Showing papers on "Open-channel flow published in 1969"
TL;DR: In this article, the relation between the flow area of a tidal inlet and the tidal prism of that inlet was studied and the relationship between the two was shown to be the same as in this paper.
Abstract: Classical paper on the relation between the flow area of a tidal inlet and the tidal prism of that inlet
343 citations
TL;DR: In this paper, a quasi-theoretical analysis for the flow retardance in vegetated channels is given, based on which a logarithmic flow formula has been derived for flow in these channels.
Abstract: A quasi-theoretical analysis has been given for the flow retardance in vegetated channels. Based on this, a logarithmic flow formula has been derived for flow in these channels. The analysis has been illustrated with flow data obtained from channels in which natural vegetation was present and from a laboratory flume having flexible artificial roughness elements fixed to the bottom.
238 citations
TL;DR: Viscous flow in a circular cylindrical tube containing an infinite line of rigid spheroidal particles equally spaced along the axis of the tube is considered for uniform axial translation of the spheroids and flow past a line of stationary spheriods and under an imposed pressure gradient as mentioned in this paper.
Abstract: Viscous flow in a circular cylindrical tube containing an infinite line of rigid spheroidal particles equally spaced along the axis of the tube is considered for (a) uniform axial translation of the spheroids (b) flow past a line of stationary spheriods and (c) flow of the suspending fluid and spheroids under an imposed pressure gradient. The fluid is assumed to be incompressible and Newtonian. The Reynolds number is assumed to be small and the equations of creeping flow are used.
175 citations
TL;DR: In this article, the stability of almost fully developed viscous flow in a rotating pipe is considered and it is shown that the flow is unstable for Reynolds numbers R = Wor0/v greater than Rc [asymp ] 82[sdot ]9.
Abstract: The stability of almost fully developed viscous flow in a rotating pipe is considered. In cylindrical polar co-ordinates (r, o, z) this flow has the velocity components
\[
\{W_0o(1),\quad\Omega r[1+o(\epsilon)],\quad W_0[1-r^2/r^2_0+o(1)]\},_{+}^{+}
\]
where e = Wo/2Ωr0 and is bounded externally by the rigid cylinder r = r0, which rotates about its axis with angular velocity Ω. In the limit of small e, the disturbance equations can be solved in terms of Bessel functions and it is shown that, in that limit, the flow is unstable for Reynolds numbers R = Wor0/v greater than Rc [asymp ] 82[sdot ]9. The unstable disturbances take the form of growing spiral waves, which are stationary relative to the rotating cylinder and the critical disturbance at R = Rc has azimuthal wave-number 1 and axial wavelength 2πr0/e. Furthermore, it is shown that the most rapidly growing disturbance for R > Rc has an azimuthal wave-number which increases with R. Some of the problems involved in testing the results by experiment are discussed and a possible application to the theory of vortex breakdown is mentioned. In an appendix this instability is shown to be an example of inertial instability.
161 citations
TL;DR: In this article, a theoretical development of the Navier-Stokes equation through analysis of the dimensionless form of Navier Stokes equation is presented, which shows that energy losses at high-flow velocities in porous medium are a result of convective acceleration effects not turbulent effects.
Abstract: Many investigators are concerned about the validity of the Forchheimer equation which represents the relationship between the velocity of flow and pressure gradient in porous media. A theoretical development of this equation through analysis of the dimensionless form of the Navier-Stokes equation is presented. It shows that energy losses at high-flow velocities in porous medium are a result of convective acceleration effects not turbulent effects. In addition, two dimensionless terms representing the flow behavior are defined and evaluated. It is shown that a constant could be used to represent the geometric properties of the medium and that a characteristic length representative of the flow exist. Both of these quantities are easily evaluated through hydraulic measurements of gradients and flow velocities. Experimental data from many sources were used to evaluate the theoretical results.
157 citations
133 citations
TL;DR: In this article, the reaeration coefficient was shown to be proportional to the vertical mass transfer coefficient at the surface and inversely to the square of the average depth, which can be expressed as k2 = Cu\D*\N/h.
Abstract: The reaeration coefficient can be shown to be proportional to the vertical mass transfer coefficient at the surface and inversely proportional to the square of the average depth. After evaluation and simplification, this can be expressed as k2 = Cu\D*\N/h. The constant is evaluated from experimental data for various scales of flow and the resulting single equation is shown to have greater accuracy, cover a wider range of flow scales, and be less sensitive to variations in basic data than any of the presently used methods of prediction.
113 citations
TL;DR: In this article, it was shown that the flow of viscous incompressible fluid in a circular pipe is stable to small axisymmetric disturbances at all Reynolds numbers and linked with known asymptotic results.
Abstract: Numerical calculations show that the flow of viscous incompressible fluid in a circular pipe is stable to small axisymmetric disturbances at all Reynolds numbers These calculations are linked with known asymptotic results
111 citations
TL;DR: One-dimensional equations of continuity, momentum, and energy for unsteady, spatially varied flow in a fixed-bed open channel of arbitrary configuration are derived from the point forms of the corresponding hydrodynamic equations by integrating the latter over a deforming region of space comprising a slice of differential thickness across the flow with a top always coincident with the fluctuating water surface as discussed by the authors.
Abstract: One-dimensional equations of continuity, momentum, and energy for unsteady, spatially varied flow in a fixed-bed open channel of arbitrary configuration are derived from the point forms of the corresponding hydrodynamic equations by integrating the latter over a deforming region of space comprising a slice of differential thickness across the flow with a top always coincident with the fluctuating water surface. To bring the equations to the form of Saint Venant in fixed and accelerating reference frames, departures from hydrostatic pressure conditions in a cross section due to lateral acceleration, viscous deformation, and turbulent Reynolds stresses are reproduced exactly; the rate of energy dissipation in a cross section is uniquely related to wall shear over the wetted perimeter; the term accounting for lateral discharge depends upon its nature; bulk outflow is considered.
105 citations
TL;DR: In this article, a new predictor for friction factors of flows in sand-bed channels is developed, based on a dimensional analysis to obtain the form of the quantities entering the relation between the geometry of the bed features, flow properties, and the equivalent shear stress due to the form-drag of the ripples, dunes, etc.
Abstract: A new predictor is developed for friction factors of flows in sand-bed channels. A dimensional analysis is pursued to obtain the form of the quantities entering the relation between the geometry of the bed features, the flow properties, and the equivalent shear stress due to the form-drag of the ripples, dunes, etc. Theoretical considerations of the bed stability lead to expressions for the length and height of the bed features in terms of the properties of the bed sediment and flow. These are introduced into the expression yielded by the dimensional analysis, and the resulting frictional relation is quantified with field and laboratory data. The graphical relation of Lovera and Kennedy is used to obtain the flat-bed friction factor. The predictor is evaluated using field data not included in preparation of the graphical relation between the bed-form friction factor, Froude number, and relative roughness. The depth-discharge relations predicted are found to be in good agreement with the measured data.
TL;DR: In this article, hot-film anemometry was used to measure the characteristics of turbulence in hydrodynamically smooth and hydroynamically rough open-channel flow and showed that the relative turbulent intensity of the vertical velocity component was about 60% of the longitudinal, and spectral energy distribution was not significantly affected by the type of flow.
Abstract: Measurements of the characteristics of turbulence in hydrodynamically smooth and hydrodynamically rough open-channel flow using hot-film anemometry technics showed: (a) that the relative turbulent intensity of the vertical velocity component was about 60% of the longitudinal, (b) that the spectral energy distribution was not significantly affected by the type of flow, (c) that most of the turbulent energy is contained in frequencies less than 5 hertz, (d) the macroscale of the turbulence as determined from the autocorrelation function was on the same order as the depth and (e) the ratio of the microscale to depth ranged from 0.1 to 0.2. The measurements were used to verify experimentally the longitudinal direction momentum terms in the Navier-Stokes equation and to determine qualitatively the magnitude of the production, diffusion, and dissipation terms in the energy equation.
TL;DR: Viscous convergent-divergent nozzle flow slender channel approximations, discussed roles of nozzle geometry, Reynolds number and wall temperature, calculating velocity, enthalpy, etc as mentioned in this paper.
Abstract: Viscous convergent-divergent nozzle flow slender channel approximations, discussing roles of nozzle geometry, Reynolds number and wall temperature, calculating velocity, enthalpy, etc
TL;DR: In this paper, the swirling motion of a laminar incompressible viscous flow in a circular duct is studied and a linearized analytical solution, valid for flows having small Reynolds numbers and large swirl ratios, is developed.
Abstract: The swirling motion of a laminar incompressible viscous flow in a circular duct is studied. The duct consists of two smoothly joined sections, one stationary and the other rotating with a constant angular velocity. A linearized analytical solution, valid for flows having small Reynolds numbers and large swirl ratios, is developed. Solutions for a wider range of Reynolds numbers and swirl ratios are obtained by numerically solving the discretized angular momentum and vorticity transport equations. The occurrence of flow reversal on the axis and near the tube wall is studied, in particular, and conditions for incipient flow reversal are established.
TL;DR: In this paper, the statistical properties of the wall pressure field determined from these recordings included the power spectral density, space-time correlations, and convection speeds embracing both broad and narrow (third-octave) frequency bands.
TL;DR: In this article, Segere et al. showed that pipe flow of a particulate suspension is defined by four dimensionless parameters of particle-fluid interactions in addition to the Reynolds number, including the Magnus effect due to fluid shear, electrostatic repulsion due to electric charges on the particles, and Brownian or turbulent diffusion.
Abstract: This study shows that fully developed pipe flow of a particulate suspension is defined by four dimensionless parameters of particle-fluid interactions in addition to the Reynolds number Effects accounted for include the Magnus effect due to fluid shear, electrostatic repulsion due to electric charges on the particles, and Brownian or turbulent diffusion In the case of a laminar liquid-solid suspension, electrostatic effect is negligible but shear effect is prominent Solution of the basic equations gives the density distribution of particles with a peak at the center (Einstein, Jeffery) or at other radii between the center and the pipe wall (Segre et al) depending on the magnitudes of the various flow parameters In the case of a turbulent gas-solid suspension, the Magnus effect is significant only within the thickness of the laminar sublayer However, charges induced on the particles by the impact of particles at the wall produce a higher density at the wall than at the center of the pipe The velocity distribution of particles is characterized by a slip velocity at the wall and a lag in velocity in the core from the fluid phase These results are verified by earlier measurements
TL;DR: In this article, the particle dynamics of a known mixture of two narrowly sized particles for the first time were determined by means of a special photographic technique (dot-streak-dot) and the results were discussed with respect to the loading ratio, pipe Reynolds number and composition of the mixtures.
Abstract: An investigation was carried out to study the particle dynamics of a known mixture of two narrowly sized particles for the first time. The flow characteristics determined by means of a special photographic technique (dot-streak-dot) were particle velocities, turbulence intensities, pressure drop, slip velocities and drag coefficients. The results are discussed with respect to the loading ratio, pipe Reynolds number, and composition of the mixtures. The particle velocity profile and the particle density distribution were analyzed in light of recent theoretical treatments on transport of solids in pipes. Moreover, the concept of volume/surface mean diameter as the representative diameter of the mixed-particle flow system is evaluated in correlating these flow parameters.
Patent•
28 Jul 1969
TL;DR: In this paper, a helically twisted ribbon baffle is axially disposed, anchored at the upstream end and floating within the flow channel for imposing vortex flow within a central core of the fluid passed therethrough.
Abstract: In tubular flow channels for heat or mass transfer between or with components of a fluid, a helically twisted ribbon baffle is axially disposed, anchored at the upstream end and floating within the flow channel for imposing vortex flow within a central core of the fluid passed therethrough. The flow channel wall comprises a porous filtration medium for through transmission or for retention of selected fluid components.
TL;DR: In this article, a theory is presented to define methods of optimum gate operation for altering flow conditions in an open channel, which is applicable to cases of initiating flow, increasing flow, decreasing flow, or stopping flow in irrigation channels, power channels, forebay channels to pumping stations, etc.
Abstract: A theory is presented to define methods of optimum gate operation for altering flow conditions in an open channel. The analytical procedure prescribes the motion of the control devices in the channel so the transient conditions are known and controlled during the period when the flow is being changed from one given situation to another desired flow condition. The method is applicable to cases of initiating flow, increasing flow, decreasing flow, or stopping flow in irrigation channels, power channels, forebay channels to pumping stations, etc. The theory is developed from the basic differential equations for unsteady flow in a prismatic channel, including frictional losses. Two examples are detailed in this study.
TL;DR: In this article, a turbulence theory has been formulated which describes, in a simplified, tractable manner, the effect of various wavenumber fluctuations on the statistical behavior of the fluid elements containing reactive species.
Abstract: A turbulence theory has been formulated which describes, in a simplified, tractable manner, the effect of various wavenumber fluctuations on the statistical behavior of the fluid elements containing reactive species. The theory was then employed, as a primary test, to analyze the turbulent Couette flow of a chemically inert fluid. In the analysis, it was shown that the present theory as applied to a chemically inert fluid is self-containi ng up to the dissipation function. An experimental value of dissipation function for a pipe flow, for lack of the same for a Couette flow, was adapted and used in the analysis. A comparison of the present theoretical results with the available experimental data on Couette flow showed a satisfactory agreement between the two. A simple relationship has been derived between the dissipation function and the other variables of the theory which would render the present theory completely self-containing for the chemically inert single-component flow.
TL;DR: In this paper, an experimental study is described which seeks to assess the effect of elasticity on the flow of elastico-viscous liquids as they are made to flow through curved pipes under a pressure gradient.
Abstract: An experimental study is described which seeks to assess the effect of elasticity on the flow of elastico-viscous liquids as they are made to flow through curved pipes under a pressure gradient. Wherever possible, the experimental results are discussed in the light of existing theoretical predictions and good agreement between theory and experiment for viscous and elastico-viscous liquids is indicated. The general flow pattern for elastico-viscous liquids is shown to be similar to that for Newtonian liquids consisting of two spirals separated by the central plane. Elasticity has a significant effect on the pitch of these spirals. The flow rate in the case of laminar flow and in the transition region between laminar and turbulent flow is significantly enhanced by the presence of elasticity in the liquids, but the opposite is the case in turbulent flow at high Reynolds numbers. Many materials of industrial importance can be classified as elastico-viscous liquids in the sense that they flow under the action of applied stresses and yet have some of the properties usually associated with solids. In technological processes, these elastico-viscous liquids are often pumped through pipes which are usually straight but are sometimes curved. It is therefore of some practical importance to study the behaviour of elastico-viscous liquids as they are made to flow through straight and curved pipes under the action of a pressure gradient. The flow of viscous and elastico-viscous liquids through straight pipes is well documented, but very little consideration appears to have been given to the flow of elastico-viscous liquids through curved pipes. In the present paper, we shall indicate the various interesting features which have arisen from an experimental study of the flow of elastico-viscous liquids through straight and curved pipes of circular cross-section. Our work has been primarily motivated by technological requirements, but it may have applications in other spheres. For example, it may throw light on the flow of blood in the larger capillaries, since it is known that whole blood is non-Newtonian in its behaviour.
TL;DR: In this paper, the authors derived robust estimates of amplification rates, wave speeds and sufficient conditions for linear stability for the manifold of solutions of the Orr-Sommerfeld problem governing parallel motion in the boundary layer and in round pipes.
Abstract: Rigorous estimates of amplification rates, wave speeds and sufficient conditions for linear stability are derived for the manifold of solutions of the Orr—Sommerfeld problem governing parallel motion in the boundary layer and in round pipes. The estimates for channel flow (part I) are improved and compared with numerical results for the neutral stability of Jeffery—Hamel flow.
TL;DR: In this article, the effect of the secondary flow on the temperature field and the primary flow at the outlet of a long electrically heated tube haying thick walls of high conductivity is analyzed for the case of large Grashof-Prandtl number for which a thin temperature boundary layer exists near the wall.
Abstract: : A study was made of the mean flow field of free turbulent layers of variable density showing that if the velocity distribution in a particular constant-density flow is known, it is possible to obtain the corresponding variable-density velocity field without the introduction of a compressible turbulent viscosity. This is accomplished by a Dorodnitsyn-Howarth type of transformation applied to the time-dependent equations of motion rather than to the mean equations of motion, as has been done previously. When the transformed equations are averaged, using Reynolds' method, the incompressible turbulent equations for the mean flow are obtained. These equations can then be handled by conventional methods. Predictions obtained by this procedure agree well with experimental results.
TL;DR: In this article, an analytical solution by Laplace transform is presented for the development region of sediment suspensions in an open-channel flow, which is indistinguishable in accuracy from the computer results.
Abstract: In a recent study, Apmann and Rumer analyzed the nonuniform diffusion of suspended sediment in an open-channel flow. Experiments were performed for the situation in which a uniform open-channel flow enters from a region of rigid bottom to a region of sediment-laden bottom. The gradual development of concentration profiles is studied by measurements across the depth and along the flow direction. Theoretical calculations were also made on the basis of an approximate convective-diffusion equation; and the predicted concentration profiles agreed well with experiments. A numerical method of finite differences was used while the possibility of analytical solutions was apparently overlooked. In view of the significance of their work in extending the validity of the diffusion model for sediment suspensions, it seems worthwhile to present herein an analytical solution by Laplace transform. An approximate formula for the development region is derived from the Laplace inversion integral, which is indistinguishable in accuracy from the computer results.
TL;DR: Flow structure in rectangular cavity in lower wall of two dimensional channel for various aspect ratios and Reynolds numbers for various Reynolds numbers and aspect ratios was described in this paper, where the Reynolds numbers were derived from the aspect ratio and Reynolds number.
Abstract: Flow structure in rectangular cavity in lower wall of two dimensional channel for various aspect ratios and Reynolds numbers
TL;DR: A computer program for solving the basic equations of unsteady flows in reservoirs and natural rivers is being used by the TVA to solve a variety of open-channel flow problems.
Abstract: A digital computer program for solving the basic equations of unsteady flows in reservoirs and natural rivers is being used by the TVA to solve a variety of open-channel flow problems. The mathematical model, which has been proven with field measurements, is capable of accurately predicting variations in water surface elevations, mean velocities, and flows with respect to time at any point along a stream.