Fluid Mechanics
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Glossary Physics (I-Introduction)
1 Glossary Physics (I-introduction) - Efficiency: The percent of the work put into a machine that is converted into useful work output; = work done / energy used [-]. = eta In machines: The work output of any machine cannot exceed the work input (<=100%); in an ideal machine, where no energy is transformed into heat: work(input) = work(output), =100%. Energy: The property of a system that enables it to do work. Conservation o. E.: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Equilibrium: The state of an object when not acted upon by a net force or net torque; an object in equilibrium may be at rest or moving at uniform velocity - not accelerating. Mechanical E.: The state of an object or system of objects for which any impressed forces cancels to zero and no acceleration occurs. Dynamic E.: Object is moving without experiencing acceleration. Static E.: Object is at rest.F Force: The influence that can cause an object to be accelerated or retarded; is always in the direction of the net force, hence a vector quantity; the four elementary forces are: Electromagnetic F.: Is an attraction or repulsion G, gravit. const.6.672E-11[Nm2/kg2] between electric charges: d, distance [m] 2 2 2 2 F = 1/(40) (q1q2/d ) [(CC/m )(Nm /C )] = [N] m,M, mass [kg] Gravitational F.: Is a mutual attraction between all masses: q, charge [As] [C] 2 2 2 2 F = GmM/d [Nm /kg kg 1/m ] = [N] 0, dielectric constant Strong F.: (nuclear force) Acts within the nuclei of atoms: 8.854E-12 [C2/Nm2] [F/m] 2 2 2 2 2 F = 1/(40) (e /d ) [(CC/m )(Nm /C )] = [N] , 3.14 [-] Weak F.: Manifests itself in special reactions among elementary e, 1.60210 E-19 [As] [C] particles, such as the reaction that occur in radioactive decay. -
10-1 CHAPTER 10 DEFORMATION 10.1 Stress-Strain Diagrams And
EN380 Naval Materials Science and Engineering Course Notes, U.S. Naval Academy CHAPTER 10 DEFORMATION 10.1 Stress-Strain Diagrams and Material Behavior 10.2 Material Characteristics 10.3 Elastic-Plastic Response of Metals 10.4 True stress and strain measures 10.5 Yielding of a Ductile Metal under a General Stress State - Mises Yield Condition. 10.6 Maximum shear stress condition 10.7 Creep Consider the bar in figure 1 subjected to a simple tension loading F. Figure 1: Bar in Tension Engineering Stress () is the quotient of load (F) and area (A). The units of stress are normally pounds per square inch (psi). = F A where: is the stress (psi) F is the force that is loading the object (lb) A is the cross sectional area of the object (in2) When stress is applied to a material, the material will deform. Elongation is defined as the difference between loaded and unloaded length ∆푙 = L - Lo where: ∆푙 is the elongation (ft) L is the loaded length of the cable (ft) Lo is the unloaded (original) length of the cable (ft) 10-1 EN380 Naval Materials Science and Engineering Course Notes, U.S. Naval Academy Strain is the concept used to compare the elongation of a material to its original, undeformed length. Strain () is the quotient of elongation (e) and original length (L0). Engineering Strain has no units but is often given the units of in/in or ft/ft. ∆푙 휀 = 퐿 where: is the strain in the cable (ft/ft) ∆푙 is the elongation (ft) Lo is the unloaded (original) length of the cable (ft) Example Find the strain in a 75 foot cable experiencing an elongation of one inch. -
Glossary: Definitions
Appendix B Glossary: Definitions The definitions given here apply to the terminology used throughout this book. Some of the terms may be defined differently by other authors; when this is the case, alternative terminology is noted. When two or more terms with identical or similar meaning are in general acceptance, they are given in the order of preference of the current writers. Allowable stress (working stress): If a member is so designed that the maximum stress as calculated for the expected conditions of service is less than some limiting value, the member will have a proper margin of security against damage or failure. This limiting value is the allowable stress subject to the material and condition of service in question. The allowable stress is made less than the damaging stress because of uncertainty as to the conditions of service, nonuniformity of material, and inaccuracy of the stress analysis (see Ref. 1). The margin between the allowable stress and the damaging stress may be reduced in proportion to the certainty with which the conditions of the service are known, the intrinsic reliability of the material, the accuracy with which the stress produced by the loading can be calculated, and the degree to which failure is unattended by danger or loss. (Compare with Damaging stress; Factor of safety; Factor of utilization; Margin of safety. See Refs. l–3.) Apparent elastic limit (useful limit point): The stress at which the rate of change of strain with respect to stress is 50% greater than at zero stress. It is more definitely determinable from the stress–strain diagram than is the proportional limit, and is useful for comparing materials of the same general class. -
Calculate the Friction Factor for a Pipe Using the Colebrook-White Equation
TOPIC T2: FLOW IN PIPES AND CHANNELS AUTUMN 2013 Objectives (1) Calculate the friction factor for a pipe using the Colebrook-White equation. (2) Undertake head loss, discharge and sizing calculations for single pipelines. (3) Use head-loss vs discharge relationships to calculate flow in pipe networks. (4) Relate normal depth to discharge for uniform flow in open channels. 1. Pipe flow 1.1 Introduction 1.2 Governing equations for circular pipes 1.3 Laminar pipe flow 1.4 Turbulent pipe flow 1.5 Expressions for the Darcy friction factor, λ 1.6 Other losses 1.7 Pipeline calculations 1.8 Energy and hydraulic grade lines 1.9 Simple pipe networks 1.10 Complex pipe networks (optional) 2. Open-channel flow 2.1 Normal flow 2.2 Hydraulic radius and the drag law 2.3 Friction laws – Chézy and Manning’s formulae 2.4 Open-channel flow calculations 2.5 Conveyance 2.6 Optimal shape of cross-section Appendix References Chadwick and Morfett (2013) – Chapters 4, 5 Hamill (2011) – Chapters 6, 8 White (2011) – Chapters 6, 10 (note: uses f = 4cf = λ for “friction factor”) Massey (2011) – Chapters 6, 7 (note: uses f = cf = λ/4 for “friction factor”) Hydraulics 2 T2-1 David Apsley 1. PIPE FLOW 1.1 Introduction The flow of water, oil, air and gas in pipes is of great importance to engineers. In particular, the design of distribution systems depends on the relationship between discharge (Q), diameter (D) and available head (h). Flow Regimes: Laminar or Turbulent laminar In 1883, Osborne Reynolds demonstrated the occurrence of two regimes of flow – laminar or turbulent – according to the size of a dimensionless parameter later named the Reynolds number. -
Intermittency As a Transition to Turbulence in Pipes: a Long Tradition from Reynolds to the 21St Century Christophe Letellier
Intermittency as a transition to turbulence in pipes: A long tradition from Reynolds to the 21st century Christophe Letellier To cite this version: Christophe Letellier. Intermittency as a transition to turbulence in pipes: A long tradition from Reynolds to the 21st century. Comptes Rendus Mécanique, Elsevier Masson, 2017, 345 (9), pp.642- 659. 10.1016/j.crme.2017.06.004. hal-02130924 HAL Id: hal-02130924 https://hal.archives-ouvertes.fr/hal-02130924 Submitted on 16 May 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution - NonCommercial - NoDerivatives| 4.0 International License C. R. Mecanique 345 (2017) 642–659 Contents lists available at ScienceDirect Comptes Rendus Mecanique www.sciencedirect.com A century of fluid mechanics: 1870–1970 / Un siècle de mécanique des fluides : 1870–1970 Intermittency as a transition to turbulence in pipes: A long tradition from Reynolds to the 21st century Les intermittencies comme transition vers la turbulence dans des tuyaux : Une longue tradition, de Reynolds au XXIe siècle Christophe Letellier Normandie Université, CORIA, avenue de l’Université, 76800 Saint-Étienne-du-Rouvray, France a r t i c l e i n f o a b s t r a c t Article history: Intermittencies are commonly observed in fluid mechanics, and particularly, in pipe Received 21 October 2016 flows. -
1 Fluid Flow Outline Fundamentals of Rheology
Fluid Flow Outline • Fundamentals and applications of rheology • Shear stress and shear rate • Viscosity and types of viscometers • Rheological classification of fluids • Apparent viscosity • Effect of temperature on viscosity • Reynolds number and types of flow • Flow in a pipe • Volumetric and mass flow rate • Friction factor (in straight pipe), friction coefficient (for fittings, expansion, contraction), pressure drop, energy loss • Pumping requirements (overcoming friction, potential energy, kinetic energy, pressure energy differences) 2 Fundamentals of Rheology • Rheology is the science of deformation and flow – The forces involved could be tensile, compressive, shear or bulk (uniform external pressure) • Food rheology is the material science of food – This can involve fluid or semi-solid foods • A rheometer is used to determine rheological properties (how a material flows under different conditions) – Viscometers are a sub-set of rheometers 3 1 Applications of Rheology • Process engineering calculations – Pumping requirements, extrusion, mixing, heat transfer, homogenization, spray coating • Determination of ingredient functionality – Consistency, stickiness etc. • Quality control of ingredients or final product – By measurement of viscosity, compressive strength etc. • Determination of shelf life – By determining changes in texture • Correlations to sensory tests – Mouthfeel 4 Stress and Strain • Stress: Force per unit area (Units: N/m2 or Pa) • Strain: (Change in dimension)/(Original dimension) (Units: None) • Strain rate: Rate -
Introduction to the CFD Module
INTRODUCTION TO CFD Module Introduction to the CFD Module © 1998–2018 COMSOL Protected by patents listed on www.comsol.com/patents, and U.S. Patents 7,519,518; 7,596,474; 7,623,991; 8,457,932; 8,954,302; 9,098,106; 9,146,652; 9,323,503; 9,372,673; and 9,454,625. Patents pending. This Documentation and the Programs described herein are furnished under the COMSOL Software License Agreement (www.comsol.com/comsol-license-agreement) and may be used or copied only under the terms of the license agreement. COMSOL, the COMSOL logo, COMSOL Multiphysics, COMSOL Desktop, COMSOL Server, and LiveLink are either registered trademarks or trademarks of COMSOL AB. All other trademarks are the property of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliated with, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademark owners, see www.comsol.com/trademarks. Version: COMSOL 5.4 Contact Information Visit the Contact COMSOL page at www.comsol.com/contact to submit general inquiries, contact Technical Support, or search for an address and phone number. You can also visit the Worldwide Sales Offices page at www.comsol.com/contact/offices for address and contact information. If you need to contact Support, an online request form is located at the COMSOL Access page at www.comsol.com/support/case. Other useful links include: • Support Center: www.comsol.com/support • Product Download: www.comsol.com/product-download • Product Updates: www.comsol.com/support/updates •COMSOL Blog: www.comsol.com/blogs • Discussion Forum: www.comsol.com/community •Events: www.comsol.com/events • COMSOL Video Gallery: www.comsol.com/video • Support Knowledge Base: www.comsol.com/support/knowledgebase Part number: CM021302 Contents Introduction . -
Basic Principles of Flow of Liquid and Particles in a Pipeline
1. BASIC PRINCIPLES OF FLOW OF LIQUID AND PARTICLES IN A PIPELINE 1.1 LIQUID FLOW The principles of the flow of a substance in a pressurised pipeline are governed by the basic physical laws of conservation of mass, momentum and energy. The conservation laws are expressed mathematically by means of balance equations. In the most general case, these are the differential equations, which describe the flow process in general conditions in an infinitesimal control volume. Simpler equations may be obtained by implementing the specific flow conditions characteristic of a chosen control volume. 1.1.1 Conservation of mass Conservation of mass in a control volume (CV) is written in the form: the rate of mass input = the rate of mass output + the rate of mass accumulation. Thus d ()mass =−()qq dt ∑ outlet inlet in which q [kg/s] is the total mass flow rate through all boundaries of the CV. In the general case of unsteady flow of a compressible substance of density ρ, the differential equation evaluating mass balance (or continuity) is ∂ρ G G +∇.()ρV =0 (1.1) ∂t G in which t denotes time and V velocity vector. For incompressible (ρ = const.) liquid and steady (∂ρ/∂t = 0) flow the equation is given in its simplest form ∂vx ∂vy ∂vz ++=0 (1.2). ∂x ∂y ∂z The physical explanation of the equation is that the mass flow rates qm = ρVA [kg/s] for steady flow at the inlet and outlet of the control volume are equal. Expressed in terms of the mean values of quantities at the inlet and outlet of the control volume, given by a pipeline length section, the equation is 1.1 1.2 CHAPTER 1 qm = ρVA = const. -
Guide to Rheological Nomenclature: Measurements in Ceramic Particulate Systems
NfST Nisr National institute of Standards and Technology Technology Administration, U.S. Department of Commerce NIST Special Publication 946 Guide to Rheological Nomenclature: Measurements in Ceramic Particulate Systems Vincent A. Hackley and Chiara F. Ferraris rhe National Institute of Standards and Technology was established in 1988 by Congress to "assist industry in the development of technology . needed to improve product quality, to modernize manufacturing processes, to ensure product reliability . and to facilitate rapid commercialization ... of products based on new scientific discoveries." NIST, originally founded as the National Bureau of Standards in 1901, works to strengthen U.S. industry's competitiveness; advance science and engineering; and improve public health, safety, and the environment. One of the agency's basic functions is to develop, maintain, and retain custody of the national standards of measurement, and provide the means and methods for comparing standards used in science, engineering, manufacturing, commerce, industry, and education with the standards adopted or recognized by the Federal Government. As an agency of the U.S. Commerce Department's Technology Administration, NIST conducts basic and applied research in the physical sciences and engineering, and develops measurement techniques, test methods, standards, and related services. The Institute does generic and precompetitive work on new and advanced technologies. NIST's research facilities are located at Gaithersburg, MD 20899, and at Boulder, CO 80303. -
Navier-Stokes-Equation
Math 613 * Fall 2018 * Victor Matveev Derivation of the Navier-Stokes Equation 1. Relationship between force (stress), stress tensor, and strain: Consider any sub-volume inside the fluid, with variable unit normal n to the surface of this sub-volume. Definition: Force per area at each point along the surface of this sub-volume is called the stress vector T. When fluid is not in motion, T is pointing parallel to the outward normal n, and its magnitude equals pressure p: T = p n. However, if there is shear flow, the two are not parallel to each other, so we need a marix (a tensor), called the stress-tensor , to express the force direction relative to the normal direction, defined as follows: T Tn or Tnkjjk As we will see below, σ is a symmetric matrix, so we can also write Tn or Tnkkjj The difference in directions of T and n is due to the non-diagonal “deviatoric” part of the stress tensor, jk, which makes the force deviate from the normal: jkp jk jk where p is the usual (scalar) pressure From general considerations, it is clear that the only source of such “skew” / ”deviatoric” force in fluid is the shear component of the flow, described by the shear (non-diagonal) part of the “strain rate” tensor e kj: 2 1 jk2ee jk mm jk where euujk j k k j (strain rate tensro) 3 2 Note: the funny construct 2/3 guarantees that the part of proportional to has a zero trace. The two terms above represent the most general (and the only possible) mathematical expression that depends on first-order velocity derivatives and is invariant under coordinate transformations like rotations. -
Hydraulics Manual Glossary G - 3
Glossary G - 1 GLOSSARY OF HIGHWAY-RELATED DRAINAGE TERMS (Reprinted from the 1999 edition of the American Association of State Highway and Transportation Officials Model Drainage Manual) G.1 Introduction This Glossary is divided into three parts: · Introduction, · Glossary, and · References. It is not intended that all the terms in this Glossary be rigorously accurate or complete. Realistically, this is impossible. Depending on the circumstance, a particular term may have several meanings; this can never change. The primary purpose of this Glossary is to define the terms found in the Highway Drainage Guidelines and Model Drainage Manual in a manner that makes them easier to interpret and understand. A lesser purpose is to provide a compendium of terms that will be useful for both the novice as well as the more experienced hydraulics engineer. This Glossary may also help those who are unfamiliar with highway drainage design to become more understanding and appreciative of this complex science as well as facilitate communication between the highway hydraulics engineer and others. Where readily available, the source of a definition has been referenced. For clarity or format purposes, cited definitions may have some additional verbiage contained in double brackets [ ]. Conversely, three “dots” (...) are used to indicate where some parts of a cited definition were eliminated. Also, as might be expected, different sources were found to use different hyphenation and terminology practices for the same words. Insignificant changes in this regard were made to some cited references and elsewhere to gain uniformity for the terms contained in this Glossary: as an example, “groundwater” vice “ground-water” or “ground water,” and “cross section area” vice “cross-sectional area.” Cited definitions were taken primarily from two sources: W.B. -
Sediment Transport & Fluid Flow
Sediment Transport & Fluid Flow • Downslope transport • Fluid Flow – Viscosity – Types of fluid flow – Laminar vs. Turbulent – Eddy Viscosity – Reynolds number – Boundary Layer • Grain Settling • Particle Transport Loss of intergrain cohesion caused by saturation of pores… before… …after 1 Different kinds of mass movements, variable velocity (and other factors) From weathering to deposition: sorting and modification of clastic particles 2 Effects of transport on rounding, sorting How are particles transported by fluids? What are the key parameters? 3 Flow regimes in a stream Fluid Flow • Fundamental Physical Properties of Fluids – Density (ρ) – Viscosity (µ) Control the ability of a fluid to erode & transport particles • Viscosity - resistance to flow, or deform under shear stress. – Air - low – Water - low – Ice- high ∆µ with ∆ T, or by mixing other materials 4 Shear Deformation Shear stress (τ) is the shearing force per unit area • generated at the boundary between two moving fluids • function of the extent to which the slower moving fluid retards motion of the faster moving fluid (i.e., viscosity) Fluid Viscosity and Flow • Dynamic viscosity(µ) - the resistance of a substance (water) to ∆ shape during flow (shear stress) ! µ = du/dy where, dy τ = shear stress (dynes/cm2) du/dy = velocity gradient (rate of deformation) • Kinematic viscosity(v) =µ/ρ 5 Behaviour of Fluids Viscous Increased fluidity Types of Fluids Water - flow properties function of sediment concentrations • Newtonian Fluids - no strength, no ∆ in viscosity as shear rate ∆’s (e.g.,