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Showing papers on "Open-channel flow published in 1987"


Journal ArticleDOI
TL;DR: In this article, a modified constitutive relation that applies everywhere in the flow field, in both yielded and practically unyielded regions, is proposed to analyze two-dimensional flows of Bingham fluids.
Abstract: Steady, two‐dimensional flows of Bingham fluids are analyzed by means of a modified constitutive relation that applies everywhere in the flow field, in both yielded and practically unyielded regions. The conservation equations and the constitutive relation are solved simultaneously by Galerkin finite element and Newton iteration. This combination eliminates the necessity for tracking yield surfaces in the flow field. The analysis is applied to a one‐dimensional channel flow, a two‐dimensional boundary layer flow, and a two‐dimensional extrusion flow. The finite element predictions compare well with available analytic solutions for limiting cases.

1,177 citations


Journal ArticleDOI
TL;DR: In this paper, the appearance of additional vortices for curved pipes of particular cross-sectional forms, existence of dual solutions, and effects of the pitch on the flow in a helically coiled pipe are presented.
Abstract: This paper brings together recent information on flow in curved pipes. As to fully developed laminar flow, the appearance of additional vortices for curved pipes of particular cross-sectional forms, existence of dual solutions, and effects of the pitch on the flow in a helically coiled pipe are presented. In the case of developing laminar flow in a curved pipe, fascinating behavior of the separation of the secondary flow boundary layer near the inner wall is shown. Flow in a rotating curved pipe and a periodically curved pipe are also discussed. Different hydrodynamic conditions at the inlet greatly affect the flow in the bend ; a strong swirl is created downstream of two 90° bends in combination according to the combination angles. A brief description of the discharge coefficients for bend flowmeters, and unsteady flow in curved pipes are also given.

391 citations


Book
01 Jan 1987
TL;DR: In this paper, the authors used an annular flow model to calculate boiling heat transfer coefficients and critical heat flux in two-phase flow in pipe fittings, and applied it to an industry reboilers.
Abstract: Introduction Two-phase flow patterns and flow pattern maps Bubbly and plug flow Annular flow Homogeneous flow Pressure drop in two-phase flow - overall methods for separated flow Drift flux model Critical two-phase flow Detailed phenomena in annular flow: Wave behaviour, deposition and entrainment Annular flow models Flooding in two-phase flow Instabilities in two-phase flow Two-phase flow in pipe fittings Boiling: Introduction and pool boiling Critical heat flux in pool boiling Flow boiling: Onset of nucleation and heat transfer Critical heat flux in flow boiling Mixture effects in boiling Calculation of boiling heat transfer coefficients and critical heat flux using an annular flow model Post-burnout heat transfer Rewetting of hot surfaces Condensation Process industry reboilers Condensers Practical calculation methods Questions Appendices Index.

357 citations


Journal ArticleDOI
TL;DR: The second revised edition of this comprehensive handbook by one of the leading experts in the field of hydraulic engineering has been completely updated and will be a valued addition to the literature as discussed by the authors.
Abstract: The second, revised edition of this comprehensive handbook by one of the leading experts in the field of hydraulic engineering has been completely updated and will be a valued addition to the literature. Partial Contents: General Information and Elements of Aerodynamics and Hydraulics of Pressure Systems; Flow in Straight Tubes and Conduits; Flow at the Entrance into Tubes and Conduits; Flow through Orifices with Sudden Changes in Velocity and Flow Area; Flow with a Smooth Change in Velocity; Flow with Changes in Stream Direction; Merging of Flow Streams and Division into Flow Streams; Flow through Barriers Uniformly Distributed over the Channel Cross Section; Flow through Pipe Fittings and Labyrinth Seals; Flow Past Obstructions in a Tube; Flow at the Exit from Tubes and Channels; Flow through Various Types of Apparatus.

309 citations



Journal ArticleDOI
TL;DR: In this paper, a series of numerical simulations with aim to document the problem of forced convection in a channel filled with a fluid-saturated porous medium is presented, where the effects of flow inertia, variable porosity and Brinkman friction are taken into account.
Abstract: This paper presents a series of numerical simulations with aim to document the problem of forced convection in a channel filled with a fluid-saturated porous medium. In modeling the flow in the channel, the effects of flow inertia, variable porosity and Brinkman friction are taken into account. Two channel configurations are investigated: parallel plates and circular pipe. In both cases, the channel wall is maintained at constant temperature. It is found that the general flow model predicts an overall enhancement in heat transfer between the fluid/porous matrix composite and the walls, compared to the predictions of the widely used Darcy flow model. This enhancement is reflected in the increase of the value of the Nusselt number. Important results documenting the dependence of the temperature and flow fields in the channel as well as the dependence of the thermal entry length on the problem parameters are also reported in the course of the study.

164 citations


Journal ArticleDOI
TL;DR: In this paper, the second-moment closure applied by Gibson & Launder (1978) to buoyant turbulent flows is used without modification to compute the effects of Coriolis forces on fully-developed flow in a rotating channel.
Abstract: The second-moment closure applied by Gibson & Launder (1978) to buoyant turbulent flows is here employed without modification to compute the effects of Coriolis forces on fully-developed flow in a rotating channel. The augmentation of turbulent transport on the pressure surface of the channel and its damping on the suction surface seem to be well captured by the computations, provided the flow near the suction surface remains turbulent. The rather striking alteration in shape of the mean velocity profile that occurs as the Rossby number is increased from 0.06 to 0.2 is shown to be explicable in terms of the modification to the intensity of the turbulent velocity fluctuations normal to the plate; for the larger value of Rossby number these fluctuations become larger than those in the flow direction causing what at low spin rates is a source of shear stress to become a sink.

159 citations



Journal ArticleDOI
TL;DR: In this article, Galerkin finite-element analysis is used to predict the isothermal free-surface flow of a Newtonian liquid near the advancing front between parallel plates, and the most interesting visualization of the calculated flow is obtained by tracking lines of material, thus producing numerical tracer experiments.
Abstract: Moldability criteria and process optimization for both reactive and thermoplastic injection molding hinge on the mold-filling step. The fluid mechanics of the filling step is typically described in terms of a one-dimensional main flow and a complex two-dimensional flow near the advancing front, often termed the “fountain flow.” A unique apparatus which permits direct observation of the fountain flow in a rectangular cavity is described. The motion of tracer lines as well as the pathlines have been photographed for both Newtonian and shear-thinning liquids. The data show clearly the main flow, the transition to the front flow, and the deceleration and acceleration zones in the fountain flow, which lead to a “mushrooming” of the tracer line. In addition, Galerkin finite-element analysis is used to predict the isothermal free-surface flow of a Newtonian liquid near the advancing front between parallel plates. The most interesting visualization of the calculated flow is obtained by tracking lines of material, thus producing numerical tracer experiments. The calculations show the widely varying residence times and the complex shear and extensional deformation histories of fluid elements as they move through the fountain flow region. The calculations are in agreement with the experiments and clarify previous results, both theoretical and experimental, that did not capture the details of the entire flow field.

128 citations


Journal ArticleDOI
TL;DR: In this article, conditions of flow are analyzed and a modified Tresca yield pyramids of the original theory with conical yield surfaces and relating the strain rates to the stresses by the Levi flow rule are considered.

112 citations


Journal ArticleDOI
TL;DR: In this article, a general finite-volume approach to the calculation of turbulent flow in geometrically complex domains, based on a non-orthogonal cordinate formulation of the governing equations with contravariant physical velocity components, is presented.

Journal ArticleDOI
TL;DR: Both axial and secondary velocities were measured, enabling a detailed description of the complete flow field, and the development of the axial flow field can be quite well explained from the secondary velocity field.
Abstract: Laser-Doppler velocity measurements were performed on the entry flow in a 90° bend of circular cross-section with a curvature ratio a/R = 1/6. The steady entry velocity profile was parabolic, having a Reynolds number Re = 700, with a corresponding Dean number ? = 286. Both axial and secondary velocities were measured, enabling a detailed description of the complete flow field. The secondary flow at the entrance of the bend was measured to be directed completely towards the inner bend. Significant disturbance of the axial velocity field was not measured until a downstream distance (aR)½. Maximum secondary velocities were measured at 1.7 (aR)½ downstream from the inlet. The development of the axial flow field can be quite well explained from the secondary velocity field.

Book
01 Jan 1987
TL;DR: In this article, the authors describe the three phases of water flow, including the free surface of water, surface tension and Capillarity, and the surface tension of water.
Abstract: 1 FUNDAMENTAL PROPERTIES OF WATER 1.1 The Earth's Atmosphere and Atmospheric Pressure 1.2 The Three Phases of Water 1.3 Mass (Density) and Weight (Specific Weight) 1.4 Viscosity of Water 1.5 Surface Tension and Capillarity 1.6 Elasticity of Water 1.7 Forces in a Fluid Field 2 PRESSURE AND PRESSURE FORCES 2.1 The Free Surface of Water 2.2 Absolute and Gage Pressures 2.3 Surfaces of Equal Pressure 2.4 Manometers 2.5 Hydrostatic Forces on Flat Surfaces 2.6 Hydrostatic Forces on Curved Surfaces 2.7 Buoyancy 2.8 Flotation Stability 3 WATER FLOW IN PIPES 3.1 Description of Pipe Flow 3.2 The Reynolds Number 3.3 Forces in Pipe Flow 3.4 Energy in Pipe Flow 3.5 Loss of Head Due to Friction 3.6 Empirical Equations for Friction Head Loss 3.7 Friction Head Loss-Discharge Relationships 3.8 Loss of Head in Pipe Contractions 3.9 Loss of Head in Pipe Expansions 3.10 Loss of Head in Pipe Bends 3.11 Loss of Head in Pipe Valves 3.12 Method of Equivalent Pipes 3.12.1 Pipes in Series 3.12.2 Pipes in Parallel 4 PIPELINES AND PIPE NETWORKS 4.1 Pipelines Connecting Two Reservoirs 4.2 Negative Pressure Scenarios (Pipelines and Pumps) 4.3 Branching Pipe Systems 4.4 Pipe Networks 4.4.1 The Hardy Cross Method 4.4.2 The Newton Method 4.5 Water Hammer Phenomenon in Pipelines 4.6 Surge Tanks 5 WATER PUMPS 5.1 Centrifugal (Radial Flow) Pumps 5.2 Propeller (Axial Flow) Pumps 5.3 Jet (Mixed Flow) Pumps 5.4 Centrifugal Pump Characteristic Curves 5.5 Single Pump and Pipeline Analysis 5.6 Pumps in Parallel or in Series 5.7 Pumps and Branching Pipes 5.8 Pumps and Pipe Networks 5.9 Cavitation in Water Pumps 5.10 Specific Speed and Pump Similarity 5.11 Selection of a Pump 6 WATER FLOW IN OPEN CHANNELS 6.1 Open Channel Flow Classifications 6.2 Uniform Flow in Open Channels 6.3 Hydraulic Efficiency of Open Channel Sections 6.4 Energy Principles in Open Channel Flow 6.5 Hydraulic Jumps 6.6 Gradually Varied Flow 6.7 Classifications of Gradually Varied Flow 6.8 Computation of Water Surface Profiles 6.9 Hydraulic Design of Open Channels 7 GROUND WATER HYDRAULICS 7.1 Movement of Ground Water 7.2 Steady Radial Flow to a Well 7.2.1 Steady Radial Flow in Confined Aquifers 7.2.2 Steady Radial Flow in Unconfined Aquifers 7.3 Unsteady Radial Flow to a Well 7.3.1 Unsteady Radial Flow in Confined Aquifers 7.3.2 Unsteady Radial Flow in Unconfined Aquifers 7.4 Field Determination of Aquifer Characteristics 7.4.1 Equilibrium Test in Confined Aquifers 7.4.2 Equilibrium Test in Unconfined Aquifers 7.4.3 Nonequilibrium Test 7.5 Aquifer Boundaries 7.6 Surface Investigations of Ground Water 7.6.1 The Electrical Resistivity Method 7.6.2 Seismic Wave Propagation Methods 7.7 Sea Water Intrusion in Coastal Areas 7.8 Seepage Through Dam Foundations 7.9 Seepage Through Earth Dams 8 HYDRAULIC STRUCTURES 8.1 Functions of Hydraulic Structures 8.2 Dams-Functions and Classifications 8.3 Stability of Gravity and Arch Dams 8.3.1 Gravity Dams 8.3.2 Arch Dams 8.4 Small Earth Dams 8.5 Weirs 8.6 Overflow Spillways 8.7 Side-Channel Spillways 8.8 Siphon Spillways 8.9 Culverts 8.10 Stilling Basins 9 WATER PRESSURE, VELOCITY, AND DISCHARGE MEASUREMENTS 9.1 Pressure Measurements 9.2 Velocity Measurements 9.3 Discharge Measurements in Pipes 9.4 Discharge Measurements in Open Channels 9.4.1 Sharp-Crested Weirs 9.4.2 Broad-Crested Weirs 9.4.3 Venturi Flumes 10 HYDRAULIC SIMILITUDE AND MODEL STUDIES 10.1 Dimensional Homogeneity 10.2 Principles of Hydraulic Similitude 10.3 Phenomena Governed by Viscous Forces -- Reynolds Number Law 10.4 Phenomena Governed by Gravity Forces -- Froude Number Law 10.5 Phenomena Governed by Surface Tension -- Weber Number Law 10.6 Phenomena Governed by Both Gravity and Viscous Forces 10.7 Models for Floating and Submerged Bodies 10.8 Open Channel Models 10.9 The Pi-Theorem 11 HYDROLOGY FOR HYDRAULIC DESIGN 11.1 The Hydrologic Cycle 11.2 Precipitation 11.3 Design Storm 11.4 Surface Runoff and Stream Flow 11.5 Rainfall-Runoff Relationships -- The Unit Hydrograph 11.6 Rainfall-Runoff Relationships -- SCS Procedures 11.6.1 Losses from Rainfall and Rainfall Excess 11.6.2 Time of Concentration 11.6.3 SCS Synthetic Hydrograph 11.6.4 Summary of SCS Procedure 11.7 Storage Routing 11.8 Hydraulic Design -- The Rational Method 11.8.1 Design of Stormwater Collection Systems 11.8.2 Design of Stormwater Pipes 12 STATISTICAL METHODS IN HYDROLOGY 12.1 Concepts of Probability 12.2 Statistical Parameters 12.3 Probability Distributions 12.3.1 Normal Distribution 12.3.2 Log-Normal Distribution 12.3.3 Gumbel Distribution 12.3.4 Log-Pearson Type III Distribution 12.4 Return Period and Hydrologic Risk 12.5 Frequency Analysis 12.5.1 Frequency Factors 12.5.2 Testing Goodness of Fit 12.5.3 Confidence Limits 12.6 Frequency Analysis Using Probability Graphs 12.6.1 Probability Graphs 12.6.2 Plotting Positions 12.6.3 Data Plotting and Theoretical Distributions 12.6.4 Estimating Future Magnitudes 12.7 Rainfall Intensity-Duration-Frequency Relationships 12.8 Applicability of Statistical Methods SYMBOLS ANSWERS TO SELECTED PROBLEMS INDEX

Journal ArticleDOI
TL;DR: In this article, the surface-tension-driven breakup of a long filament of fluid in a general linear flow, v = L·x, was studied, and it was shown that the flow around the filament is an axisymmetric extensional flow with a time-dependent strength.

Book ChapterDOI
01 Jan 1987
TL;DR: In this article, the authors describe the simulation of turbulent boundary layers by direct numerical solution of the three-dimensional time-dependent Navier-Stokes equations, using a spectral method.
Abstract: This paper describes the simulation of turbulent boundary layers by direct numerical solution of the three-dimensional time-dependent Navier-Stokes equations, using a spectral method. The flow is incompressible, and Re δ * = 1000 for most cases. The equations are written in the similarity coordinate system and normalized by the local friction velocity. Periodic streamwise and spanwise boundary conditions are then imposed. A family of nine “equilibrium” boundary layers, from the strongly accelerated “sink” flow to Stratford’s separating flow, is treated. Good general agreement with experiments is observed. The effects of the pressure gradient and of the Reynolds number are discussed.

Journal ArticleDOI
TL;DR: In this article, the authors used a conservative form of the Arakawa type for the convective terms in the Navier-Stokes equations and compared the results with earlier ones of Moin and Kim.

PatentDOI
TL;DR: In this paper, the authors proposed to reduce the point of transition from laminar flow to turbulent flow in aerodynamic boundary layers on the surfaces of aircraft by radiating acoustic energy at frequencies greater than twice the critical TollmeinSchlichting frequency into the boundary layer.
Abstract: Retarding of the point of transition from laminar flow to turbulent flow in aerodynamic boundary layers on the surfaces of aircraft is accomplished by radiating acoustic energy at frequencies greater than twice the critical Tollmein-Schlichting frequency into the boundary layer. The acoustic energy interferes with the formation of Tollmein-Schlichting waves, thereby increasing the incidence of laminar flow and reducing aerodynamic drag.

Journal ArticleDOI
TL;DR: In this article, a two-dimensional steady potential flow over a semicircular obstacle at the bottom of a channel is considered and the problem is solved numerically by using an integrodifferential equation formulation derived by Forbes and Schwartz.
Abstract: Two‐dimensional steady potential flow over a semicircular obstacle at the bottom of a channel is considered. The problem is solved numerically by using an integrodifferential equation formulation derived by Forbes and Schwartz [J. Fluid Mech. 114, 299 (1982)]. This equation is reduced to a set of algebraic equations by a difference method and solved by Newton’s method together with parameter variation. The numerical results for subcritical flows agree with those of Forbes and Schwartz. However, it is found that supercritical solutions exist only for values of the Froude number greater than some particular value. Furthermore, for some values of the Froude number, there are two supercritical solutions. One is a perturbation of a uniform stream whereas the other is a perturbation of a solitary wave.

01 May 1987
TL;DR: In this paper, the naphthalene sublimation technique was used to investigate the heat transfer characteristics of turbulent air flow in a two-pass channel and a test section that resembles the internal cooling passages of gas turbine airfoils was employed.
Abstract: The naphthalene sublimation technique is used to investigate the heat transfer characteristics of turbulent air flow in a two-pass channel. A test section that resembles the internal cooling passages of gas turbine airfoils is employed. The local Sherwood numbers on the ribbed walls were found to be 1.5-6.5 times those for a fully developed flow in a smooth square duct. Depending on the rib angle-of-attack and the Reynolds number, the average ribbed-wall Sherwood numbers were 2.5-3.5 times higher than the fully developed values.

Journal ArticleDOI
TL;DR: In this paper, direct numerical simulations of several homogeneous flows and fully developed turbulent channel flow indicate that the probability distribution function (pdf) of relative helicity density exhibits at most a 20 percent deviation from a flat distribution.
Abstract: Results from direct numerical simulations of several homogeneous flows and fully developed turbulent channel flow indicate that the probability distribution function (pdf) of relative helicity density exhibits at most a 20 percent deviation from a flat distribution. Isotropic flows exhibit a slight helical nature but the presence of mean strain in homogeneous turbulence suppresses helical behavior. All the homogeneous turbulent flows studied show no correlation between relative helicity density and the dissipation of turbulent kinetic energy. The channel flow simulations indicate that, except for low-dissipation regions near the outer edge of the buffer layer, there is no tendency for the flow to be helical. The strong peaks in the relative helicity density pdf and the association of these peaks with regions of low dissipation found in previous simulations by Pelz et al.(1985) are not observed.


Journal ArticleDOI
TL;DR: In this article, the mean velocity distribution and turbulence characteristics were revealed in and around the separated shear layer and recirculation region (separation bubble), and the exchange processes of mean-flow and turbulent energies as well as momentum were examined downstream of the step.
Abstract: Turbulence measurements of the backward-facing step flow, including the reverse flow region, in an open channel were conducted using a two-component Laser Doppler anemometer. The mean velocity distribution and turbulence characteristics were revealed in and around the separated shear layer and recirculation region (separation bubble). Reattachment properties and the dynamic pressure distribution were analyzed varying the Reynolds and Froude numbers. The structure of the shear stress was also analyzed on the basis of the momentum equation. The separated step flow and its recirculation in an open channel are similar to that in boundary layer and duct flows. But, the former is more complicated than the latter, because the pressure is relaxed by the existence of the free surface. Finally, the exchange processes of mean-flow and turbulent energies as well as momentum were examined downstream of the step.

01 Jun 1987
TL;DR: In this article, the authors compute the budgets for the turbulent kinetic energy (k) and its dissipation rate (epsilon) from a turbulent channel simulation using data from boundary layer simulations and analyze the dependence of the eddy-viscosity damping function on the Reynolds number and the distance from the wall.
Abstract: The flow fields from a turbulent channel simulation are used to compute the budgets for the turbulent kinetic energy (k) and its dissipation rate (epsilon). Data from boundary layer simulations are used to analyze the dependence of the eddy-viscosity damping-function on the Reynolds number and the distance from the wall. The computed budgets are used to test existing near-wall turbulence models of the k-epsilon type. It was found that the turbulent transport models should be modified in the vicinity of the wall. It was also found that existing models for the different terms in the epsilon-budget are adequate in the region from the wall, but need modification near the wall. The channel flow is computed using a k-epsilon model with an eddy-viscosity damping function from the data and no damping functions in the epsilon-equation. These computations show that the k-profile can be adequately predicted, but to correctly predict the epsilon-profile, damping functions in the epsilon-equation are needed.

Patent
28 Jan 1987
TL;DR: In this paper, an iterative calculation makes it possible to obtain a density measurement corrected to allow for flow friction and individual flow rates of the two components, having regard to slippage therebetween.
Abstract: A gradiomanometer 1 measures the difference in pressure between points 3 and 4 to indicate density and hence proportions of two phases (e.g. liquid and gas), each of known density flowing as indicated by arrow 6. A venturi meter 2 measures the difference in pressure between points 4 and 5 to indicate flow rate, initially assumed to be that of the heavier phase only. An iterative calculation makes it possible to obtain a density measurement corrected to allow for flow friction and individual flow rates of the two components, having regard to slippage therebetween. A step discontinuity 8 may be provided downstream to create turbulence and render the flow homogenous.

DOI
01 Dec 1987
TL;DR: A submitted manuscript is the author's version of the article upon submission and before peer-review as mentioned in this paper, and the final published version features the final layout of the paper including the volume, issue and page numbers.
Abstract: • A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.

Journal ArticleDOI
TL;DR: In this paper, the complete hydrodynamic equations of the shallow water theory in one dimension are employed to compute the flood wave resulting from the total and instantaneous collapse of a dam in a broad rectangular channel.
Abstract: The complete hydrodynamic equations of the shallow‐water theory in one dimension are employed to compute the flood wave resulting from the total and instantaneous collapse of a dam in a broad rectangular channel. The MacCormack numerical scheme is employed to solve the system of flow equations in a conservation‐law form. The actual upstream and downstream boundary conditions of the flow field, i.e., a depth of flow equal to zero at these boundaries and beyond, are used for the solution of the flow equations. The results obtained are compared with computational and experimental data obtained by other investigators. The broad rectangular channel was employed for the purpose of comparing results. The method can easily be applied to channels of arbitrary cross‐sectional shapes, as well as to almost any other unsteady open‐channel flow problem by incorporating the appropriate initial and boundary conditions.

Journal ArticleDOI
TL;DR: In this article, an IBM PC was used to obtain finite-difference solutions to a complex heat transfer and fluid flow problem in which the solution domain contained nearly 6000 grid points.
Abstract: An IBM PC was used to obtain finite-difference solutions to a complex heat transfer and fluid flow problem in which the solution domain contained nearly 6000 grid points. The investigated problem was the abrupt, asymmetric enlargement of a parallel-plate channel. The enlargement lakes the form of a backward-facing step, the presence of which causes separation of the flow. Heat transfer occurred at the channel wall which extended downstream from the foot of the step. The present velocity solutions were shown to be at least as accurate as prior numerical solutions and served to extend the range of investigated enlargements. The variation of the local Nusselt number with the Reynolds number took on different forms at various axial distances from the enlargement step. In a region extending downstream from the step, the Nusselt number actually decreased monotonically with increasing Reynolds number. Farther downstream, the Nusselt-Reynolds variation was monotonically increasing, while still farther downstream,...

Patent
26 Oct 1987
TL;DR: In this paper, Fanning friction factor (f) is calculated for a pipe viscometer section from known values of friction pressure drop over a predetermined length of a pipe section at a known flow velocity, known fluid density and known hydraulic radius of the pipe section, and the actual pressure drop is determined using the calculated value of friction factor and measured values of fluid density, flow velocity and conduit dimensions.
Abstract: Friction pressure losses are obtained for non-Newtonian or generalized Newtonian fluids being pumped through conduits at high flow rates, such as in hydraulic fracturing of subterranean formations, by measuring friction pressure losses in a pipe viscometer under laminar flow conditions. The pipe viscometer includes a pump which supplies fluid to a continuous loop having three pipe sections of different diameter for measuring pressure drop at different flow velocities. Sets of data points of generalized shear stress and shear rate are measured for determining the consistency index (K") and the Power Law or flow behavior index (n'). The generalized Reynolds number of the fluid being pumped is determined using the values of consistency index and flow behavior index and this Reynolds number is maintained in a second pipe viscometer section arranged in parallel with the laminar flow loop by pumping the same fluid wherein the second pipe viscometer section has the same roughness as the conduit through which friction pressure loss is to be determined. The Fanning friction factor (f) is determined for the pipe viscometer section from known values of friction pressure drop over a predetermined length of the pipe viscometer section at a known flow velocity, known fluid density and known hydraulic radius of the pipe viscometer section. The actual pressure drop over a predetermined length of conduit is determined using the calculated value of friction factor (f) and measured values of fluid density, flow velocity and conduit dimensions.


Journal ArticleDOI
TL;DR: In this article, the laminarization phenomenon of the flow in an axially rotating pipe when a fully developed turbulent flow is introduced into it is described, and bursts of turbulence appear, which is also confirmed by the use of a flow visualization technique.
Abstract: This paper describes the laminarization phenomenon of the flow in an axially rotating pipe when a fully developed turbulent flow is introduced into it. The rotating boundary layer is initially strongly stabilized by the centrifugal force due to the rotating velocity component, resulting in a laminarization of flow. This flow laminarization has been found to be more remarkable in the inlet region where a non-rotating inner core exists in the pipe section. The laminarized flow tends to be unstable as the flow goes downstream, and bursts of turbulence appear, which was also confirmed by the use of a flow visualization technique.