Showing papers on "Pipe flow published in 1975"

Engineering Fluid Mechanics

Abstract: PREFACE. CHAPTER 1 Introduction. 1.1 Liquids and Gases. 1.2 The Continuum Assumption. 1.3 Dimensions, Units, and Resources. 1.4 Topics in Dimensional Analysis. 1.5 Engineering Analysis. 1.6 Applications and Connections. CHAPTER 2 Fluid Properties. 2.1 Properties Involving Mass and Weight. 2.2 Ideal Gas Law. 2.3 Properties Involving Thermal Energy. 2.4 Viscosity. 2.5 Bulk Modulus of Elasticity. 2.6 Surface Tension. 2.7 Vapor Pressure. 2.8 Summary. CHAPTER 3 Fluid Statics. 3.1 Pressure. 3.2 Pressure Variation with Elevation. 3.3 Pressure Measurements. 3.4 Forces on Plane Surfaces (Panels). 3.5 Forces on Curved Surfaces. 3.6 Buoyancy. 3.7 Stability of Immersed and Floating Bodies. 3.8 Summary. CHAPTER 4 Flowing Fluids and Pressure Variation. 4.1 Descriptions of Fluid Motion. 4.2 Acceleration. 4.3 Euler's Equation. 4.4 Pressure Distribution in Rotating Flows. 4.5 The Bernoulli Equation Along a Streamline. 4.6 Rotation and Vorticity. 4.7 The Bernoulli Equation in Irrotational Flow. 4.8 Separation. 4.9 Summary. CHAPTER 5 Control Volume Approach and Continuity Equation. 5.1 Rate of Flow. 5.2 Control Volume Approach. 5.3 Continuity Equation. 5.4 Cavitation. 5.5 Differential Form of the Continuity Equation. 5.6 Summary. CHAPTER 6 Momentum Equation. 6.1 Momentum Equation: Derivation. 6.2 Momentum Equation: Interpretation. 6.3 Common Applications. 6.4 Additional Applications. 6.5 Moment-of-Momentum Equation. 6.6 Navier-Stokes Equation. 6.7 Summary. CHAPTER 7 The Energy Equation. 7.1 Energy, Work, and Power. 7.2 Energy Equation: General Form. 7.3 Energy Equation: Pipe Flow. 7.4 Power Equation. 7.5 Contrasting the Bernoulli Equation and the Energy Equation. 7.6 Transitions. 7.7 Hydraulic and Energy Grade Lines. 7.8 Summary. CHAPTER 8 Dimensional Analysis and Similitude. 8.1 Need for Dimensional Analysis. 8.2 Buckingham Theorem. 8.3 Dimensional Analysis. 8.4 Common-Groups. 8.5 Similitude. 8.6 Model Studies for Flows Without Free-Surface Effects. 8.7 Model-Prototype Performance. 8.8 Approximate Similitude at High Reynolds Numbers. 8.9 Free-Surface Model Studies. 8.10 Summary. CHAPTER 9 Surface Resistance. 9.1 Surface Resistance with Uniform Laminar Flow. 9.2 Qualitative Description of the Boundary Layer. 9.3 Laminar Boundary Layer. 9.4 Boundary Layer Transition. 9.5 Turbulent Boundary Layer. 9.6 Pressure Gradient Effects on Boundary Layers. 9.7 Summary. CHAPTER 10 Flow in Conduits. 10.1 Classifying Flow. 10.2 Specifying Pipe Sizes. 10.3 Pipe Head Loss. 10.4 Stress Distributions in Pipe Flow. 10.5 Laminar Flow in a Round Tube. 10.6 Turbulent Flow and the Moody Diagram. 10.7 Solving Turbulent Flow Problems. 10.8 Combined Head Loss 10.9 Nonround Conduits. 10.10 Pumps and Systems of Pipes. 10.11 Summary. CHAPTER 11 Drag and Lift. 11.1 Relating Lift and Drag to Stress Distributions. 11.2 Calculating Drag Force. 11.3 Drag of Axisymmetric and 3D Bodies. 11.4 Terminal Velocity. 11.5 Vortex Shedding. 11.6 Reducing Drag by Streamlining. 11.7 Drag in Compressible Flow. 11.8 Theory of Lift. 11.9 Lift and Drag on Airfoils. 11.10 Lift and Drag on Road Vehicles. 11.11 Summary. CHAPTER 12 Compressible Flow. 12.1 Wave Propagation in Compressible Fluids. 12.2 Mach Number Relationships. 12.3 Normal Shock Waves. 12.4 Isentropic Compressible Flow Through a Duct with Varying Area. 12.5 Summary. CHAPTER 13 Flow Measurements. 13.1 Measuring Velocity and Pressure 13.2 Measuring Flow Rate (Discharge). 13.3 Measurement in Compressible Flow. 13.4 Accuracy of Measurements. 13.5 Summary. CHAPTER 14 Turbomachinery. 14.1 Propellers. 14.2 Axial-Flow Pumps. 14.3 Radial-Flow Machines. 14.4 Specific Speed. 14.5 Suction Limitations of Pumps. 14.6 Viscous Effects. 14.7 Centrifugal Compressors. 14.8 Turbines. 14.9 Summary. CHAPTER 15 Flow in Open Channels. 15.1 Description of Open-Channel Flow. 15.2 Energy Equation for Steady Open-Channel Flow. 15.3 Steady Uniform Flow. 15.4 Steady Nonuniform Flow. 15.5 Rapidly Varied Flow. 15.6 Hydraulic Jump. 15.7 Gradually Varied Flow. 15.8 Summary. Appendix A-1. Answers A-11. Index I-1.

The instability of capillary jets

Abstract: At high jet velocity the aerodynamic interaction between a capillary jet and the surrounding medium leads to an enhanced growth rate of axisymmetric disturbances. The available theories which account for this effect fail to agree with experimental observations. The difference is attributed, in part, to the relaxation of the velocity profile in jets formed by fully developed laminar pipe flow. The profile relaxation has a destabilizing effect just as does the aerodynamic interaction. In the absence of velocity-profile relaxation it is shown that the available theories overestimate the aerodynamic effect. A consideration of the viscosity of the ambient fluid yields a semi-empirical modification to the theory which shows good agreement with experimental values.

Transition to turbulence in oscillating pipe flow

Abstract: Published results on transition in a Stokes layer indicate a wide range of transition Reynolds numbers. As thermal effects in a resonance tube (Merkli & Thomann 1975) depend on the state of the boundary layer, the transition Reynolds number was determined, and a critical Reynolds number Ac ≈ 400 was found. The observations were made with hot wires and with flow visualization by means of smoke, and provide new details on turbulence in a Stokes layer. With this knowledge an explanation of the large discrepancies between some stability theories and the experiments is suggested. The main point is that turbulence occurs in the form of periodic bursts which are followed by relaminarimtion in the same cycle and do not lead to turbulent flow during the whole cycle.A further, unexpected result of the present investigation is the discovery of vortex patterns superimposed on the normal laminar acoustic motion.

On transition in a pipe. Part 2. The equilibrium puff

Abstract: Conditionally sampled hot-wire measurements were taken in a pipe at low Reynolds numbers (2700 > Re > 2000) corresponding to the onset of turbulence as a result of a large perturbation in the flow. This type of transition gives rise to a turbulent puff which maintains itself indefinitely at around Re = 2200. The structure of puffs was investigated in some detail and was found to be very different from the structure of fully developed turbulent pipe flow. Nevertheless, it is independent of the character of the disturbance which created it. The purpose of the study was to gain some insight into the mechanism of transition in a pipe.

Thermoacoustic effects in a resonance tube

Abstract: New experiments with a gas-filled resonance tube have shown that not only heating, but also cooling of the tube wall is possible and that these phenomena are not restricted to oscillation amplitudes that generate shocks. The present paper concentrates on amplitudes outside the shock region. For this case, an extended acoustic theory is worked out. The results show cooling in the section of the tube with maximum velocity amplitude (and thus dissipation) and marked heating in the region of the velocity nodes. A strong dependence of these effects on the Prandtl number is noted. The results are in good agreement with experiments. Although the theory is not valid for proper resonance conditions, it nevertheless sheds some light on what happens when nonlinear effects dominate.Closely related to the limit of validity of the thermoacoustic theory is the question of transition from laminar to turbulent flow in the viscous boundary layer (Stokes layer). This problem has also been investigated; the results are given in a separate paper (Merkli & Thomann 1975). In the present article laminar flow is assumed.

Prediction of turbulent flow in curved pipes

Abstract: A finite-difference procedure is employed to predict the development of turbulent flow in curved pipes. The turbulence model used involves the solution of two differential equations, one for the kinetic energy of the turbulence and the other for its dissipation rate. The predicted total-velocity contours for the developing flow in a 180° bend are compared with the experimental data. Predictions of fully developed velocity profiles for long helically wound pipes are also presented and compared with experimental measurements.

Entry flow in a curved pipe

Abstract: A secondary flow is set up when a fluid flows through a stationary curved pipe. The fluid in the middle of the pipe moves outwards and that near the wall inwards. Dean showed that the dynamical similarity of this fully developed flow depends on a non-dimensional parameter is the mean velocity along the pipe, v is the coefficient of kinematic viscosity and a is the radius of the pipe, which is bent into a coil of radius R. Dean's analysis was limited to small values of D. Later, Barua developed an asymptotic boundary-layer theory for large values of D and showed for these values of D that the resistance coefficient γc is much larger than that for the corresponding straight pipe. The present work deals with the flow in a curved pipe as it develops from a uniformly distributed velocity at the entrance to a fully developed profile. Barua's results for the fully developed flow are adopted as downstream conditions in the present work. The ratio of the entry lengths of the curved ipe and the corresponding straight one is shown to be proportional to D−1/2 when D is large. Thus, the entry length for a curved pipe is much shorter than that for the corresponding straight pipe.

Method for effecting heat or mass transfer

Abstract: A method and apparatus for effecting heat or mass transfer between two fluids through a membrane comprises a conduit for flow of one fluid, said conduit being at least partly defined by said membrane and the configuration of said conduit in a plane orthogonal to the general direction of flow varying periodically along the general direction of flow either inherently or in response to fluid pressure therein in such a manner that when said fluid is pulsated along the line of the general direction of flow a component of motion is induced therein which is mutually orthogonal to the surface of the membrane and general direction of flow. In preferred embodiments the conduit configuration varies periodically along the general direction of flow in order to give rise to separation and reattachment of flow at a multiplicity of zones within the conduit, whereby secondary flow is induced within said zones. The apparatus is particularly applicable to blood oxygenation and dialysis.

An experimental investigation of low Reynolds number secondary streaming effects associated with an oscillating viscous flow in a curved pipe

Abstract: This paper deals with nonlinear streaming effects in an oscillating fluid in a curved pipe. The secondary steady velocity field in the cross-sectional plane of the pipe is studied in detail. Our experimental results are compared with the theory of Lyne (1970; that part of his theory which is valid for Reynolds numbers Rs [Lt ] 1) and the theory of Zalosh & Nelson (1973). On the basis of these comparisons we conclude that the theories are in practice valid for higher Reynolds numbers Rs than was formally expected.

Slurry Flow Velocity, Concentration and Particle Size Measurement Using Flow Noise and Correlation Techniques

Abstract: Three areas of slurry pipe flow measurement using flow noise and correlation techniques are described. Signals generated by the natural turbulence inherent in the flow of two-component fluids can be used to enable the total volume flow rate, concentration and particle size of the discontinuous component to be measured.Total volume flow is measured by a cross correlation method which involves obtaining the time of flight of a tagging signal due to the turbulence between two transducers spaced axially along the direction of flow. Both ultrasonic and conductivity transducers are used to detect the flow turbulence. Results show that a measurement accuracy within ±2% can be achieved in all systems tested. The intensity of the flow noise detected by a simple transducer is related to the quantity of the discontinuous component present in the flow. This flow noise is measured by an AC method and gives direct indication of the concentration of the discontinuous component. Turbulent flow consists of eddies which ha...

The laminar decay of suddenly blocked channel and pipe flows

Abstract: This paper is a theoretical investigation of the stable laminar decay of a fully established channel or pipe flow following a sudden blockage such as would be caused by the rapid closure of a valve or imposition of an end wall or gate. The development of the subsequent velocity and pressure fields is examined from the instant the initial pressure wave passes until the final decay of all motion. Three time scales of hydrodynamic interest are identified and the relevant solutions are obtained. The time scales are as follows: (i) a very short time characteristic of the passage of the pressure wave during which the velocity field adjusts inviscidly to the new boundary conditions imposed by the presence of the end wall, (ii) a short diffusion time during which the displacement interaction generated by the diffusion of the primary Rayleigh layer induces a substantial secondary motion with distinct side-wall boundary layers and an inviscid core and (iii) a long diffusion time during which the boundary layers fill the entire channel or pipe and the residual motion then dies out. The secondary flow for short diffusion times is of special interest in that it is an example of an unsteady boundary layer where the external pressure gradient and inviscid outer flow are unknown and determined by the integrated time history of the combined mass flow displacement generated by the primary- and secondary-flow boundary layers. The paper closes with some preliminary comments and experimental observations on decelerating pipe flows.

Fluid flow in soft-walled tubes part 1: Steady flow

Abstract: The channel-flow form of the equations describing fluid flow in soft-walled tubes is analysed. Several analytical solutions for the properties of the flow existing in tubes with various analytical forms of pressure/ area relationships are presented. The vital relationship of the tube mechanical stability to the flow Mach number is established. The necessary conditions for the formation of a hydraulic jump are established, and the resultant degradation in total pressure determined. Finally, an example numerical result for an hydraulic jump is given.

Experimental results for oscillating flow in a curved pipe

Abstract: Experimental results are presented describing the character of the secondary flow developed within a curved pipe for which the primary (axial) flow is driven by an oscillating pressure gradient. The comparison between previous theory and experiment is excellent.

Water Hammer in Coaxial Pipe Systems

Abstract: Transporting fluids involves the use of coaxial pipe systems in which water hammer may occur due to pump failure or valve operation. Investigations into the behavior of water hammer phenomena in such pipe systems of several different flow sections are reported. The solution of the differential equations covering nonstationary fluid flow in pipe systems of several different flow sections by means of the method of characteristics is sketched. The wave propagation as well as the transmission and reflection of waves at changes in diameter or density, and at pipe junctions, are expressed by the simplest possible formulas.

The start-up response of pipe flow to a step change in flow rate

Abstract: The start-up response of pipe flow to a step input of constant flow rate given by an automatic solenoid valve has been studied experimentally by the use of electrochemical technique. The variation of velocity distribution and velocity gradient at the pipe wall with the passage of time has been measured far downstream from the inlet section, where flow becomes fully developed in the steady state. The velocity profiles of the start-up flow development show a trend essentially different from those of steady-state flow development at different distances in the entrance region of a circular pipe: they show a minimum at the axis and a maximum in the intermediate region between the axis and the wall as the result of non-uniformity of acceleration in the central core (annular jet effect). The development of the laminar boundary layer with time could be regarded as that of the constant-stress layer near the wall. Still, the velocity profiles in the laminar boundary layer at different times are similar to each other.

Transitional and Turbulent Pipeflow of Pseudoplastic Fluids

Abstract: A modified mixing length model is developed which permits the computation of velocity distributions and frictional pressure losses for transitional and turbulent pipe flow of viscous, inelastic non-Newtonian fluids. The rheological model assumed is the empirical power law. The method represents an improvement over previous workers' results. The data of several authors, most of which could not be harmonized by previous models, are shown to be fully compatible with the present method. The Dodge-Metzner-Reed, "generalized Reynolds number" method of correlation is shown to be inappropriate for transitional and turbulent flow. It is further shown that acceptable models of transitional and turbulent flow must correctly account for Theological behavior of the fluid. The proposed method expressly excludes viscoelastic effects. The method is suitable for engineering pipeline design computations and requires only a knowledge of power-law index n to permit computation of velocity profiles and friction factors.

Heat and pressure effect in viscous flow through a pipe

Abstract: The basic relations governing viscous flow of liquids with variable transport properties is considered. A dimensional analysis of the problem is given, and the basic equations of generalizedNewtonian flow through a pipe are derived. A perturbation solution is given for the special case of aNewtonian liquid with pressure and temperature dependent viscosity and expressions for the velocity components, pressure distribution and flow rate are obtained for both isothermal and adiabatic wall conditions. It is shown that pressure and viscous heating effects may result in apparently nonNewtonian behaviour.

Maximum discharge rate of liquid-vapor mixtures from vessels

Abstract: A discrepancy exists in theoretical predictions of the two-phase equilibrium discharge rate from pipes attached to vessels. Theory which predicts critical flow data in terms of pipe exit pressure and quality severely overpredicts flow rates in terms of vessel fluid properties. This study shows that the discrepancy is explained by the flow pattern. Due to decompression and flashing as fluid accelerates into the pipe entrance, the maximum discharge rate from a vessel is limited by choking of a homogeneous bubbly mixture. The mixture tends toward a slip flow pattern as it travels through the pipe, finally reaching a different choked condition at the pipe exit.

Developing flow in circular conduits: transition from plug flow to tube flow

Abstract: A numerical solution of the complete Navier–Stokes equations of motion by means of an implicit finite-difference method is presented for the following developing-flow problem: a piston forced with constant speed through an infinitely long tube of circular cross-section. The transition of the velocity profile of an incompressible isothermal Newtonian fluid from the plug-flow profile in front of the piston to the parabolic profile of developed flow is analysed. Streamlines, vorticity distributions, velocity profiles, the excess pressure drop and the entrance length are given for Reynolds numbers from 0 to 800.

Zero-G experiments in two-phase fluids flow regimes

Abstract: The two-phase flows studied were liquid and gas mixtures in a straight flow channel of circular cross-section. Boundaries between flow regimes have been defined for normogravity on coordinates of gas quality and total mass velocity; and, when combined with boundary expressions having a Froude number term, an analytical model was derived predicting boundary shifts with changes in gravity level. Experiments with air and water were performed, first in the normogravity environment of a ground laboratory and then in 'zero gravity' aboard a KC-135 aircraft flying parabolic trajectories. Data reduction confirmed regime boundary shifts in the direction predicted, although the magnitude was a little less than predicted. Pressure drop measurements showed significant increases for the low gravity condition.

Pumps and Reservoirs in Networks by Linear Theory

Abstract: In a paper, Wood and Charles presented a linear theory method (LTM) for analyzing steady flow in pipe networks. The linear theory method does not require an initialization, as do other commonly used methods, e.g., the Hardy-Cross and Newton-Raphson methods. It also converges to the solution very rapidly. The LTM solves the system of equations that considers as unknowns the flow rates in individual pipes of the network, in contrast to the Hardy-Cross or Newton-Raphson methods, which commonly consider as unknowns either the heads at the junctions or corrective flow rates around loops of the network.