that spawns new ideas of fluid friction and a new generation of accurate, manageable application-engineering tools. Investigating and developing the subject matter has been an adventure of new discoveries that the author would like to share.
Over 230 years have elapsed since the introduction of an analytical approach to predicting the flow of water through channels and pipe by Chezy8. The interim result to the present is an assortment of inaccurate equations, as the mechanics of fluid flow are not clearly understood. During the 1930''''s, Theodore von Karman published a series of technical articles11, 12, 13 proposing an explanation of turbulent flow. The Prandtl-von-Karman smooth and rough-pipe functions are introduced in these articles. The Colebrook/White transition equation 3 introduced in 1939 seemingly provided the one missing element needed to complete the functions. At the same time, it also marked the end of an era of analytic efforts toward formulating the resistance to flow. The purpose of this text is to renew these efforts and thus develop the science on a sound base.
In spite of the warning by von Karman that the constants in his smooth and rough-pipe functions may be variable, his functions quickly appeared in engineering texts. Colebrook appears to be the first to classify the functions as the smooth and rough-pipe laws. The engineering community quickly adopted the Colebrook/White transition equation. Rouse8 and then Moody2 converted the equation to graphic form as it was regarded as too complex for practical use.
Experimenters and observers noted early on that the equation did not conform very well to observed results. The equation should have worked, but the equation did not work. Modified equations for smooth-pipe have accrued through the following years as engineers have not been satisfied with the law. The rough-pipe law seems to have remained unscathed; however, empirical equations have been developed that some engineers prefer to use. As a result, the newly formed relationships acquired the status of empirical equations in that engineers still choose the equation deemed best to fit the problem.
The unresolved topic is very old – so old that many probably regard the status quo of the science as mature and as complete as it is going to get.
The initial scope of interest in water flow through channels and pipe has broadened to fluid flow, and has become more complex as new disciplines have evolved. Air conditioning, for example, involves balanced flow achieved through duct sizing and accounting for temperature changes of the air. Municipal and building water systems, gas transmission systems, etc. involve expansive networks of conduit. The geometry of any conduit may be round, rectangular, oval, etc. The unresolved complexities of friction, heat transfer, circuitry, and geometry serve to highlight the inadequacies of our current knowledge of conduit fluid flow. The consequences have been uncertainty in the integrity of a design caused by a lack of backup with the fundamental facts needed to synthesize all the isolated elements of conduit fluid flow.
The basis of the developments presented in this text is introduced in an article1 by the author and published in 1961. Expressions are derived to adjust outlet air quantities in an air-conditioning system for duct heat gain. The expressions are first derived in terms of round duct and are then broadened to include rectangular duct. The rectangular duct is expressed in terms of the equivalent round duct for equal friction rate and flow. An empirical expression for the diameter of this equivalent round duct has been determined experimentally14 and is shown in this text to also have a rational origin. The purpose of the article is to propose a less cumbersome method than the prevailing one to balance the distribution of air in an air-conditioning system by considering its static pressure and temperature changes. The same equivalent round duct used to determine friction loss is also used to evaluate the effects of duct heat gain. By referring all calculations to the one round conduit, the procedure of duct sizing is streamlined. The essence of the article is repeated in the text.
The text is characterized by the progressive developments in conduit fluid flow analysis. The means are thus provided to go back to square one to complete the development of the Prandtl-von-Karman and Colebrook/White functions that is required to expand the science. The relationships are developed herein through the principles of equivalence, similar flow, and the similarity of flow. The principles serve to free the state-of-the-art from domination by empiricism. A significant expansion of the science results from Ludwig Prandtl''''s invention of the "mixing length" that leads to correlating the mechanism of friction due to mixing with the transfer of heat by way of "Reynolds'''' analogy." Engineers involved with conduit as a fluid transfer means are now enabled to predict flows, friction loss, the transfer of heat, and required conduit sizes on a sound scientific basis. The tools to analyze the laminar and turbulent flows of fluids in conduit are the product of the text. In spite of the extensive developments in the text, the results are surprisingly manageable relationships and understandabl
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About the Book
The mechanics of fluid friction and the transfer of heat are not understood to this day. The use of pipes, ducts, and channels is not being hampered by the lack of this basic knowledge, as conduit systems are everywhere. What is being hampered that the book addresses are efficient design and the predictability of performance. Since the discovery of the principles of equivalence, similar flow and the similarity of flow, it has become clear that flow relationships as they are currently presented have to be revisited. The chapter BASICS OF FLOW is created to provide a background for the fundamental information needed to evaluate flow relationships. Equivalence means that an equivalent round conduit can always be found to represent a noncircular surface configuration for the purpose of calculating friction losses and/or the transfer of heat. The equivalent round conduit is introduced also as a device to analyze the properties of flow. A new perspective of fluid friction evolves that supports the principle of equivalence The principle of similar flow leads the way to new fundamentals of fluid flow, such as the natural friction factor. Equivalence and similar flow combine to provide direct solutions to networks. The discovery of the mixed boundary layer leads to, among other things, the derivation of the inside coefficient of heat transfer. Fluid friction and the transfer of heat are mathematically correlated which means that the friction loss can be determined from the heat transferred, and the heat transferred can be determined from the friction loss.
About the Author
I'm a graduate of Purdue University with a BSME degree and have since been engaged in the air-conditioning and related engineering fields. I am currently retired. Engagements include the design of air-conditioning systems, application engineering, troubleshooting, product managing, and the position of principle in the sales-engineering firm of Plenum Systems, Inc. (psi). While active with psi, I introduced applications of the underfloor plenum for air and electric distribution, and was granted patents titled "Double Plenum Air Distribution System" and "Damper Assembly." My background provides the inspiration for the subject matter. The long lingering absence of sound application engineering tools involving the flow and distribution of fluids is addressed, and as will be shown, the devil is in the fundamentals.