Unsteady flow in pipe networks lecure notes csaba hos l aszl o kullmann botond erdos viktor szab o march 27, 2014 1. The flow of a fluid in a pipe may be laminar flow or it may be turbulent flow. In this tutorial, a fluid flow simulation of water flow through a pipe junction is carried out. Oil and natural gas are transported hundreds of miles by large pipelines. Between re 2,100 and re 4,000, we observe a transition regime with uncertain and sometimes fluctuating flow. Any of these piping configurations can result in sonic choking a crosssectional flow area of a pipe d diameter of a pipe e pipe wall roughness f friction factor ff, g. Understanding compressible flow fluid flow articles. Boundary layer approximations, displacement and momentum thickness b. The reynolds nuu be o o ese p pesmber for flow in these pipes is based on the hydraulic diameter d h 4a c p, where a c is the crosssectional area of. Usually extremes are considered like adiabatic and isothermal flow. The existence of a specific flow pattern regime at given flow conditions is in fact believed not to be affected by the path through which the final state is reached.
It continues a respected tradition of providing the most comprehensive coverage of the subject in an exceptionally clear, unified, and carefully paced introduction to. Initially fluid conditions inside the pipe on both sides of the break are similar. Wall thickness of the pipe is small compared to the diameter. Flow is steady, fully developed, parallel and, symmetric with respect to pipe axis. Head loss in pipe systems laminar flow and introduction to. Most closed conduits in engineering applications are either circular or rectangular in cross section. Chapter 2 incompressible flow through pipes free download as powerpoint presentation. Lectures in computational fluid dynamics of incompressible flow. External flows considers bodies fully immersed in a fluid stream. From the experiment, volumetric flow is calculated with the help of analogue flow meter. The flow through short straight pipes iii a compressible viscous stream j.
Bernoullis equation steady, inviscid, incompressible. A duct is a solid walled channel, whereas a streamtube is defined by considering a closed curve drawn in a fluid flow. Laminar flows and reynolds number for a circular pipe, the laminar flow is defined to have the flow reynolds number flow for a noncircular conduit, the diameter has to be replaced by hydraulic radius defined as. No theory for transition, but recent direct numerical. Theoretical fluid mechanics laminar flow velocity profile. Determine the head loss in each kilometer of pipeline and the shear stress at the pipe. The choked flow calculation computes the mass flow rate through a pipe based on tank pressure and temperature, pipe length and diameter, minor losses, discharge pressure, and gas properties. Fluid flow instrumentation in the physical world, mechanical engineers are frequently required to monitor or control the flow of various fluids through pipes, ducts and assorted vessels. In fluid mechanics or more generally continuum mechanics, incompressible flow isochoric flow refers to a flow in which the material density is constant within a fluid parcelan infinitesimal volume that moves with the flow velocity. F ma v in general, most real flows are 3d, unsteady x, y, z, t. In external flows we are concerned with fluid drag forces and lift forces. Flow quantities for turbulent flow effect of roughness. The equation is named after henry darcy and julius weisbach the darcyweisbach equation contains a dimensionless friction factor, known as.
Laminar flow in noncircular pipes the friction factor f relations are given in table 81 for fully dl dli fli noncircular pipes developed laminar flow n pipes of various cross sections. Flow in pipes fluid flow in circular and noncircular pipes is commonly encountered in practice. Viscous flow in pipes, laminar pipe flow characteristics 16 of 34 duration. For turbulent flow f determined from turbulence modeling since exact solutions not known. Flows completely filling the pipecompletely filling the pipe. Computational fluid dynamics of incompressible flow pdf 155p currently this section contains no detailed description for. Fundamentals of fluid mechanicsfluid mechanics chapter 8.
Large temperature variations result in density variations. If he needs a test section of 10 ft of fully developed flow, what should be the minimum. Indications as to the possibility for transition from stratified flow to other flow patterns may therefore be obtained from a stability analysis of the stratified flow configuration. While all flows are compressible, flows are usually treated as being incompressible when the mach number the ratio of the speed of the flow to the speed of sound is less than 0. Steady incompressible flow through pipes springerlink. However, for many flow situations, the changes of density due to changes in pressure associated with the flow are ve.
Explain and solve problems involving laminar flow though pipes and. Each material of construction has its own characteristic roughness parameter. The situation is further complicated by the fact that heat may be transferred through the walls of the pipe. What is the fluid speed at a location where the diameter has narrowed to 4.
In the design of mall models of aircraft or tolssiles for testing in supersonic tunnels, it may be desrred to represent jet engine nacelles by means of simple hollow pipes. An example compressible pipe flow calculator spreadsheet is partially shown in the image below. The main difference between compressible flow and almost incompressible flow is not the fact that compressibility has to be considered. Rather, the difference is in two phenomena that do not exist in incompressible flow. The flow through short straight pipes in a compressible. Fluid mass flowrate is calculated by iteratively solving following equation in imperial units. The pressure and temperature of the gas may change. A typical situation is a pipe into which gas enters at a given pressure and temperature and flows at a rate determined by the length and diameter of the pipe and. Pdf modeling of newtonian fluids in annular geometries with. C 1 i ntroduction to f luid f low stanford university. As a civil engineer, you will be mostly dealing with incompressible fluid or water in many. Compressible flow refresher in production plants, there are many situations where pressure drops of process vapors and gases need to be calculated. An incompressible fluid flows steadily through a pipe that has a change in diameter.
Determine the pressure in the tank if the flow is steady. While some techniques work better with some groups of. Pdf unsteady incompressible stokes flow through porous. Flows in closed conduits or channels, like pipes or air ducts, are entirely in contact with rigid boundaries. Ducts with area change 1 onedimensional, isentropic flow model. The velocity v in equations 7 and 8 is the average velocity over the pipe cross section.
Significant changes in velocity and pressure result in density variations throughout a flow field 4. Incompressible flow water hammer pipes fluid mechanics. Compressible flow in pipe, adiabatic, isothermal flow, specific volume, pressure drop in compressible flow, exact relation between pressure and specific volume is required, but it is not easily determined in each specific problem. As a result we now have two new variables we must solve for. As the valve closes the pressure at the valve rises decelerating the water column. Flows without completely filling the without completely filling the pipe. He selects a 1inchdiameter pipe and uses a glycerinwater mixture as the fluid, which has a kinematics viscosity equal to i04 ft2s. Applications of viscous flows through pipes and compressible flow. Quasisteady mass flux is calculated using the moody steady slip flow model with subcooling.
The most teachable book on incompressible flow now fully revised, updated, and expanded. This condition for incompressible flow is given by the equation below, where v is the fluid velocity and a is the speed of sound of the fluid. The equation gives for a known pipe, the maximum pressure rise given any closure time. Incompressible flow software fluid mechanics isoapi. It is therefore broadly possible to treat liquid and gas flows with common fundamental principles in fluid mechanics. The primary purpose of this book is to provide an integrated overview of incompressible flow turbomachines and their design, in this case pumps and turbines. Analysis and fem simulation of flow of fluids in pipes supervisor arcada. Can air be considered incompressible as long flow velocities. The gravitational effects mass for ces will be neglect. The flow is then no longer a function of the pressure difference but is a. Determine the head loss in each kilometer of pipeline and the shear stress at the pipe wall. A valve is a device that regulates, directs or controls the flow of a fluid by opening, closing, or partially obstructing various passageways. Consider a pipe diameter d, lenght l used to transport gas molar mass m, ratio of speci. Mathematically, this constraint implies that the material derivative discussed below of the density must vanish to ensure incompressible flow.
Theory and empirical knowledge of turbomachines are brought together in detail to form a framework for a basic understanding of this complex subject. Oil and gas pipeline design, maintenance and repair. Firstly, the experiment is performed in arcada laboratory for fluid flow in a pipe. External flows memorial university of newfoundland. Pressure losses are very important factories that effects on the flow in piping systems where concludes different length of pipes, diameters, fittings, elbows and valves. Fluid mechanics course 123 compressible flow flow of compressible fluids in a ppe involves not only change of pressure in the downstream direction but also a change of both density of the fluid and the velocity of flow. Unsteady incompressible stokes flow through porous pipe of uniform circular cross section with periodic suction and injection article pdf available june. For the field of steady flow of incompressible fluids. For compressible fluids, including gases and twophase mixtures, it is necessary to consider critical flow. An equivalent statement that implies incompressibility is that the divergence of the flow velocity is zero see the derivation below, which illustrates why. 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. Flow of fluids through a closed duct under some form of pressure is referred to as a closed conduit or pressure flow.
In fluid dynamics, the darcyweisbach equation is an empirical equation, which relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid. Newtonians flowing in pipes exhibit two distinct types of flow, laminar or streamline when re 4,000. If, for such a fluid, the upstream pressure is high relative to the downstream pressure, the flow is choked. Adiabatic flow of a compressible fluid through a conduit flow through pipes in a typical plant where line lengths are short, or the pipe is well insulated can be considered adiabatic. The fluid speed at a location where the pipe diameter is 8. They are different than compressible flows mainly due to the missing equation of state. Density is not an unknown and pressure does not have any thermodynamic meaning. Flow of incompressible newtonian fluids in pipes springerlink. It continues a respected tradition of providing the most comprehensive coverage of the subject in an exceptionally clear, unified, and carefully paced introduction to advanced concepts in fluid mechanics. Compressible fluid flow calculation methods article pdf available in chemical engineering new york mcgraw hill incorporated then chemical week publishing llc 1212. Friction factor definition based on turbulent flow analysis where.
Ncompressible flow the compressibility of a medium becomes important when the speed of a body begins to approach the speed of sound in the medium. Mod29 lec29 incompressible viscous flows part i youtube. Turbulent flow in pipes 1 consider the instantaneous velocity at a point in a pipe when the. Ch3 the bernoulli equation the most used and the most abused equation in fluid mechanics. Figure 8 applying the steady flow energy equation between 1 and 2 we. Compressible gas flow in pipelines fluidflow pipe flow. Compressible flow analyses are much more sensitive to the applied boundary conditions and material properties than incompressible analyses.
Compressibility becomes important for high speed flows where m 0. Consider gas flowing in a duct which varies in size. This book deals with an introduction to the flow of compressible substances gases. In lees loss prevention in the process industries third edition, 2005. Mcdonough departments of mechanical engineering and mathematics university of kentucky c 1991, 2003, 2007. Crude oil of density 925 kgm 3 and absolute viscosity 0. Temperatures, pressures, densities, velocities, and mach numbers are computed at all transition points in the tank, at the pipe entrance, in the pipe at. Chapter 7 incompressible flow solutions incompressible flows are by far the most common type of flows encountered in engineering problems. 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. Made by faculty at the university of colorado boulder, department of chemical and biological engineering. Flow chokes at resriction in pipe flow chokes at expansion in pipe area 0. Flows which include flows through pipes round cross section, ducts not round cross. Jan 22, 2016 in fluid mechanics or more generally continuum mechanics, incompressible flow isochoric flow refers to a flow in which the material density is constant within a fluid parcelan infinitesimal.
All clean, new commercial pipes seem to have the same type of roughness. Analysis and fem simulation of flow of fluids in pipes. Jan 11, 2018 in this video you will learn about how to decide whether the flow will be compressible or incompressible. Fluid statics, kinematics of fluid, conservation equations and analysis of finite control volume, equations of motion and mechanical energy, principles of physical similarity and dimensional analysis, flow of ideal fluids viscous incompressible flows, laminar boundary layers, turbulent flow, applications of viscous flows through pipes and compressible flow. Introduction to compressible flow me 322 lecture slides, winter 2007 gerald recktenwald. Flow in an open duct exposed to an approximately constant pressure at the surface is known as a freesurface or an openchannel flow. Then the average velocity for incompressible flow in a circular pipe of radius r can be expressed as 82 therefore, when we know the flow rate or the velocity profile, the average velocity can be determined easily. Flow of incompressible fluids in pipelines crude oil of density 925 kgm 3 and absolute viscosity 0. This fluid can range from thick oils to light gasses. Both liquids and gases can be transported through closed conduits. Mod35 lec35 application of viscousflow through pipes part iii. The first phenomenon is the very sharp discontinuity jump in the flow.
Compressible fluid an overview sciencedirect topics. Define the rate of flow rate of flow for a fluid and solve problems using velocity and cross section. This excel spreadsheet can be used to calculate the frictional pressure drop, or the gas flow rate, or the required minimum pipe diameter. Indication of laminar or turbulent flow the term fl tflowrate shldbhould be e reprepldbr ldlaced by reynolds number,where v is the average velocity in the pipe, and l is the characteristic dimension of a flow. The fundamental requirement for incompressible flow is that the density, is constant within a small element volume, dv, which moves at the flow velocity u. Chapter 2 incompressible flow through pipes fluid dynamics.
An incompressible fluid is a fluid whose density does not change when the pressure changes. Compressible flow refers to gas flow where the temperature of the gas is significantly affected by the conversion of pressure differences to kinetic energy. Introduction to compressible flow mechanical engineering. Incompressible water flow through a pipe junction simscale. Pdf in general, the computation of single phase subsonic mass velocity of gas flowing through a pipe requires a computerized iterative. If the applied settings do not define a physically real flow situation, then the analysis can be very unstable and may fail to reach a converged solution. There are two inlets and one outlet for this configuration. Fundamentals of compressible flow mechanics pdf 376p. At a typical instant, the assumed equation of flow is sin 2 p vv g zd. Computational fluid dynamics of incompressible flow. Example compressible pipe flow calculator spreadsheet. Pressure tapping in a wall parallel to the flow records static pressure pitot tube records the stagnation pressure flow is brought isentropically to rest. Compressible and incompressible flow fluid mechanics 36.
The equation of steady onedimensional compressible fluid flow 8. This tool calculates flow of a single phase compressible fluid through a pipe for a given pressure drop. Compressible flowalong pipelines multiphase flow lab. Incompressible flow, fourth edition is the updated and revised edition of ronald pantons classic text. Incompressible flow article about incompressible flow by. The hot and cold water that we use in our homes is pumped through pipes. Compressible flow or gas dynamics is the branch of fluid mechanics that deals with flows having significant changes in fluid density.
These are often experimentally obtained, but some laminar flow results are theoretical. Write and apply bernoullis equation s equation for the general case and apply for a a fluid at rest, b a fluid at constant pressure, and c flow through a horizontal pipe. He also selects a mean flow velocity of 2 fps for the test. All these flow regimes may occur in a horizontal pipe flow. For incompressible flow all the fluid in the pipe is moving at the same speed u. Chapter 4 flow in channels introduction 1 flows in conduits or channels are of interest in science, engineering, and everyday life. Analysis of lift and drag is usually facilitated by defining lift and drag coefficients. An incompressible fluid flows steadily through a p. The term compressible flow is rather misleading, but unfortunately, it is what the fluiddynamics folks have chosen to use. The density of a gas changes significantly along a streamline compressible flow definition of compressibility. The actual flow regime will depend on fluid velocities and properties.
Associate professor, mechanical and materials engineering department portland state university, portland, oregon. Compressible pipe flow calculator spreadsheet low cost easy. To download the solution of the following problem in pdf format, click here. Old, foul and corroded pipe can be very rough, and the character of the roughness differs from that of clean pipe. Incompressible flow by study mechanical engineering youtube.
Water in a city is distributed by extensive piping networks. 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. In this case we will consider the flow to be adiabatic also, that is, with no heat transfer. The energy equation for incompressible, steady flow between two.
Compressible gas flow in pipelines may 2, 2018 james mcloone many equations used for the solution of gas flow in pipelines do not take into consideration rigorously the deviation of natural gas from ideal gas behaviour. Unlike liquids, gases are compressible, and the change in the conditions of the fluid as it moves down the pipe must be considered in these calculations. Introduces the use of the mechanical energy balance in solving pipe flow type problems. The objective is to get insight of the flow field at the junction of the pipe.
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