Showing papers on "Pipe flow published in 1972"

Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow.

Abstract: Experiments on fully developed turbulent flow in a channel which is rotating at a steady rate about a spanwise axis are described. The Coriolis force components in the region of two-dimensional mean flow affect both local and global stability. Three stability-related phenomena were observed or inferred: (1) the reduction (increase) of the rate of wall-layer streak bursting in locally stabilized (destabilized) wall layers; (2) the total suppression of transition to turbulence in a stabilized layer; (3) the development of large-scale roll cells on the destabilized side of the channel by growth of a Taylor-Gortler vortex instability. Local effects of rotational stabilization, such as reduction of the turbulent stress in wall layers, can be related to the local Richardson number in a simple way. This paper not only investigates this effect, but also, by methods of flow visualization, exposes some of the underlying structure changes caused by rotation.-

Applied Fluid Mechanics

Abstract: (NOTE: Most chapters begins with The Big Picture and Objectives and concludes with References, Internet Sites, Practice Problems, and Computer Programming Assignments sections) 1 The Nature of Fluids and the Study of Fluid Mechanics Basic Introductory Concepts The International System of Units (SI) The US Customary System Weight and Mass Temperature Consistent Units in an Equation The Definition of Pressure Compressibility Density, Specific Weight, and Specific Gravity Surface Tension 2 Viscosity of Fluids Dynamic Viscosity Kinematic Viscosity Newtonian Fluids and Nonnewtonian Fluids Variation of Viscosity with Temperature Viscosity Measurement SAE Viscosity Grades ISO Viscosity Grades Hydraulic Fluids for Fluid Power Systems 3 Pressure Measurement Absolute and Gage Pressure Relationship Between Pressure and Elevation Development of the Pressure-Elevation Relation Pascal's Paradox Manometers Barometers Pressure Expressed as the Height of a Column of Liquid Pressure Gages and Transducers 4 Forces Due to Static Fluids Gases Under Pressure Horizontal Flat Surfaces Under Liquids Rectangular Walls Submerged Plane Areas-General Development of the General Procedure for Forces on Submerged Plane Areas Piezometric Head Distribution of Force on a Submerged Curved Surface Effect of a Pressure Above the Fluid Surface Forces on a Curved Surface with Fluid Below It Forces on Curved Surfaces with Fluid Above and Below 5 Buoyancy and Stability Buoyancy Buoyancy Materials Stability of Completely Submerged Bodies Stability of Floating Bodies Degree of Stability 6 Flow of Fluids and Bernoulli's Equation Fluid Flow Rate and the Continuity Equation Commercially Available Pipe and Tubing Recommended Velocity of Flow in Pipe and Tubing Conservation of Energy-Bernoulli's Equation Interpretation of Bernoulli's Equation Restrictions on Bernoulli's Equation Applications of Bernoulli's Equation Torricelli's Theorem Flow Due to a Falling Head 7 General Energy Equation Energy Losses and Additions Nomenclature of Energy Losses sand Additions General Energy Equation Power Required by Pumps Power Delivered to Fluid Motors 8 Reynolds Number, Laminar Flow, Turbulent Flow, and Energy Losses Due to Friction Reynolds Number Critical Reynolds Numbers Darcy's Equation Friction Lass in Laminar Flow Friction Loss in Turbulent Flow Equations for Friction Factor Hazen-Williams Formula for Water Flow Other Forms of the Hazen-Williams Formula Nomograph for Solving Hazen-Williams Formula 9 Velocity Profiles for Circular Sections and Flow in Noncircular Sections Velocity Profiles Velocity Profile for Laminar Flow Velocity Profile for Turbulent Flow Flow in Noncircular Sections 10 Minor Losses Resistance Coefficient Sudden Enlargement Exit Loss Gradual Enlargement Sudden Contraction Gradual Contraction Entrance Loss Resistance Coefficients for Valves and Fittings Application of Standard Valves Pipe Bends Pressure Drop in Fluid Power Valves Flow Coefficients for Valves Using Cv Plastic Valves 11 Series Pipe Line Systems Class I Systems Spreadsheet Aid for Class I Problems Class II Systems Class III Systems Pipeline Design for Structural Integrity 12 Parallel Pipe Line Systems Systems with Two Branches Systems with Three or More Branches-Networks 13 Pump Selection and Application Parameters Involved in Pump Selection Types of Pumps Positive Displacement Pumps Kinetic Pumps Performance Data for Centrifugal Pumps Affinity Laws for Centrifugal Pumps Manufacturer's Data for Centrifugal Pumps The Operating Point of a Pump and Pump Selection Net Positive Suction Head Suction Line Details Discharge Line Details Piping System Design and Pump Selection Procedure Alternate System Operating Modes Pump Selection and Specific Speed Life Cycle Costs for Pumped Fluid System Software for Piping System Design and Pump Selection 14 Open Channel Flow Classification of Open Channel Flow Hydraulic Radius and Reynolds Number in Open Channel Flow Kinds of Open Channel Flow Uniform Steady Flow in Open Channels The Geometry of Typical Open Channels The Most Efficient Shapes for Open Channels Critical Flow and Specific Energy Hydraulic Jump Open Channel Flow Measurement 15 Flow Measurement Flowmeter Selection Factors Variable Head Meters Variable Area Meters Turbine Flowmeter Vortex Flowmeter Magnetic Flowmeter Ultrasonic Flowmeters Positive Displacement Meters Mass Flow Measurement Velocity Probes Level Measurement Computer-Based Data Acquisition and Processing 16 Forces Due to Fluids in Motion Force Equation Impulse-Momentum Equation Problem-Solving Method Using the Force Equations Forces on Stationary Objects Forces on Bends in Pipe Lines Forces on Moving Objects 17 Drag and Lift Drag Force Equation Pressure Drag Drag Coefficient Friction Drag on Spheres in Laminar Flow Vehicle Drag Compressibility Effects and Cavitation Lift and Drag on Airfoils 18 Fans, Blowers, Compressors, And The Flow Of Gases Gas Flow Rates and Pressures Classification of Fans, Blowers, and Compressors Flow of Compressed Air and Other Gases in Pipes Flow of Air and Other Gases through Nozzles 19 Flow Of Air In Ducts Energy Losses in Ducts Duct Design Energy Efficiency and Practical Consideration in Duct Design Appendixes Properties of Water Properties of Common Liquids Typical Properties of Petroleum Lubricating Oils Variation of Viscosity with Temperature Properties of Air Dimensions of Steel Pipe Dimensions of Steel Tubing Dimensions of Type K Copper Tubing Dimensions of Ductile Iron Pipe Areas of Circles Conversion Factors Properties of Areas Properties of Solids Gas Constant, Adiabatic Exponent, and Critical Pressure Ratio for Selected Gases Answers to Selected Problems Index

Laminar Flow in Tubes with Constriction

Abstract: To understand the abnormal flow conditions caused by the presence of stenoses in arteries, an analytical solution is obtained for the steady laminar flow of an incompressible Newtonian fluid in an axisymmetric conduit with irregular surface where the spread of the surface roughness is large compared with the mean radius of the conduit. Numerical results are presented for the streamlines, the distributions of velocity, vorticity, and pressure, the energy dissipation, and the separation and reattachment points for conduits with sinusoidal wall variations. The analysis is also applicable to a locally constricted conduit, provided the separation zone does not extend into the straight wall portion of the conduit.

The stability of Poiseuille flow in a pipe of circular cross-section

Abstract: The stability of Poiseuille flow in a pipe of circular cross-section to azimuthally varying as well as axisymmetric disturbances has been studied. The perturbation velocity and pressure were expanded in a complete set of orthonormal functions which satisfy the boundary conditions. Truncating the expansion yielded a matrix differential equation for the time dependence of the expansion coefficients. The stability characteristics were determined from the eigenvalues of the matrix, which were calculated numerically. Calculations were carried out for the azimuthal wavenumbers n = 0,…, 5, axial wavenumbers α between 0·1 and 10·0 and αR [les ] 50000, R being the Reynolds number. Our results show that pipe flow is stable to infinitesimal disturbances for all values of α, R and n in these ranges.

Transient Flow in Free-Surface, Pressurized Systems

Abstract: Transients may arise in a hydraulic system such that flow conditions may alternate between free surface and submerged or pressurized behavior. Analytical considerations begin with the open-channel surge equations, and the resulting method-of-characteristics solution. The surge wave in the tunnel is described after Meyer-Peter and Favre. At the free-surface, pressurized interface, a method of solution similar to the movement of a hydraulic bore is arrived at. An experimental study is presented which describes the phenomena and gives verification to the numerical mode. As an application the Wettingen system is analyzed and shown to agree favorably with earlier results.

Velocity measurements made with a laser dopplermeter on the turbulent pipe flow of a dilute polymer solution

Abstract: This paper presents some new measurements which have been made on a drag-reducing polymer solution in pipe flow. A novel type of laser dopplermeter, which has been developed by the author, is briefly described and the measurements which have been obtained are given. These results and their implications are then discussed in terms of conventional models for turbulent flow in a pipe. These suggest that the polymer has very little effect upon the turbulent core of the flow, but thickens and stabilizes the viscous sublayer. The turbulent intensity inside the sublayer is unchanged but, owing to its thickening, the velocity fluctuations just outside are greater. There is not a general suppression of turbulence within the sublayer although well inside the sublayer the spanwise velocity component is found to be reduced.

Behavior of dispersed particles in turbulent liquid flow

Abstract: Turbulent motion of particles suspended in water in a stirred tank and that of drops supplied to turbulent pipe flow of water are studied with emphasis on their scales. The scales considered are 1) sampling time scale : the very small time interval in which the displacement of a particle is measured, 2) measuring time scale : the time-duration during which a continuous measurement is run, and 3) sampling spatial scale : the width of a location in which the displacement of a particle is followed. The effects of these scales on the magnitude of turbulence velocity components are examined, and the magnitudes are evaluated with a set of values of scales which seem most appropriate to each particle motion. The magnitudes are correlated uniformly in both dispersions with particle diameters and energy dissipation rates of surrounding liquid.

Asymptotic analysis of turbulent channel and boundary-layer flow

Abstract: : Asymptotic expansion techniques are used in the limit of large Reynolds number, to study the structure of fully turbulent shear layers. Two cases examined are channel (or pipe) flow and two-dimensional boundary layer flow with an applied pressure gradient, upstream of any separation. Attention, for these two cases, is confined to the flow of incompressible constant-property fluids. Closure is effected through the introduction of an eddy viscosity model formulated with sufficient generality so that most existing models are special cases.

Laminar Flow Past a Circle in a Shear Flow

Abstract: A numerical solution of the equations governing time‐dependent, viscous, incompressible fluid flow past a circle is presented for Reynolds number 400. The free‐stream velocity profile corresponds to the time‐averaged flow of a turbulent jet. The location and strength of the jet are adjusted so that the free stream approximates a linear shear flow in the vicinity of the circle. The asymmetry of the free stream causes a shift of the upstream stagnation streamline (the Pitot‐tube displacement effect) and small biases in the lift and torque exerted upon the circle. This lift bias is suggested as a contributing factor in the observed stability of raindrops in vertical wind tunnels. Contour plots of the vorticity and stream function are compared with histories of the pressure distribution, drag, lift, torque, and separation angles. These comparisons show how the asymmetry of the free stream manifests itself in terms of fine details within the flow pattern around the circle.

Closed Streamlines Associated with Channel Flow over a Cavity

Abstract: The viscous Stokes flow induced in a rectangular cavity by a parallel shear flow is calculated by a direct finite difference method. The separating streamline and the intensity of the circulation of the closed streamline flow within the cavity are shown as a function of cavity shape, relative channel size to cavity size, and the parallel velocity profile within the channel. Application of the results to viscous flow observations are indicated.

Observations of early turbulence in the pipe flow of drag reducing polymer solutions

Abstract: Early turbulence has for the first time been observed in the flow of very dilute polymer solutions in tubes larger than capillary size. Flow rate-wall shear stress measurements were conducted in 0.553 and 0.660 cm. diameter pipes. Polyethylene oxide samples of two molecular weights were employed, dissolved in water-glycerine mixtures with viscosities ranging from 0.0261 to 0.160 poise. The flow rate-wall shear stress relationship for these solutions corresponded to Poiseuille's Law below a well-defined onset wall shear stress, at which the Reynolds number was less than the transition value for Newtonian fluids. As the flow rate was increased from the onset condition, however, the wall shear stress became progessively larger than that predicted by the Poiseuille relationship. The onset wall shear stress for the phenomenon increased linearly with solvent viscosity. Its relationship to polymer concentration was dependent on the solvent viscosity. An explanation for early turbulence is suggested on the basis of these results, and the relationship of the phenomenon to turbulent flow drag reduction is discussed.

Turbulent Flow in Smooth and Rough Pipes

Abstract: Fully developed turbulent flow in both smooth and rough-walled pipes is investigated for Reynolds number from 30,000 to 480,000. The values of mean velocity, root-mean-square values of the fluctuating velocity components, and cross-correlation values of the fluctuating velocities are presented for flow in a smooth pipe and two sand roughened pipes. Differences between smooth and rough pipe results, suggests that the accepted reduction of the Reynolds equations for flow in smooth pipes is not valid for flow in rough pipes. Thus, the Reynolds equations are re-examined for flow in rough pipes, and it is shown that these equations can be satisfied by the experimental data if secondary flows and angular variations in the mean velocity are postulated.

Transition to turbulence in pipe flow for water and dilute solutions of polyethylene oxide

Abstract: An experimental study of the transition from laminar to turbulent flow in a long 0·248in. I.D. pipe is reported for both water and dilute water solutions of polyethylene oxide which exhibit turbulent flow drag reduction (the Toms phenomenon). The drag-reducing solutions, ranging in effectiveness from near zero to the maximum attainable, are observed to undergo transition in a similar way to the Newtonian solvent in that the solutions exhibit intermittency and the growth rates of the turbulent patches are essentially equal to those of the pure solvent. The growth rate of turbulent patches indicates that drag reduction is associated with the small-scale structure of the turbulence near the pipe wall while patch growth is associated with the larger-scale turbulence in the outer flow. For low-disturbance pipe inlet conditions the strong drag-reducing solutions are observed to undergo transition at lower Reynolds numbers than the pure solvent.

Drag reduction in dilute flowing gas‐solid suspensions

Abstract: The effect of solids loading ratio, particle size, and gas Reynolds number on the pressure drop and flow characteristics of a dilute gas-solid suspension in turbulent pipe flow has been studied experimentally in both vertical and horizontal test sections. Glass beads of 10 to 60μ diameter were used at air Reynolds numbers of 10,000 to 25,000 and solids loading ratios of up to 2.5 Drag reduction was observed in the vertical test section for all of the particles studied, with the 30μ particles yielding a maximum drag reduction of about 75% at a loading ratio of 1.5. In the horizontal test section, drag reduction was observed only with the smallest sized particles, indicating a gravity effect. An explanation of these results based on the particles interacting with the turbulent structure of the gas near the wall has been proposed.

Laminarization of turbulent pipe flow by fluid injection

Abstract: The effects of fluid injection on the structure of an initially fully developed, low Reynolds number, turbulent pipe flow have been studied by means of a hot-film anemometer. Measurements were made of the axial turbulence intensity field and of the time-mean streamwise velocity distribution, both in the porous-walled pipe and in the solid-walled hydrodynamic development section. Oscilloscope traces showing the timewise pattern of the local velocity fluctuations were also monitored. The Reynolds number of the air flow at the inlet of the porous pipe was varied from 3090 to 6350, and the Reynolds number of the injected air ranged from 60 to 160.Near the tube wall, the initial effect of injection is a significant reduction of the axial turbulence level and an increase in the thickness of the viscous and buffer layers. The degree by which turbulence is reduced in this region is more or less proportional to the ratio of the injection to entrance Reynolds numbers. In the core region of the flow, which is centred about the tube axis, there is also an initial reduction in the magnitude of the axial component of turbulence which is thought to be due to injection-induced acceleration of the flow. There is also an annular region, which separates the wall and core regions, in which the turbulence intensity initially increases. In the downstream portion of the porous tube the entire flow undergoes a re-transition to fully developed turbulence.

Reverse flow sensing hot wire anemometer

Abstract: The technique described was developed to enable measurements of velocity to be made in essentially unidirectional pipe flow, under pulsating conditions where reversals of flow direction occurred. The technique uses an ordinary hot wire anemometer but with two additional fine resistance thermometer wires placed one on either side of the hot wire and at right angles to it. The resistance thermometers sense the heated wake of the hot wire and this signal is used to correct the 'rectifying' effect of the hot wire, upon the indicated velocity, under reverse flow conditions. The problem, like the standard hot wire probe, will, however, only quantify the components of velocity normal to the axis of the hot wire and so is unsuitable for use in cases where the flow angle varies appreciably from 0 or 180 degrees . During a study of pulsating air flow in a pipe, flow reversal over part of the pulsation cycle was encountered. A hot wire anemometer was used to record mean values of velocity and root mean square values of the a.c. component of velocity, but due to the inability of the anemometer to sense flow reversals, the measurements of the air velocities were subject to serious error.

Supercritical Flow in Rectangular Expansions

Abstract: In recent years, the occasions for design of channels to contain supercritical flow have increased considerably. A need has developed for a method of predicting the physical characteristics of such flow based on theory. Use has been made of the analogy between supersonic gas flow and supercritical fluid flow to apply the method of characteristics, originally developed for gas dynamics, to fluid mechanics. The writers have checked experimentally the validity of the assumptions made by Bagge and Herbich in the analysis of supercritical flow passing through a rectangular expansion. An experimental model was constructed in the laboratory and the resultant surface profiles obtained for different sets of parameters compared to those predicted by the mathematical model. Results indicated that the assumptions of frictionless flow and negligible velocity perpendicular to the bed of the channel were too important to be neglected. Several graphs comparing theoretical profiles with those obtained in an experimental model are presented.

Resistance Coefficients for Steady Spatially Varied Flow

Abstract: In spatially varied flow three coefficients in Weisbach f form are involved which are sometimes termed resistance coefficients. They are the frictional resistance coefficient, the dissipated energy coefficient, and the total head-loss coefficient. In general these three coefficients are not equal whether there is lateral flow or not. Only for steady uniform flow without lateral flow are these three coefficients equal to one another and to the corresponding f in the Moody diagram. Theoretical solution of steady two-dimensional Stokes flow with lateral flow is obtained to show the difference among these three coefficients. Experimental data for steady two-dimensional sheet flow under simulated rainfall are also analyzed to illustrate numerically the variations of these coefficients. In practice, hydraulic engineers should keep in mind the difference in these different resistance coefficients, to avoid unnecessary errors.

Stream filament mixer for pipe flow

Abstract: A stream filament mixer for reducing stratification of velocitystratified flows and net vortex flows within a piping system, which includes: a housing to be connected in the piping system forming a fluid flow passage having an inlet and an outlet; associated guide surfaces formed by a plurality of circumferentially disposed oppositely twisted adjacent strips connected in the longitudinal line of the housing, for generating a plurality of oppositely rotating vortexes of equal strength in the fluid passing through the fluid flow passage formed by the housing so that the fluid will be delivered in a substantially homogeneous, unstratified flow from the outlet of the housing into the associate piping of the piping system in which the stream filament mixer is connected without generating substantial differential pressure across the point where the stream filament is connected in the piping system.

Degradation of Dilute Solutions of Drag-reducing Polymer

Abstract: DILUTE solutions of certain long-chain polymers exhibit the Toms phenomenon whereby the resistance to flow is reduced in comparison with that of the pure solvent1. For pipe flow it is possible, in favourable conditions, to increase the discharge produced by a particular pressure gradient by 50% or more by the addition of 10 parts per million by weight (p.p.m.w.) of polymer2, provided that the Reynolds number is sufficiently large.

Orifice Losses for Laminar Approach Flow

Abstract: In all, 25 orifices are studied which include sharp-edged concentric, eccentric and segmental orifices, quadrant-edged concentric orifices and square-edged long orifices. The β ratio (ratio of orifice diameter to pipe diameter) is varied from 0.2 to 0.8 except for the long orifice for which studies are conducted for β = 0.2. The nature of variation of the loss coefficient with the Reynolds number is analyzed for different orifices. The loss coefficient curves for several orifices give an indication of the value of the critical Reynolds number at which the flow immediately downstream of the orifice ceases to be laminar even though the approach flow is laminar. In paritcular, for β = 0.8, a very sharp transition is seen in the loss coefficient curve. Based on interpolation of the experimental results, a comparison is made of the loss characteristics of the different types of orifices. The effect of Reynolds number, β ratio, edge radius, eccentricity, segmental opening and orifice length are studied.