Revision notes on flow of liquids and viscosity askiitians. Viscous flow through a sharpedged orifice sciencedirect. The standard convention for relating orifice flow rate to differential pressure is through the use of the orifice discharge coefficient cd as seen in equation 1. In the flow experiments the vertical tube was filled with liquid, the orifice being meanwhile closed by one finger. I understand the concept of shear viscosity and why the liquid in contact with moving plate has highest velocity. This hole or opening is called an orifice, so long as the level of the liquid on the upstream side is above the top of the orifice.
Twodimensional and axisymmetric viscous flow in apertures. Note that the outer surface of this shell has a larger area than the inner surface. Pdf chapter 6 viscous flow in ducts abdullah alhaifi. A steady flow problem of a viscous, incompressible fluid through an orifice is widely applicable to many physical phenomena and has been studied previously by many researchers.
When measuring a viscous fluid such as fossil oil, lube, beverages. Viscous fluid flow viscous fluid flow third edition frank m. We encounter pipe flows almost everywhere for water and gas supply at houses and offices, in fluid machinery, for transporting oil over long distances and at many other places. For a non viscous, incompressible fluid in a steady flow, the sum of pressure, potential and kinetic energies per unit volume is constant at any point.
However, viscous flow boundary layer characteristics for external flows are significantly different. Introduction to fluid dynamics batchelor, second edition. To determine the coefficient of discharge of the orifice meter 1. Flow of liquids from containers volume flow and emptying. Before we can define viscosity, then, we need to define laminar flow and turbulent. Experiments on the flow of viscous fluids through orifices. This course is distinctive in that it shows how quite advanced. This article provides calculation methods for correlating design, flow rate and pressure loss as a fluid passes through a nozzle or orifice.
Engsoft that an orifice does not exhibit a maximum flow. Jobson by making certain basic assumptions, the author has determined a theoretical expression for the contraction coefficient, c, appropriate to an orifice when transmitting a compressible fluid, either. What happens if the fluid passes through a valve of some type, or through an elbow bend in the pipe, or through a region where sudden expansion or contraction occur figure 2. Calculation of flow through nozzles and orifices neutrium. Determining the coefficient of discharge for a draining container. Their experiment, while not exactly the same as judd and king, showed that the discharge coefficient is a function of the flow s exit velocity through the orifice, especially for reynolds numbers between 1 and 10,000. The discharge velocity of fluid from a vessel or reservoir, through an orifice in the. The liquid particles, in order to flow out through the orifice, move towards the orifice from all directions. White university of rhode island me graw hill higher education boston burr ridge, il dubuque, ia madison, wl new york filename.
When the experiments were first undertaken it was hoped by comparing experiments with orifices of different sizes, and in which the viscosity and rate of flow were. Pdf an infiniteseries solution for the creeping motion through. When a viscous liquid flows through a tube in a laminar flow, why is its velocity highest at the center. When a fluid whether liquid or gaseous passes through the orifice, its pressure builds up slightly upstream of the orifice but as the fluid is forced to converge to pass through the hole, the velocity increases and the fluid pressure decreases. Centre of pressure, proof of bernoullis theorem, flow through venturimeter, flow through orifice, flow through mouthpiece, flow over vnotch, flow over sharp crested weir, fluid friction in pipe, head loss due to sudden expansion and sudden contraction of pipe. Pdf download for numerical solutions of viscous flow through a pipe orifice at. Proceedings of the 3rd international conference on fluid flow, heat and mass transfer ffhmt16 ottawa, canada may 2 3, 2016 paper no. There are many types of losses of head for flowing liquids such as friction, inlet and outlet losses. Theory for this calculator can be found on pages 42 thru 45 in the 2009 edition of tp410. The only way this book should be used in a classroom is if it is only a reference book, or if you have a good professor who will take his time going through each section in detail.
However, in reality, the fluid is viscous, and noslip boundary conditions prevail. An integral equation resulting from a surface distribution of vorticity is used to solve numerically for the flow through a circular orifice. The discharge through the orifice jet area x jet velocity. Flow through orifices flow through nozzles pump power gas volume and density unit converters demo home. Semantic scholar extracted view of flow and pressure drop of highly viscous fluids in small aperture orifices by lalit kumar bohra. Pdf this paper presents an infiniteseries solution to the creeping viscous motion of a. Flow through orifices flow through nozzles pump power. The effects of fluid viscosity on the orifice rotameter.
Poiseuille 17991869, who derived it in an attempt to understand the flow of blood, an often turbulent fluid. Numerical solution of a viscous incompressible flow. Discharge coefficient of high viscosity liquids through. In this section, entrance and exit effects are assumed to be negligible where viscous flow predominates and momentum effects are negligible. Viscous damping force is a formulation of the damping phenomena, in which the source of damping force is modeled as a function of the volume, shape, and velocity of an object traversing through a real fluid with viscosity. Their experiment, while not exactly the same as judd and king, showed that the discharge coefficient is a function of the flows exit velocity through the orifice, especially for reynolds numbers between 1 and 10,000. One maintained a steady flow by keeping a constant level in the circular tanks. Pdf twodimensional and axisymmetric viscous flow in.
Orifice plates are most commonly used primary elements for flow measurement in pipelines based on the principle of measurement of differential pressure created when an obstruction is placed in the fluid flow, due to increase in fluid velocity. The resulting system of linear equations is solved by hockneys method 2. Laminar flow is characterized by the smooth flow of the fluid in layers that do not mix. Flow measurement of high viscosity fluids chris mills, craig marshall, andy kay, marc macdonald nel. These fluids oils are highly viscous, and in many instances, their properties show steep dependence on temperature and pressure. As shown in the figure, the jet narrows over a short distance beyond the orifice that is comparable with the jet diameter to form what is generally known as a vena contracta that is. Pdf solution manual for viscous fluid flow by frank. Fluid flow occurs with the motion of liquid and gaseous materials and pressure sensors play a critical role in determining many aspects of fluid flow. This does depend on viscosity but this effect is lumped into the discharge coefficient. Why does fluid flow through an orifice under pressure not. By making the orifice with a knife edge, it becomes insensitive to temperature, and the flow and pressure drop will remain the same over a reasonable range of oil temperatures and viscosity changes. Flow through restrictors is further described in section 2.
Rq2ulilfhorzv orifices and short tubes d w dye and l. Viscous damping force is a formulation of the damping phenomena, in which the source of damping force is modeled as a function of the volume, shape, and velocity of an object traversing through a real fluid with viscosity typical examples of viscous damping in mechanical systems include. These include the higher viscous friction of the fluid being metered, the possibility of extreme or varying velocity profiles, and the. Wall jet and concentric annulus laminar theories were adapted to study the influence of viscosity. Numerical solution of a viscous incompressible flow problem through an orifice by adomian decomposition method. The control volume is a cylindrical shell of thickness r and length x. C d measures how much of the flow area is used by the liquid flowing through the final discharge orifice, in this case, the nozzle. By default, the calculator will show an orifice plate calculation example. Modeling compressible flow through an orifice 5 june 23, 2010 applied flow technology 2955 professional place, colorado springs, co 80904 usa 719 686 fax 719 6861001.
In viscous fluid flow, the authors develop and rationalize the mathematics behind the study of fluid mechanics and examine the flows of newtonian fluids. Article pdf available in journal of fluid mechanics 1151. At points along a horizontal streamline, higher pressure regions have lower fluid speed and lower pressure regions have higher fluid. The various types of fluid flow are dis cussed, and the euler equations are developed. Solution manual for viscous fluid flow by frank white. Viscosity compensation factor v for a single orifice. Ijermce vol 2, issue 4, april 2017 discharge coefficient. But, i cannot understand how it explains liquid flow in a tube or whether it explains at all. It is reasonable to predict that different metering devices will be affected by these phenomena in different ways, but to date the most appropriate technologies for viscous flow measurement are not yet well defined. Online library viscous fluid flow solutions manual viscous fluid flow solutions manual. Freesurface profiles and contraction coefficients are determined for four different ratios of orifice area to pipe area, and a comparison is made between the numerical and experimental results of both. The problem of creeping flow through a finitelength orifice has eluded exact. Experimental results were obtained using molasses having a viscosity of the order of poise. I would say that ch could have been an entire semester, but we went through ch 15, which left a very unsatisfying feeling of having learned very little in the end.
The flow rate through a single orifice is reduced due to viscosity according to these charts below. Numerical solutions of the navierstokes equations have been obtained in the low range of reynolds numbers for steady, axially symmetric, viscous, incompressible fluid flow through an orifice in a circular pipe with a fixed orifice pipe diameter ratio. This equation is called poiseuilles law for resistance after the french scientist j. Compressible flow through orifice and venturi meters two types of devices are treated together. The default calculation involves air passing through a mediumsized orifice in a 4. Determining the coefficient of discharge for a draining. An airtight cover was placed on the top of the tube to prevent flow taking place till desired.
Viscous fluid flow through a pipe with orifices springerlink. A fluid passing though an orifice constriction will experience a drop in pressure across the orifice. Orifice plates are mainly used as a device of flow measurement for fluid delivery systems is based on the measurement of the pressure difference created when forcing the fluid to flow through a restriction in the pipe. Solution of viscous fluid flow white free pdf file sharing. Flow and pressure drop of highly viscous fluids through. Numerical solution of an integral equation for flow from a. Orifice fluid mechanics engineering numerical components. In case you need to convert fromto normal or standard flow rate use the links above. Typical examples of viscous damping in mechanical systems include. A theoretical solution is proposed for the problem of flow through a thin orifice plate placed between chambers having large dimensions relative to the orifice diameter. Superballistic flow of viscous electron fluid through graphene constrictions.
The effects of fluid viscosity on the orifice rotameter in. Numerical solutions of viscous flow through a pipe orifice at low. Numerical solutions of viscous flow through a pipe orifice at. Velocity of a viscous fluid through a tube physics stack. Supplementary information pdf 810 kb rights and permissions. The fluid viscosity effects on the orifice rotameter are investigated using experimental and theoretical models. Stresses on an infinitesimal volume of a viscous fluid. Viscosity is a property of all fluids and manifests itself as internal friction. Agree ment between predicted and measured values in both water and air of orifice impedance is excellent. In a typical variable area flow meter 1, the orifice rotameter has the advantages of simple structure, high reliability, convenient maintenance, low pressure loss, etc. Alexandrou department of mechanical engineering worcester polytechnic institute worcester, ma by boca raton london new york washington, d. Substituting the value of a for the area of the orifice in the equation for fluid flow through an orifice, we can get an additional viscosity dependence part on the same equation. A flow can be an internal flow or an external flow, the distinction being obvious. The flow is therefore considered to be reversible and adiabatic.
Flow through orifices womack machine supply company. Poiseuille did the original derivation shown below which relates pressure loss in a pipe to the velocity and viscosity for laminar flow. The boundary of the small recess may form an annular orifice restriction so as to reduce inlet pressure. To calculate the flowrate of a fluid passing through an orifice plate, enter the parameters below. When you have completed this tutorial, you should be able to do the following.
In red you will find an orifice calculation, feel free to substitute this numbers with your own ones. The three different topologies arising from equation 14as. Fluid dynamics provides the means of understanding the parameters that impact fluid flow. This change can be used to measure the flowrate of the fluid. The spacing between the plates is exaggerated in relation to their length. On the flow of a compressible fluid through orifices. Dynamic behaviour of flow through multistage restricting. In the case of a simple concentric restriction orifice the fluid is accelerated as it passes.
An opening, in a vessel, through which the liquid flows out is known as orifice. It is non viscous c flow of ideal fluid is irrational d it is capable of exhibiting steady flow. Although the material deals with newtonian fluids, the concepts can be easily generalized to nonnewtonian fluid mechanics. A fluid mechanical model of the acoustic behavior of small orifices is presented which predicts orifice resis tance and reactance as a function of incident sound pressure level, frequency, and orifice geometry. Lecture notes course synopsis overview viscous uids are important in so many facets of everyday life that everyone has some intuition about the diverse ow phenomena that occur in practice. Flow of a liquid fluid is said to be streamlined if the velocity of a molecule. An orifice plate is a thin plate with a hole in it, which is usually placed in a pipe. Pdf numerical solution of a viscous incompressible flow. A few of the particles first move downward, then take a turn to enter into the orifice and then finally flow through it. A million newtons is a lot, so this sounds like an awfully high flow rate. Each time the fluid was mixed, a viscositytemperature curve was plotted. Alaa elhazek 48 chapter 7 flow through pipes 71 friction losses of head in pipes 72 secondary losses of head in pipes 73 flow through pipe systems 71 friction losses of head in pipes. The flow was determined by means of the volumetric method, by measuring the volume in time, the fluid temperature values varying.
Specific gravity of the fluid makes a significant difference in the pressure drop through a given orifice, and increases approximately as the. Fluid mechanics apparatus demonstrates the flow through different orifices for different flow rates. Flow and pressure drop of highly viscous fluids through small aperture orifices background in many automotive and hydraulic applications, oil flows through small openings that can be simulated by smalldiameter, squareedged orifices. A set of interchangeable orifices and nozzles for use with the h4 flow through an orifice apparatus. Fluid x y z coordinate system large width narrow gap, 2d fig. A problem of such type has been solved by applying lad method given by roache 1. Flow through an orifice consider the situation, illustrated in figure 4. Orifice, nozzle and venturi flow rate meters the orifice, nozzle and venturi flow rate meters use the bernoulli equation to calculate fluid flow rate using pressure difference through obstructions in the flow. V factor curve may vary depending on specific geometry of the device. The multi hole orifice plates or perforated plates are. Nozzles and orifices are often used to deliberately reduce pressure, restrict flow or to measure flow rate. In the previous section, we discussed frictional losses for flow through a straight length of pipe. Download file pdf solutions manual viscous fluid flow frank white solutions manual viscous fluid flow frank white fluid dynamics simple viscous solutions viscous flow between two flat plates, covering two specific solutions of couette flow movement of top plate with no pressure. An approximate solution is obtained to the problem of fluid flow through a pipe with orifices, in close agreement with the solution obtained numerically.
Georgiou department of mathematics and statistics university of cyprus nicosia, cyprus andreas n. The orifice, nozzle and venturi flow rate meters use the bernoulli equation to calculate fluid flow rate using pressure difference through obstructions in the flow sponsored links in a flow metering device based on the bernoulli equation the downstream pressure after an obstruction will be lower than the upstream pressure before. Loss coefficients for flow through valves and fittings. Flow of liquids through orifices find more information in the tp410 2009 edition. Orifice plates cover a wide range of applications of fluid and operating conditions.
271 849 1302 888 1153 70 474 535 1297 1478 27 712 1427 120 1189 1327 1369 1576 915 923 630 585 255 1163 231 48 879 874 1124 1382 1005 895 809 895 953 234 157