Flow of newtonian fluids in pipes pdf

There are a number of common rheology models or methods often used to characterise non newtonian fluids. A generic model for calculation of frictional losses in. Whitelaw skip to main content accessibility help we use cookies to distinguish you from other users and to provide you with a. Fluid slip as mentioned above, many experimental results of newtonian fluids flow agree well. Deposition velocities of newtonian and non newtonian slurries in pipelines ap poloski f nigl. Thermal analysis included with comprehensive databases. Newtonian fluids in pipes with large roughnesses can be accurately predicted by using a constricted diameter, where the diameter measurement is taken as the typical minimum of the rough pipe.

Newtonians in pipes have been correlated on the conventional friction factor reynolds number plot for newtonian fluids. Encyclopedia of life support systems eolss summary rheology is the study of how fluids flow and solids deform when subjected to forces. Basics of fluid flow a fluid is a substance that flows when subjected to a shearing stress layers of the fluid slide relative to each other both gases and liquids are defined as fluids fluid mechanics is the study of the flow of gases and liquids the degree of resistance to shear stress is represented by the term viscosity. This site is like a library, use search box in the widget to get ebook that you want.

Newtonian and powerlaw fluids, since for newtonian fluids the behavior index, n, equals 1, and the consistency index, k, equals the dynamic viscosity. That is equivalent to saying those forces are proportional to the rates of change of the fluids velocity vector as one moves away from the point in question in various directions. Studies of the reduction of pipe friction with the non. Introduction in curved pipes there exists a secondary flow by the action of centrifugal force which has attracted the attention of manyinvestigators. A nonnewtonian fluid flow model for blood flow through a. Flow of newtonian and nonnewtonian fluids in concentric. Fullydeveloped circularpipe flow of a nonnewtonian. Nonnewtonian fluids powerlaw fluids for newtonian fluids, the ratio of shear stress to shear rate is independent of the magnitude of shear rate this ratio of shear stress to shear rate is called viscosity eg. Pdf this paper solves fluidstructure interaction between flexible wall and two types of fluid.

Unsteady flow of a newtonian fluid in a contracting and. Newtonian flows often display instability at a critical flow speed or, more strictly, at a critical reynolds number. Fully developed flow it is good practice to number the assumptions. Experimental tests have shown that laminar flow of non newtonian fluids in pipes with large roughnesses can be accurately predicted by using a constricted diameter, where the diameter measurement. This relationship is now known as newtons law of viscosity, where the proportionality constant. Pdf transition to turbulence in pipe flow of newtonian and non. A newtonian fluid is a fluid in which the viscous stresses arising from its flow, at every point, are linearly correlated to the local strain ratethe rate of change of its deformation over time. Theoretical fluid mechanics laminar flow velocity profile. Chapter 2 flow of incompressible newtonian fluids in pipes. To observe the heat transfer during the flow of fluids in a pipe and compare it with the results obtained in the laboratory i. However, unlike the shearthinning viscosity which is finite at zero shear rate, the bingham plastic or viscoplastic viscosity tends to infinity as shear rate is reduced to zero. In case of non newtonian fluids, it was shown that pressure drop can be predicted by using rheological properties of the flow ing fluid.

Introduction this course assumes that the reader is familiar the engineering principles of fluid dynamics. Resistance coefficients for non newtonian flows in pipe fittings 155 similar to that for a shearthinning fluid, figure 5b. Nonnewtonian fluids are studied in rheology, which is the science of deformation and fluid flow. Experimental results indicate that for newtonian fluids, the design guide is conservative. Deposition velocities of newtonian and nonnewtonian. Theoretical fluid mechanics laminar flow velocity profile by james c.

Deposition velocities of newtonian and nonnewtonian slurries. These roughnesses can be much larger than are accounted for in the moody diagram. The wall shear rate in non newtonian turbulent pipe flow. A nonnewtonian fluid flow in a pipe case studies in fluid. We know in laminar flow, the fluid particles have an orderly motion along stream lines. Explain and solve problems involving laminar flow though pipes and.

Download flow of fluids through valves fittings and pipes technical paper no 410 iv crane flow of fluids technical paper no 410 chapter 2 21 flow of fluids through valves and fittings 21 introduction 21 types of valves and fittings used in pipe. The wall shear rate in nonnewtonian turbulent pipe flow. Gbhepegflo304 pipeline design for isothermal, turbulent flow of nonnewtonian fluids information contained in this publication or as otherwise supplied to users is believed to be accurate and correct at time of going to press, and is given in good faith, but it is for. Newtonian and purely viscous nonnewtonian fluids, when normalised with the. Experimental investigation on characteristics of non. Flow of nonnewtonian fluids in pipes with large roughness. The instantaneous wall viscosity in pipe flow of power law fluids. Unsteady flow of viscous fluids in pipes produced by a simple contraction or expansion of the wall has applications in blood flow in coronary arteries, physiological flow pumps etc. Title epub flow of fluids through valves fittings and pipes technical paper no 410 author.

If the apparent viscosity of a generalized newtonian. In newtonian fluids like water, air, milk, and so on, the shear stress applied to a fluid element is proportional to the shear rate, namely the local velocity gradients, where the proportionality constant is the fluids viscosity. Pdf experimental investigations were carried out in pipe flow of newtonian and non newtonian fluids. Pdf flow of newtonian and nonnewtonian fluid through pipe with. Accuracy of flow meters is based on the steady flow of a homogenous, singlephase newtonian fluid and for turbine and ultrasonic meters a defined velocity profile that does not alter the coefficient in long, straight runs of pipe.

Pdf the flow of rheologically complex fluids in industrial equipment poses a number of challenges, not least from a modeling point of view. The study that is first of this kind was by uchida and aoki who considered the flow of newtonian fluid in a semi infinite contracting and expanding. Perhaps the most important case is the transition from poiseuille flow to turbulent flow in pipes and channels, at a reynolds number of around 2000. The newtonian and non newtonian kind of fluids flow are generally used in industrial and nonindustrial applications and the flow. All gases, liquid water, and liquids of simple molecules ammonia, alcohol, benzene, oil, chloroform, butane, etc. Nonnewtonian viscosity in suspensions of negligible interparticle attraction alderman, 1997. Download flow of fluids through valves fittings and pipes technical paper no 410 iv crane flow of fluids technical paper no 410 chapter 2 21 flow of fluids through valves and fittings 21 introduction 21 types of valves and fittings used in pipe systems 22. As the correlation does not depend on the type of fluid encountered, it may be used with newtonian and non. Newtonian flow and lead to an increased wall shear stress and pressure drop. Fundamentals of fluid mechanicsfluid mechanics chapter 8 pipe. Losses by pipe friction let us study the flow in the region where the velocity distribution is fully developed after passing through the inlet region as shown below.

There are two types of flow namely laminar flow and turbulent flow. Analysis and fem simulation of flow of fluids in pipes. Non newtonian materials are encountered in virtually all of the chemical and process industries and a full understanding of their nature and flow characteristics is an essential requirement for engineers and scientists involved in their formulation and handling. Newtonian fluids in pipes with large roughnesses can be accurately predicted by using a constricted diameter, where the diameter. Reynolds number for newtonian fluids dh hydraulic diameter 4 acrosssectionwetted perimeter inside diameter of pipe d for flow in a pipe diodoifor flow in an annulus diois the inside diameter of the outer pipe and doiis the outside diameter of the inner pipe for flow inside a pipe of diameter, d. Pipes with large roughnesses can occur due to erosion, corrosion, and scale. This tool calculates pressure drop in a straight pipe due to flow of a non newtonian power law fluid.

Studies will be made on how to express losses caused by a change in the cross sectional area of a pipe, a pipe bend and a valve, in addition to the frictional loss of a pipe. At very low velocities or high viscosities, r d reynolds number is low and the fluid flows in smooth layers with the highest velocity at the center of the pipe and low velocities at the pipe wall where the viscous forces restrain it. Incompressible flow software fluid mechanics isoapi. Newtonians are fluids in which the relative slip of fluid elements past each other is proportional to the shear on the fluid, as shown in fig. Fluid flow in tjunction of pipes masters thesis 2007 61 pages, 39. Hence a non newtonian fluid like yoghurt or fruit juice concentrate being pumped in a pipe shows decreased apparent viscosity if flow rate is increased. Oct 17, 20 pipeline design for isothermal, turbulent flow of nonnewtonian fluids 1. Flow of newtonian and non newtonian fluids in concentric and eccentric annuli volume 253 j. The rate of entropy generation in pipeline flow of newtonian fluids is quantified through measurements of pressure gradient as a function of flow.

Ii newtonian and non newtonian flow ibarz, albert, castellperez, elena, barbosa canovas, gustavo v. Newtonian fluid but in certain occasions the twophase flow encountered in the industry has the behaviour of non newtonian fluids. Intro to fluid flow dublin institute of technology. Newtonian fluids are named after sir issac newton 1642 1726 who described the flow behavior of fluids with a simple linear relation between shear stress mpa and shear rate 1s.

Turbulent flow of nonnewtonian fluids in a partially blocked. In this article we will discuss about turbulent flow in pipes. Apply the newtons second law to the cylinder of fluid. The flow of a fluid in a pipe may be laminar flow or it may be turbulent flow. But the viscosity of some fluids is affected by factors other than temperature.

Thus the velocity gradient, as given by equa tions 1 or 4, is greatest at the wall where u u. Incompressible non newtonian fluid flows quochung nguyen and ngocdiep nguyen mechanical faculty, ho chi minh university of industry, vietnam 1. Flow of incompressible newtonian fluids in pipes newtonians are. Flow of newtonian and nonnewtonian fluids in concentric and. Measurements of mean axial velocity and of the three normal stresses have been obtained in fully developed pipe flow with four concentrations of a polymer sodium carboxymethyl cellulose in aqueous solution and with water and viscous newtonian fluids encompassing a range of reynolds numbers from 240 to 111,000. Most commonly the viscosity of non newtonian fluids is not independent. Non newtonian fluids on the other hand typically exhibit either shear thinning or shear thickening behaviour and in some cases, exhibit a yield stress, i. Introduction a non newtonian fluid is a fluid whose flow properties differ in many ways from those of newtonian fluids. A new analysis of the turbulent flow of nonanewtonian fluids. Most of the earlier studies were confined to laminar flow and turbulent flow of newtonian fluids through helical coils dean2. Th fl i d b b l f i ht d ithe flow is governed by a balance of pressure, weight, and viscous forces in the flow direction.

This guide presents the basis for the prediction of flow rate pressure drop relationships for the laminar flow of non newtonian fluid through circular pipes and selected fittings under isothermal conditions. Turbulent flow of newtonian fluids is described in terms of the fanning friction factor, which is correlated against the reynolds number with the relative roughness of the pipe wall as a parameter. Laminar flow in pipes can be analyzed quite readily for most of the fluid models, and a considerable amount of experimental work has been performed on turbulent flow of non newtonian fluids in pipes. Any fluid flowing in a pipe had to enter the pipe at some location. The same approach is adopted for non newtonian flow but the generalized reynolds number is. Nonnewtonian turbulent and transitional pipe flow m. Measurements of mean axial velocity and of the three normal stresses have been obtained in fully developed pipeflow with four concentrations of a polymer sodium carboxymethyl cellulose in aqueous solution and with water and viscous newtonian fluids encompassing a range of reynolds numbers from 240 to 111,000. Furthermore, understanding the rheological behavior of fluids in pipe flow conditions is important for the designand control of the industrial process. If a fluid is flowing in the round pipe of diameter d at the average flow velocity v, let the pressures at. Between these two values is critical zone where the flow can be laminar or turbulent or in the process of change and is mainly unpredictable. Case study for a theory of turbulence in timeindependent non newtonian fluids trinh, khanh tuoc institute of food nutrition and human health massey university, new.

Pipeline design for isothermal, turbulent flow of non. In spite of the great range of the available experimetnal data, further work is necessary in the transition and turbulent. However, for laminar flow of a newtonian fluid, the shear stress is simply. The region of flow near where the fluid enters the pipe is termed the entrance entryyg regionion or develo or developpgfing flow region. The present newtonian fluid flows correspond to bulk flow reynolds numbers, based on bulk velocity, hydraulic diameter and fluid viscosity, of 8900 and 26600, in a concentric annulus with diameter ratio of 0. This paper presents a method for calculating the wall shear rate in pipe turbulent flow.

This paper describes the typical examples of laminar drag reduction 1 for a newtonian liquid flow. For steady fully developed flow in a pipesteady, fully developed flow in a pipe, the velocitythe velocity contains only an axial component, which is, which is a function of a function of. Fluid handling is still at the heart of new, more complex processes and applications. To observe the heat transfer during the flow of fluids in a pipe and compare it. The following work only applies to newtonian fluids. Nonnewtonian flow in the process industries sciencedirect. Flow of nonnewtonian fluids in a pipe sciencedirect. Basics equations for fluid flow the continuity equation q v. The region of flow near where the fluid enters the pipe is. Flow in pipes is considered to be laminar if reynolds number is less than 2320, and turbulent if the reynolds number is greater than 4000.

Turbulent flow of nonnewtonian fluids in a partially. If fluid slip occurs at the solid boundary, the drag reduction occurs even in laminar flow range. Transition to turbulence in pipe flow of newtonian and non newtonian fluids. Liquid flows through pipes or ducts are commonly used in heating and cooling applications and fluid distribution networks. Design your liquid pipe flow systems and fluid mechanics in an instant with fluidflow incompressible flow software to calculate plant pressure loss and flow distribution. Chhabra abstract the objective of this chapter is to introduce and to illustrate the frequent and wide occurrence of nonnewtonian. Incompressible nonnewtonian fluid flows intechopen. In this case the generalized reynolds number equation 6 reduces to re dv p 12 p f. A generic model for calculation of frictional losses in pipe and annular flows s. Resistance coefficients for nonnewtonian flows in pipe.

He also discovered that the critical velocity at which it changed back again. Experimental tests have shown that laminar flow of nonnewtonian fluids in pipes with large roughnesses can be accurately predicted by using a. In steady shear flow, a viscoelastic fluid exhibits not only the shear rrate dependent viscosity but also unequal normal stresses. In particular familiar with concepts of newtonian fluids such as viscosity, engineering units of viscosity, reynolds number.

Pullum2 1department of mechanical and aerospace engineering monash university, clayton, vic 3800, australia. The nature of flow in pipe, by the work of osborne reynolds, is depending on the pipe diameter, the density and viscosity of the flowing fluid and the velocity of the flow. Experimental tests have shown that laminar flow of non. Pdf pipeline design for isothermal, laminar flow of non. Dimensionless reynolds number is used, and is combination of these four variables and may be considered to be ratio of dynamic forces of mass flow to the shear stress due to viscosity. Non newtonian flow in the process industries download ebook. This correlation, theoretically rigorous in the laminar flow region, was tested with data on 16 different non. The nonnewtonian fluids are according to their properties, established in the steady flow, divided into the fluids the properties of which are. Demonstrate the use of comsol for the simulation of fluid flow. Pdf transition to turbulence in pipe flow of newtonian. It collapses adequately the data measured in laminar flow and turbulent flow into a. In this paper the effects catheterization and non newtonian nature of blood in small arteries of diameter less than 100. Chapter 3 nonnewtonian fluid almustansiriya university.

Experimental measurements of the velocity profile in turbulent pipe flow. Epub flow of fluids through valves fittings and pipes. A central finding of this testing is that particle deposition in non newtonian slurries usually occurs near the flow velocity required to reach turbulent flow. This means in practice that the pressure drop of a non newtonian fluid in laminar flow is not directly proportional to the flow rate as for newtonian fluids in laminar flow.