Pipe flow

About: Pipe flow is a research topic. Over the lifetime, 13826 publications have been published within this topic receiving 351605 citations.

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 minimal flow unit in near-wall turbulence

Abstract: Direct numerical simulations of unsteady channel flow were performed at low to moderate Reynolds numbers on computational boxes chosen small enough so that the flow consists of a doubly periodic (in x and z) array of identical structures. The goal is to isolate the basic flow unit, to study its morphology and dynamics, and to evaluate its contribution to turbulence in fully developed channels. For boxes wider than approximately 100 wall units in the spanwise direction, the flow is turbulent and the low-order turbulence statistics are in good agreement with experiments in the near-wall region. For a narrow range of widths below that threshold, the flow near only one wall remains turbulent, but its statistics are still in fairly good agreement with experimental data when scaled with the local wall stress. For narrower boxes only laminar solutions are found. In all cases, the elementary box contains a single low-velocity streak, consisting of a longitudinal strip on which a thin layer of spanwise vorticity is lifted away from the wall. A fundamental period of intermittency for the regeneration of turbulence is identified, and that process is observed to consist of the wrapping of the wall-layer vorticity around a single inclined longitudinal vortex.