scispace - formally typeset
Search or ask a question

Showing papers on "Pipe flow published in 1976"



Journal ArticleDOI
TL;DR: In this paper, the authors present explicit and accurate equations for pipe diameter and head loss and a closed form solution for the discharge through the pipe, based on Colebrook-White equation.
Abstract: Direct solutions of pipe flow problems are not possible because of the implicit form of Colebrook-White equation which expresses the hydraulic resistancee of commercial pipes. The three basic and major problems encountered in hydraulic engineering practice are the determination of pipe diameter, the discharge and the head loss. The solution of these problems on conventional lines involves many trials and tedious computations. Some research workers have proposed graphical solutions which have their own inherent limitations. Reported herein are explicit and accurate equations for pipe diameter and head loss and a closed form solution for the discharge through the pipe, based on Colebrook-White equation. These explicit equations can also be utilized with advantage in optimization studies of pipelines and water distribution systems.

620 citations


Journal ArticleDOI
TL;DR: In this article, the transition to turbulence in a purely oscillatory pipe flow was performed for values of the Reynolds number Rδ, defined using the Stokes-layer thickness δ = (2ν/ω)½ and the cross-sectional mean velocity amplitude U, from 19 to 1530 (or for values in the range from 105 to 5830) and for values with Stokes parameter λ = ½d(ω/2ν)½ (ν = kinematic viscosity and ω = angular frequency) from 1·35 to 6·
Abstract: Experiments on transition to turbulence in a purely oscillatory pipe flow were performed for values of the Reynolds number Rδ, defined using the Stokes-layer thickness δ = (2ν/ω)½ and the cross-sectional mean velocity amplitude U, from 19 to 1530 (or for values of the Reynolds number Re, defined using the pipe diameter d and U, from 105 to 5830) and for values of the Stokes parameter λ = ½d(ω/2ν)½ (ν = kinematic viscosity and ω = angular frequency) from 1·35 to 6·19. Three types of turbulent flow regime have been detected: weakly turbulent flow, conditionally turbulent flow and fully turbulent flow. Demarcation of the flow regimes is possible on Rλ, λ or Re, λ diagrams. The critical Reynolds number of the first transition decreases as the Stokes parameter increases. In the conditionally turbulent flow, turbulence is generated suddenly in the decelerating phase and the profile of the velocity distribution changes drastically. In the accelerating phase, the flow recovers to laminar. This type of partially turbulent flow persists even at Reynolds numbers as high as Re = 5830 if the value of the Stokes parameter is high.

357 citations


01 Nov 1976

214 citations



Journal ArticleDOI
TL;DR: In this article, a simple analytical model is used to explain the observation that maximum hot spot elevations on the Mid-Oceanic Ridge fall dramatically with increasing spreading rate (there are no Icelands or Afars on the East Pacific Rise!) a hot spot under a fast spreading ridge has a broad pipe in which to discharge its partial melts; hence, only a slight topographic gradient and a low elevation is needed to discharge the mass flux rising out of the deeper mantle at the hot spot center.

153 citations


Journal ArticleDOI
TL;DR: In this paper, a satisfactory flow equation is derived from momentum principles and this is further developed into a computer technique for calculating flow profiles and spill discharges for side weirs, which is used to calculate flow profiles.
Abstract: Observations at numerous cross sections in a side weir channel showed that the total energy of flow decreases substantially along the channel, contrary to the assumption that has frequently been made. The decrease in total energy occurs because the longitudinal component of velocity of the spill flow is greater than the longitudinal velocity of the flow remaining in the channel. A satisfactory flow equation is derived from momentum principles and this is further developed into a computer technique for calculating flow profiles and spill discharges for side weirs.

135 citations


Journal ArticleDOI
TL;DR: In this article, two distinct mass-transfer regimes, associated with energy-containing and energy-dissipating turbulent motions, are identified, and a criterion, based on the turbulence Reynolds number, is determined for the applicability of each regime.

117 citations


Journal ArticleDOI
TL;DR: In this article, a simulative study is presented to clarify the characteristics of the flowfield in the grain port of a solid rocket motor under erosive burning conditions, where the experiments are performed by using channels with porous walls and air flow at ambient temperature.
Abstract: A simulative study is presented to clarify the characteristics of the flowfield in the grain port of a solid rocket motor under erosive burning conditions. The experiments are performed by using channels with porous walls and air flow at ambient temperature. It is shown that the boundary layer along the port develops rapidly similarly to pipe flow, which differs from Green's prediction. An empirical relation, similar to LenoirRobillard's semiempirical relation is obtained by correlating turbulence intensity with velocities and geometrical parameters of the channel. Thus, it is implied that an intimate relation exists between turbulence intensity and erosive burning.

114 citations


Journal ArticleDOI
TL;DR: In this article, the effects of gas velocity and particle diameter on the electrification of a metal pipe were examined both theoretically and experimentally with particular attention to the collision between particles and pipe wall.
Abstract: Electrostatic characteristics in gas-solids flow in a metal pipe are studied both theoretically and experimentally with particular attention to the collision between particles and pipe wall. Effects of gas velocity and particle diameter on the electrification are also examined.

105 citations


Journal ArticleDOI
TL;DR: In this article, the linear stability of Hagen-Poiseuille flow with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers.
Abstract: The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

Journal ArticleDOI
TL;DR: In this paper, an amplitude analysis of the Reynolds shear stress fluctuation u1 u2, sorted into four quadrants of the u1, u2 plane, was carried out in a turbulent pipe flow.
Abstract: The present investigation is oriented towards a better understanding of the turbulent structure in the core region of fully developed and completely wall-bounded flows. In view of the already existing results concerning the bursting process in boundary layers (which are semi-bounded flows), an amplitude analysis of the Reynolds shear stress fluctuation u1 u2, sorted into four quadrants of the u1, u2 plane, was carried out in a turbulent pipe flow. For the wall side of the core region, in which the correlation coefficient u1u2/u’1 u’2 does not change appreciably with the distance from the wall, the structure of the Reynolds stress is found to be similar to that obtained in boundary layers: bursts, i.e. ejections of low speed fluid, make the dominant contribution to the Reynolds stress; the regions of violent Reynolds stress are small fractions of the overall flow; and the mean time interval between bursts is found to be almost constant across the flow. For the core region, the large cross-stream evolution of the correlation coefficient u1 u2/u’1 u’2 is associated with a new structure of the Reynolds stress induced by the completely wall-bounded nature of the flow. Very large amplitudes of u1u2 are still observed, but two distinct burst-like patterns are now identified and related to ejections originating from the two opposite halves of the flow. In addition to this interaction, a focusing effect caused by the circular section of the pipe is observed. As a result of these two effects, the mean time interval between the bursts decreases significantly in the core region and reaches a minimum on the pipe axis. Investigation of specific space-time velocity correlations reveals the possible existence of rotating structures similar to those observed at the outer edge of turbulent boundary layers. These coherent motions are found to have a scale noticeably larger than that of the bursts.

Journal ArticleDOI
TL;DR: In this article, the authors developed a suitable relationship and diagrams to predict results compatible with prototype measurements, based on systematic experiments backed by theoretical considerations, and found that no linear relationship has been found between the head and the maximum air-entraining capacity of the flow.
Abstract: For the successful operation of high head gated conduits, adequate supply of air is of paramount importance. However, no dependable solution is yet available to determine the required quantity of air for different flow types. Based on systematic experiments backed by theoretical considerations, suitable relationships and diagrams have been developed that predict results compatible with prototype measurements. Conduit roughness has no significant effect on air-entrainment. No linear relationship has been found to exist between the head and the maximum air-entraining capacity of the flow. Measurements of air velocity by means of high speed cinematography indicate that the velocity at the interface is much higher than the mean velocity of water flow and that the air velocity distribution is far removed from being logarithmic.

Journal ArticleDOI
TL;DR: Comparison of the universal spectral density function of wall pressure spectra obtained at various x D positions downstream of axisymmetric cylindrical obstructions positioned within a latex rubber tube containing a steady water flow shows that these spectra are similar but not identical.

Journal ArticleDOI
TL;DR: In this article, a stochastic model of particle deposition is presented which explains the observed decline in particle deposition velocities on the walls of a pipe in turbulent flow, with increasing particle size beyond a critical particle size.

Journal ArticleDOI
TL;DR: In this article, two types of stepwise change in the flow rate of a fully developed pipe flow showed apparently different behaviours in this turbulence, and the dominant feature was the generation and propagation of a new turbulence.
Abstract: The dynamic structure of turbulence in transient pipe flows was studied experimentally. Two types of stepwise change in the flow rate of a fully developed pipe flow showed apparently different behaviours in this turbulence. With a stepwise increase in the flow rate, the dominant feature was the generation and propagation of a new turbulence. With a stepwise decrease in the flow rate the dominant feature was the decay of an old turbulence. However, a comparison of these two types of stepwise change indicates a coherent structure in the propagation of a new turbulence in both transient pipe flows. The propagation time of new turbulence is determined by the condition at its generation. Moreover, this coherent character is also applicable to the propagation of an old turbulence, and the beginning of the decay of the old turbulence is predicted by the propagation time in initial steady state. On the basis of these facts the dynamic behaviours of turbulence in both these types of transient flow are interpreted consistently. For the decay of the old turbulence, the ''linear'' decay law is applicable and the decay rate is governed by the flow condition during decay, although the propagation time is not affected by the transient flow.

Journal ArticleDOI
TL;DR: In this article, the authors extended Vickery's method for calculating the drag of plane lattice structures normal to a turbulent stream to cases of increased solidity, incorporating an extended version of Taylor's theory for the flow through a porous plate, and a simplified version of Hunt's analysis of the distortion of a turbulent flow by the mean flow field of a body.
Abstract: The method of Vickery for calculating the drag of plane lattice structures normal to a turbulent stream is extended to cases of increased solidity. The analysis incorporates an extended version of Taylor's theory for the flow through a porous plate, and a simplified version of Hunt's analysis of the distortion of a turbulent flow by the mean flow field of a body. Some comparisons are made with experimental data.

Journal ArticleDOI
TL;DR: In this article, the influence of curvature on a pipeflow is discussed for a pipe that starts bending uniformly after an initial straight section, and the motion is examined first for distances from the starting of the bend that are com-parable with the tubewidth.
Abstract: The influence of curvature on a pipeflow is discussed for a pipe that starts bending uniformly after an initial straight section. The Reynolds number and curvature are assumed large and small respectively, and the motion is examined first for distances from the starting of the bend that are com­parable with the tubewidth. When the Dean number is finite, the coreflow remains practically undisturbed, i. e. unidirectional, until the bend and thereafter streams uniformly towards the outside of the curve, inducing a three dimensional boundary layer. This layer, however, has to react before the bending in order to adjust to the downstream conditions. It does so by means of a novel kind of upstream response. The azimuthal pressure variation generated by the bend is felt upstream and therefore both drives an inwards azimuthal motion in the boundary layer and produces an axial shear maximum at the inside wall. In the curved section the centrifuging then causes the maximum to shift to the outer bend at 1.51 pipe-radii beyond the start of bending. Finally, the theory is extended to longer lengthscales, to large Dean numbers and to general initial profiles.

Journal ArticleDOI
TL;DR: In this paper, three separate systems of equations that are in common use in solving steady flow problems in pipe networks are described and the method for including pressure reducing valves in each of these systems is given The emphasis is on use of efficient computer oriented methods.
Abstract: The three separate systems of equations that are in common use in solving steady flow problems in pipe networks are described and the method for including pressure reducing valves in each of these systems is given The emphasis is on use of efficient computer oriented methods In the method presented the pressure reducing valves are permitted to operate normally in maintaining a constant downstream pressure, or are permitted to act as check valves, preventing reverse flow should downstream pressures exceed valve settings The inclusion of pressure reducing valves as an integral part of the network of pipes, pumps, reservoirs, and minor loss devices causes no appreciable reduction in the performance of computer programs that have been specifically written to carry out the computations for solutions

Journal ArticleDOI
TL;DR: In this paper, the temperature profile and the radiative and convective wall-heat fluxes for a hydro-dynamically established flow of a nongray gas in a cylinder are calculated numerically for laminar or turbulent flow.
Abstract: The temperature profile and the radiative and convective wall-heat fluxes for a hydro-dynamically established flow of a nongray gas in a cylinder are calculated numerically for laminar or turbulent flow. Turbulent eddy viscosity is represented by a two-region model having a near-wall-region and a far-from-wall region. Gas properties are represented by the exponential-winged band model. Qualitatively the results for a gas with a single major band agree with a previous solution for a cylinder with internal heat generation.

Journal ArticleDOI
TL;DR: In this article, the stability of the decaying laminar flow in a suddenly blocked channel is investigated using a WKB type of approach, and it is shown that the first term of the WKB expansion of the disturbance velocity field is just that obtained by a quasi-steady approach.
Abstract: The stability of the decaying laminar flow in a suddenly blocked channel is investigated. The partial differential system governing the stability of the flow is solved using a WKB type of approach. It is shown that the first term of the WKB expansion of the disturbance velocity field is just that obtained by a quasi-steady approach. The flow is found to be unstable at quite small Reynolds numbers. This instability is associated with the inflexional nature of the velocity profiles of the decaying flow.

Journal ArticleDOI
TL;DR: In this article, the fundamental equations for pulsating turbulent flow in a circular tube containing a slightly compressible fluid are derived by describing Reynolds stress in terms of eddy viscosity, for whose distribution five models are introduced.
Abstract: Fundamental equations for pulsating turbulent flow in a circular tube containing a slightly compressible fluid are derived by describing Reynolds stress in terms of eddy viscosity, for whose distribution five models are introduced. Analytical solutions based on each model are developed for steady flow velocity, oscillating velocity and wave propagation constant. Comparison of these solutions for each model shows that the four-region model proposed by Karman is rather reasonable enough to illustrate the flow behaviours. The distributions of oscillating velocities, wave propagation constant, and oscillating pressures based on the four-region model at low frequencies and small Reynolds numbers are similar to those at high frequencies and small Reynolds numbers are similar to those at high frequencies and large Reynolds numbers. Because of the assumption of time-invariant eddy viscosity profile, the low frequency values of wave propagation constant should not be reliable. The analogy of these turbulent flow solutions with the laminar ones is shown schematically.

Journal ArticleDOI
TL;DR: In this paper, the authors show that the features of the steady laminar flow produced by a particular small distortion of the walls of a channel or pipe are shown to alter first from those of the corresponding external situation when the distortion is in an adjustment zone, sited a large distance O(R⅗l) from the inlet; R ([Gt ] 1) and l signify respectively a typical Reynolds number and length scale of the incompressible fluid motion.
Abstract: For practically uniform entry conditions, the features of the steady laminar flow produced by a particular small distortion of the walls of a channel or pipe are shown to alter first from those of the corresponding external situation when the distortion is in an ‘adjustment zone’, sited a large distance O(R⅗l) from the inlet; R ([Gt ] 1) and l signify respectively a typical Reynolds number and length scale of the incompressible fluid motion. The planar channel flow there develops an extended triple-deck structure, with an unknown inviscid core motion bounded by two-tiered boundary layers near the walls. In three-dimensional pipe flow, where a similar structure occurs, the induced secondary motion has a jet-like nature close to the wall. The size and position of the indentation govern the flow properties within this adjustment regime and both can lead to large-scale effects being propagated. The most substantial effects occur if an indentation, interior blockage or bifurcation is sited just downstream of the adjustment stage in a channel. In a pipe, however, such a siting induces much less upstream influence, and instead the most significant long-scale disturbances are generated when the pipe is constricted asymmetrically over a small length. Vortex motion can then be provoked far beyond the constriction, the sense of rotation changing as the fluid moves further downstream, while upstream source-like secondary flow is found.


Journal ArticleDOI
TL;DR: In this article, the parallel flow between two fixed corrugated plates is investigated and the question is given a constant pressure gradient, is the flow rate affected by the phase difference?
Abstract: The present paper investigates the parallel flow between two fixed corrugated plates. The question is given a constant pressure gradient, is the flow rate affected by the phase difference?

01 Aug 1976
TL;DR: In this paper, the results from an investigation of flow resistance and velocity profiles of turbulent fiber suspensions are reviewed and analytical expressions relating velocity profiles and flow resistance are derived and supported with experimental data.
Abstract: Under certain conditions of turbulent flow, values of friction loss for wood pulp fiber suspensions are lower than those for water at the same flow rate This phenomenon of drag reduction is discussed with reference to pipe flow, and results from an investigation of flow resistance and velocity profiles of turbulent fiber suspensions are reviewed Analytical expressions relating velocity profiles and flow resistance are derived and supported with experimental data These relationships can be used to predict flow resistance in piping systems Drag reduction also occurs when a rotating disk is immersed in a suspension of wood pulp fibers, and a method is proposed for predicting pipe friction loss and velocity profiles for fully developed turbulent flow in pipes from torque measurements obtained from a rotating disk The method has been applied successfully over a limited range of conditions

Journal ArticleDOI
TL;DR: In this paper, the theoretical Poiseuille flow and the thermal creep flow for rarefied gases in a long rectangular channel are computed using the BGK model of the Boltzmann equation and diffuse scattering from the walls.
Abstract: The theoretical Poiseuille flow and the thermal creep flow for rarefied gases in a long, rectangular channel are computed using the BGK model of the Boltzmann equation and diffuse scattering from the walls. These results are compared with available experimental data for Poiseulle flow. The present work provides a way to compute flow in a rectangular channel that is estimated to be accurate to ±5% for common gases.

Journal ArticleDOI
TL;DR: In this paper, a turbulence model involving the solution of partial differential equations for two turbulence quantities has been employed to predict turbulent flow and heat transfer in a circular tube and between parallel and diverging plates.

Journal ArticleDOI
TL;DR: Dimensionless approximate solutions for slightly compressible fluid flow are derived from the exact solutions of the fundamental linear equations for unsteady viscous compressible flow, and shown to be reasonable within the region w'≤3c' and c'≥3375×104 (w' =R2w/v, c'=Rc/v ; w, angular frequency ; c, speed of sound ; R, pipe radius ; v, kinematic viscosity).
Abstract: Dimensionless approximate solution for slightly compressible fluid flow are derived from the exact solutions of the fundamental linear equations for unsteady viscous compressible flow, and shown to be reasonable within the region w'≤3c' and c'≥3375×104(w'=R2w/v, c'=Rc/v ; w, angular frequency ; c, speed of sound ; R, pipe radius ; v, kinematic viscosity) In this region radial velocity and cross-sectional variation of pressure are shown to be negligibly small Pressure and velocity of air and water flow pulsating through a vertical pipe by means of a piston are measured by the use of a strain-gauge-type pressure transducer and a hot-wire anemometer, respectively Comparisons of experimental results with approximate solutions show that cross-sectional distribution of oscillating velocities agree closely with the theoretical value within the frequency range 002 l f l 12 Hz, independently of Reynolds number, piston amplitude, pipe radius, and fluid, and that oscillating pressure distribution within the pipe and oscillating velocity distribution along the pipe axis also agree well with the theoretical values

Journal ArticleDOI
TL;DR: In this paper, the authors compared the mixing of three single-point injection systems: a center line source, a wall source, and a jet at the wall issuing perpendicularly to the pipe flow.
Abstract: For applications such as using tracer techniques for discharge measurements in pipes or using a segment of a pipe as a mixing chamber, it is desirable to know the rate at which the concentration of injected material becomes mixed within the pipe cross section. The distance required to achieve a given degree of mixing depends on the injection system and the pipe flow characteristics. The mixing for three single-point injection systems is compared. The three systems are a center line source, a wall source, and a jet at the wall issuing perpendicularly to the pipe flow. A center line source can provide the most rapid mixing, but it is extremely difficult to maintain the symmetry necessary to achieve the rapid mixing. The wall source gives the slowest mixing. The mixing for a jet injection depends on M, the ratio of the jet momentum to the pipe momentum. For a jet injection, there is an optimum M which gives the most rapid mixing for given flow characteristics, and this mixing is more rapid than either a wall source or most practically achievable center line sources.