Boundary Layer Concept Research Articles

Inclusion of localized forces due to turbulent boundary layer convected pressure at junctions of coplanar structural sections

Previous researchers showed that the concept of turbulent boundary layer (TBL) "edge forces," which are related to the convection peak of the TBL pressure wave number spectral density, is useful and important when using a finite element model to compute the bending response to TBL excitation of a plate that has a free edge. This paper examines the applicability of more general localized forces to the junction of two distinct coplanar sections that are joined along a line transverse to the flow. A formalism is developed for introducing these forces and applying them to a structure. The approach is made plausible by using two string sections as a simple structural model and showing that the sum of the localized force response and that due to the low wave number excitation matches the separately computed response corresponding to the full wave number spectral density. These localized forces can have a noticeable effect when the connection between sections is resilient.

Analysis of mass-transfer phenomena in the dendritic net of solidifying steel ingots. 2. Convective diffusion of the impurity in the dendritic net of solidifying ingots

An analysis of the interaction of the melt flow with the surface of dendritic crystallites has been performed using the concept of a diffusion boundary layer, and the regularities of the impurity distribution over the cross section of ingots and castings in the process of their solidification have been revealed.

Internal boundary layers in a well-mixed equatorial atmosphere/ocean

It is known that a non-viscous homogeneous fluid confined to a rotating spherical shell neither possesses a discrete eigenvalue spectrum nor smooth eigenmodes. Mathematically, the motion of a fluid in a rotating spherical shell is governed by a hyperbolic boundary value problem. Generic features of such problems are singularities in the flow field, referred to as internal boundary layers. Physically, these singularities correspond to wave attractors, that are regions to which all inertial waves in the fluid are inevitably drawn. This focusing results from multiple reflections of the inertial waves at boundaries. Therefore, internal boundary layers typically occur for enclosed fluids. The model studied here is a certain approximation to the equatorial region of a rotating spherical shell. It describes the structure of slow, zonally symmetric inertial waves of a homogeneous fluid in the neighborhood of the equator, enclosed between a flat lower and upper boundary. Exact solutions, computed by a method that can handle hyperbolic boundary value problems, are discussed. Solutions for different frequencies show inertial boundary layers, corresponding with internal wave attractors. The boundary layers consist of alternating shear layers aligned along the wave attractor. They show a self-similar pattern that becomes infinitely thin at the position of the attractor. In addition to the results discussed, the paper is intended to introduce the concept of internal boundary layers and wave attractors to the broader meteorologic and oceanographic community. As in almost all theoretical studies of geophysical flows, strong model simplifications are required to find solutions analytically. Nevertheless, it is believed that this approach is useful to highlight fundamental properties of equatorial internal boundary layers that might be important for atmosphere and ocean.

Phemonenological model of heat transfer in an infiltrated granular bed at moderate Reynolds numbers

A model of heat transfer in an infiltrated granular bed, which allows for most important special features of the process, viz., anisotropy of thermal properties and nonuniform distribution of the porosity and gas (liquid) velocity over the cross section, has been formulated. The concepts of the filtration boundary layer and viscous sublayer have been introduced and identified. Temperature fields and values of the coefficient of heat exchange between the bed and the wall of the tube bounding it have been calculated. The latter are generalized in the form of the dimensionless correlation which is compared with the available experimental data. It is shown that at Re ∞ ⩽ 2000 the developed model describes the process of heat transfer in the granular bed well.

Boundary layers, Prandtl’s and others

As John D. Anderson Jr pointed out in his excellent article (Physics Today, December 2005, page 42), Ludwig Prandtl was a leader in developing the concept of two-dimensional boundary layers, so important in aerodynamics and related fluid problems in which the flow does not change direction with distance from the boundary. However, the equally important and slightly earlier work of Vagn W. Ekman 1 1. V. W. Ekman, Archive Math. Astron. Phys. 2, 11 (1905). deserves equal exposure and recognition. Ekman was the first to develop the concept of 3D boundary layers, those in which rotation (or curved flow) in a viscous fluid causes a boundary layer with a well-defined depth. The depth of such boundary layers is quite generally (v/Ω)1/2, the Ekman depth, where ν is the kinematic viscosity (or an appropriate eddy viscosity) and Ω is some appropriate rotation rate.Ekman was inspired by reports that icebergs in the Northern Hemisphere generally drifted at an angle to the right of the wind direction, and he sought an explanation in the effect of Earth’s rotation. Prior to Ekman’s discovery, oceanographers had often assumed that the wind acting on the ocean would produce a surface current in the wind direction; if the wind persisted long enough, they thought, it would lead to a linear decrease of the current from the top of the ocean to the bottom. Ekman discovered that because of the Coriolis force the effect of wind stress would be limited to a boundary layer around 5 to 50 meters deep, depending on wind speed and turbulence. Moreover, for a steady wind stress the net transport in the boundary layer would be exactly 90 degrees to the wind stress and independent of the amount of turbulence, to the right in the Northern Hemisphere and to the left in the Southern.For the ideal condition of constant viscosity, Ekman found an exact analytical solution for his spiral boundary-layer flow. He also found a second spiral solution for the case in which the mixing coefficient is proportional to the square of the rate of gliding. Curiously, that second solution has a defined finite depth below which the wind has no direct effect. Ekman also conducted laboratory experiments with wind over a rotating tank of water; they clearly showed the predicted effect of the Coriolis force. In an ordinary laboratory case, a laminar Ekman boundary layer is about 1 mm deep. Ekman also recognized that similar turbulent boundary layers occur in the atmosphere and at the bottom of the ocean due to flow over rigid boundaries. Theodore von Karman and U. T. Boedewadt 2 2. T. von Karman, Z. Angew. Math. Mech. 1, 233 (1921); https://doi.org/10.1002/zamm.19210010401 U. T. Boedewadt, Z. Angew. Math. Mech. 20, 241 (1940) https://doi.org/10.1002/zamm.19400200502. also found analytical solutions to 3D boundary layers: von Karman to the flow due to a rotating disk in a stationary fluid and Boedewadt to the boundary layer beneath a vortex in solid rotation over a stationary boundary. Both of these spiral boundary layers are rather like the Ekman spiral and sometimes are loosely referred to as Ekman layers.The stability and transition to turbulence in 3D boundary layers is today perhaps of more general application (airfoils, curved pipes, rotating machinery, curved rivers, and so on) than Prandtl’s 2D boundary layer. In the geophysical sciences, the wind-driven Ekman transport in the surface Ekman layer is fundamental to all theories of ocean circulation, and in the atmosphere the Ekman spiral and transport toward low pressure are fundamental to theories of hurricanes and all atmospheric vortices. In past years when I discussed my studies of the Ekman boundary layer with friends in the physics community, the response frequently was “oh yes, the Einstein teacup effect,” as though Einstein was the first in this area of study. But when one reviews Einstein’s paper 3 3. A. Einstein, Ideas and Opinions, Crown Publishers, New York (1954), p. 250. it is clear that the notion of a thin boundary layer was absent from his work. So perhaps this note will correct some misimpressions.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. V. W. Ekman, Archive Math. Astron. Phys. 2, 11 (1905). Google Scholar2. T. von Karman, Z. Angew. Math. Mech. 1, 233 (1921); https://doi.org/10.1002/zamm.19210010401 , Google ScholarCrossref U. T. Boedewadt, Z. Angew. Math. Mech. 20, 241 (1940) https://doi.org/10.1002/zamm.19400200502. , Google ScholarCrossref3. A. Einstein, Ideas and Opinions, Crown Publishers, New York (1954), p. 250. Google Scholar© 2006 American Institute of Physics.

Boundary layers, Prandtl’s and others

John Anderson’s article on Ludwig Prandtl’s boundary layer is both interesting and informative. More recently, beginning in 1961, the boundary layer concept has been applied to flow about a type of surface called “continuous.” 1 1. B. C. Sakiadis, AIChE J. 7, 26; 7, 221; 7, 469 (1961) https://doi.org/10.1002/aic.690070108. A characteristic of flows over continuous surfaces is that, for any given period, any two solid surface elements exhibit different drag-time histories, as contrasted with finite-surface flows, in which all surface elements exhibit equal drag-time histories. As a result the formation and termination of the boundary layer are not identified with any part of the surface, but are determined by the system’s boundaries.Flows over continuous surfaces constitute a new class of boundary-layer problem. Although the differential equations governing flow around the continuous and finite surfaces are the same, the boundary conditions are different, which results in substantially different solutions for the two types of surfaces. Continuous surfaces are primarily encountered in industrial processes—for example, in fiber spinning, 2 2. C. Miller, AIChE J. 50, 898 (2004) https://doi.org/10.1002/aic.10088. sheet casting, 3 3. P. J. Abraham, E. M. Sparrow, Int. J. Heat Fluid Flow 26, 289 (2005) https://doi.org/10.1016/j.ijheatfluidflow.2004.08.007. and film coating 4 4. S. J. Weinstein, K. J. Ruschak, Annu. Rev. Fluid Mech. 36, 29 (2004) https://doi.org/10.1146/annurev.fluid.36.050802.122049.—where the production of such surfaces is technically feasible and economically desirable.REFERENCESSection:ChooseTop of pageREFERENCES <<1. B. C. Sakiadis, AIChE J. 7, 26; 7, 221; 7, 469 (1961) https://doi.org/10.1002/aic.690070108. Google ScholarCrossref, CAS2. C. Miller, AIChE J. 50, 898 (2004) https://doi.org/10.1002/aic.10088. Google ScholarCrossref, CAS3. P. J. Abraham, E. M. Sparrow, Int. J. Heat Fluid Flow 26, 289 (2005) https://doi.org/10.1016/j.ijheatfluidflow.2004.08.007. Google ScholarCrossref4. S. J. Weinstein, K. J. Ruschak, Annu. Rev. Fluid Mech. 36, 29 (2004) https://doi.org/10.1146/annurev.fluid.36.050802.122049. Google ScholarCrossref© 2006 American Institute of Physics.

Bulk boundary-layer concepts for simplified models of tropical dynamics

We review bulk representations of tropical and subtropical maritime atmospheric boundary layers. Three types of bulk representations are studied in detail: stratocumulus topped mixed layers, trade-wind layers, and sub-cloud mixed layers. Through the development of a consistent description of these disparate regimes, connections among their varied representations are emphasized, as well as their relation to regions of deeper convection. New results relating to the equilibrium mass flux and cloud fraction in the trade winds; the ability of bulk models to represent qualitatively major cloud regimes; and the relationship amongst different bulk representations of the surface layer are presented. Throughout we emphasize the identification of consistent and physically based mixing and cloud regime rules for use in intermediate complexity models of the tropical climate, which in turn can be used to study cloud and dynamical interactions on larger scales.

Meteorology applied to urban air pollution problems: concepts from COST 715

Abstract. The outcome of COST 715 is reviewed from the viewpoint of a potential user who is required to consider urban meteorology within an air pollution assessment. It is shown that descriptive concepts are helpful for understanding the complex structure of the urban boundary layer, but that they only apply under a limited number of conditions. However such concepts are necessary to gain insight into both simple and complex air pollution models. It is argued that wider considerations are needed when considering routine air quality assessments involving an air quality model's formulation and pedigree. Moreover there appears to be a reluctance from model developers to move away from familiar concepts of the atmospheric boundary layer even if they are not appropriate to urban areas. An example is given from COST 715 as to how routine urban meteorological measurements of wind speed may be used and adapted for air quality assessments. Reference to the full COST 715 study is made which provides further details.

Stresses Near a Disk-Shaped Sharp Slot with Tangential Contact Interaction Between Its Surfaces

We propose a new statement of the problem of elastic equilibrium of a disk-shaped slot whose surfaces are loaded by an arbitrary normal load vanishing on its front according to a certain law. By the method of discontinuous Weber-Schafheitlin integrals, it is shown that, in this case, there exists a unique state of elastic equilibrium with regular distribution of stresses over the front of the slot. According to the concept of boundary layer, the jump of tangential stresses formed on the surfaces of the slot due to the continuity of the components of the vector of local rigid rotation Ω on its front is continued in the plane of the slot and guarantees the validity of the equilibrium conditions provided that the normal stresses are equal to zero (the effect of boundary layer). The numerical analysis shows that the jump of tangential stresses in the boundary layer outside the slot rapidly decreases with the distance from the front in complete agreement with the Saint-Venant principle. If a jump of tangential stresses on the surfaces of the slot is absent (and exists outside the slot), then these surfaces have a kink in the front of the slot and the volume strains possess a logarithmic singularity. This situation can be regarded as the limiting state corresponding to the onset of plastic deformation or brittle fracture. If the tangential stresses do not have jump in the entire plane of the slot, then the solution of the problem does not exist.

Oxygen Demand by a Sediment Bed of Finite Length

A model of sedimentary oxygen demand (SOD) for a sediment bed of finite length is presented. The responses of diffusive oxygen transfer in turbulent flow above the sediment surface and of microbial activity inside the sediment to a developing diffusive boundary layer are modeled numerically. The developing diffusive boundary layer above the sediment/water interface is modeled based on shear velocity and turbulent boundary layer concepts, and dissolved oxygen (DO) uptake inside the sediment is modeled as a function of the microbial growth rate. The model predicts that the diffusive boundary layer above the sediment/water interface thickens in flow direction, and that DO penetration depth into the sediment is practically constant over the length of the sediment bed. The effect of the developing diffusive boundary layer on SOD is minor, except at very low shear/flow velocities (shear velocity U*<0.01cm∕s) and/or high microbial density inside the sediment. The average SOD over the sediment bed therefore varies only slightly with its length. SOD varies somewhat in flow direction, i.e., SOD is largest near the leading edge (x=0), decreases with distance, and finally, approaches a nearly constant value for fully developed boundary layer. Including microbial activity in the sediment makes the change of SOD in flow direction much smaller than is predicted by a pure vertical diffusive flux model. The diffusive boundary layer is nearly fully developed at a dimensionless distance x+=10,000, regardless of microbial activity inside the sediment. Longer sediment beds are required to eliminate the small leading edge effect on any measured average SOD value. SOD depends strongly on the diffusion coefficient of DO inside the sediment bed. This effect becomes more significant as shear/flow velocity is increased. Overall, SOD is found to be controlled principally by shear velocity of the water flowing above the sediment/water interface, microbial activity inside the sediment, and diffusion of DO inside the sediment. The length of the sediment bed is of lesser influence.

Accelerated Gradient Based Optimization Using Adjoint Sensitivities

An electromagnetic feasible adjoint sensitivity technique (EM-FAST) has been proposed recently for use with frequency-domain solvers . It makes the implementation of the adjoint variable approach to design sensitivity analysis straightforward while preserving the accuracy at a level comparable to that of the exact sensitivities. The overhead computations associated with the estimation of the sensitivities in addition to the system analysis are due largely to the calculation of the derivatives of the system matrix. Here, we describe the integration of the EM-FAST with two methods for accelerated estimation of these derivatives: the boundary-layer concept and the Broyden update. We show that the Broyden update approach (Broyden-FAST) leads to an algorithm whose efficiency is problem independent and allows the computation of the response and its gradient through a single system analysis with practically no overhead. Both approaches are illustrated through the design of simple antennas using method of moments solvers.

Pesticide volatilization from plants: improvement of the PEC model PELMO based on a boundary-layer concept.

Calculation of pesticide volatilization from plants as an integral component of pesticide fate models is of utmost importance, especially as part of PEC (predicted environmental concentrations) models used in the registration procedures for pesticides. A mechanistic approach using a laminar air-boundary layer concept to predict volatilization from plant surfaces was compared to data obtained in a wind-tunnel study after simultaneous application of parathion-methyl, fenpropimorph, and quinoxyfen to winter wheat. Parathion-methyl was shown to have the highest volatilization during the wind-tunnel study of 10 days (29.2%). Volatilization of quinoxyfen was about 15.0%, revealing a higher volatilization tendency than fenpropimorph (6.0%), which is attributed to enhanced penetration of fenpropimorph counteracting volatilization. Predictions of the boundary-layer approach were markedly influenced by the selected values for the equivalent thickness of the boundary layer and rate coefficients, thus indicating that future improvements of the approach will require a deeper understanding of the kinetics of the underlying processes, e.g. phototransformation and penetration. The boundary-layer volatilization module was included in the European registration model PELMO, enabling simultaneous calculation of volatilization from plants and soil. Application of PELMO to experimental findings were the first comprehensive PEC model calculations to imply the relevant processes affecting the postapplication fate of pesticides.

Introduction to Symmetry Analysis

Introduction to Symmetry Analysis

Blasius: A life in research and education

The Blasius boundary layer solution is a basic feature of fluid mechanics, and the first application of Prandtl's boundary layer concept as a significant issue in engineering. This work highlights the contributions of Blasius to hydrodynamics over a period of only six years, which marked the initiation of boundary layer theory. His main papers relating to aerodynamics and smooth turbulent pipe flow are also reviewed, and a biography puts his career into the general environment of Germany over the period of two World Wars. A complete bibliography of Blasius is provided.

Numerical Simulation of Continuous Stirred Ultrafiltration Process: An Approach Based on Moving Boundary Layer Concept

A mass transfer model based on unsteady state mass balance over concentration boundary layer coupled with gradual development of so called "gel" or "cake" layer has been formulated in this study. The model considers the boundary layer problem simultaneously with the film theory of mass transfer and resistance in series model. The resulting equations are solved first by reducing the set of partial differential equations to nonlinear equations utilizing orthogonal collocation technique and then applying multidimensional Newton–Raphson method with suitable seeding scheme to solve the above-mentioned nonlinear equations together with some additional constraints. The problem of determination of membrane surface concentration is eliminated by this simultaneous solution of boundary layer equation together with gel layer. The model is found to be capable of predicting permeate flux and rejection under different experimental conditions. The main feature of this model is that it takes into account realistically the effect of gel layer formation within concentration boundary layer whereas in most of the previous studies this effect has not been considered. The dependency of concentration profile, gel thickness, and permeate concentration with different operating variables are also studied and the variations are found to be quite reasonable.

Mathematical simulation of the kinetics of high-temperature silicon oxidation and the structure of the boundary layer in the Si-SiO2 system

Structural complexes formed in the Si-SiO2 boundary layer under high-temperature thermal oxidation of silicon are considered. A mathematical model of the kinetics of silicon-oxygen cluster polymerization was suggested using the boundary-layer concept. The influence of the diffusion flow of these clusters on the percentage of SiO4 tetrahedral chains of various lengths in the SiO2 bulk was noted.

Principles of Fluid Mechanics

3R42. Principles of Fluid Mechanics. - AN Alexandrou (Dept of Mech Eng, Worcester Polytechnic Inst). Prentice Hall, Upper Saddle River NJ. 2001. 573 pp. ISBN 0-13-801762-X. $100.00. Reviewed by R Verzicco (Dept di Ingegneria Meccanica e Gestionale, Politecnico di Bari, Via Re David 200, Bari, 70125, Italy).This book is an introductory text for fluid dynamics which contains enough material for two semesters of undergraduate courses. The organization of the material reflects the particular point of view of the author, and this gives the opportunity to have a look at standard concepts from a different perspective. The book contains also some material from experimental and computational fluid dynamics which have become of fundamental importance in modern courses. The text contains 13 chapters and five appendices. Each chapter is focused on a particular topic and contains its own references and exercises. In the appendices, some complementary material is provided which is very useful for the application of theory to practical examples. The book closes with a subject index. Chapter 1 opens the book with an introduction to fluid dynamics and its impact to design. Some solution methods are mentioned thus anticipating successive concepts. Standard fluid properties and system of units are then introduced. Chapter 2 is devoted to conservation laws for closed systems including the basic thermodynamics principles. In this chapter, a particular view of the hydrostatics is given in contrast to the standard approach which considers hydrostatics as a separate topic. Chapter 3 derives the conservation laws for open systems starting from the Reynolds transport theorem. The successive chapter gives the concepts of position, velocity, and acceleration vectors thus introducing the Lagrangian and Eulerian perspectives and the deformation of a fluid element. Using these results, Chapter 5 reconsiders the conservation laws in differential form. The chapter is completed with a description of boundary conditions, constitutive relations, Navier-Stokes equations, and non-isothermal flows. Chapter 6 is concerned with non-dimensional analysis and similitude, including the Buckingham theorem and the distorted- or incomplete-similarity. Chapter 7 deals with the exact analytical solutions of the Navier-Stokes equations; there are some unusual solutions like the film drawing of the fully developed non-Newtonian channel flow even if the Couette plane channel is not considered; this solution, however, can be easily derived since the basic principles are described with enough details. The concepts of boundary layer and separation together with exact and approximate solutions are given in Chapter 8. Turbulent boundary layers are analyzed using empirical laws and giving quantitative correlations. This chapter has a very broad content; it includes external flows, force coefficients (for wings and general shape objects), internal flow with a particular attention to viscous flows in pipes. Chapter 9 considers ideal inviscid flows. In the first part, the Euler equations along streamline coordinates and the Bernoulli equations are discussed, while in the second part, the basic theory for two-dimensional potential flow is introduced. No mention is made of the three-dimensional potential flows.The successive four chapters present additional material which could be taught as complementary material in a course. Chapter 10 deals with the dynamics of rotating fluids and turbo-machineries starting from the conservation of angular momentum for closed and open systems. Particular examples are then illustrated showing pumps, turbines, and propellers. Chapter 11 describes compressible flows starting from the speed of sound up to normal and oblique shocks and expansions. At the end of the chapter, Rayleigh and Fanno flows are described. In Chapter 12, some basic concepts of experimental fluid dynamics are given by describing the main components of a data acquisition system and the main measurement techniques. The last chapter provides the fundamentals of computational fluid dynamics with solution schemes for algebraic, ordinary differential, and partial differential equations. Finally, simple techniques for the solution of viscous and inviscid flows are yielded. The five appendices contain, respectively, fluid properties, compressible flow tables, differential form of the equations in Cartesian, cylindrical-polar and spherical coordinates, and some simple computer programs and background material (such as vector and tensor algebra and elementary calculus) for a better comprehension of the material in the book. This reviewer believes that the quality of the book is adequate for the intended scope. The presented material is well explained and completed with a lot of examples whose solution can be used as a guideline for the numerous exercises at the end of each chapter. Many good-quality pictures contribute to make the exposition clear and pleasant. In conclusion, Principles of Fluid Mechanics is suitable for adoption as a text for the undergraduate level. Concerning libraries, it could complete the existing literature for undergraduates providing an additional viewpoint.

채터링 없는 슬라이딩 모드를 이용한 로봇 매니퓰레이터의 제어

A new chattering free sliding made control is proposed for robot manipulators. The control input is derived from the reaching law and the Lyapunov stability criteria, which is only composed of continuous terms. It has a chattering free characteristics and a concise farm. In implementing procedures, no change of equations is needed. Thus, it does not degrade the original merits of the sliding mode control. And it is applied to a 2-link SCARA robot manipulator. It is shown that the proposed control has good trajectory tracking performance compared with the PD control and the conventional sliding mode control which uses the boundary layer concept.

Fundamental correlations for laminar and turbulent free convection from a uniformly heated vertical plate

A dimensionless parameter Π Q is introduced for the correlation of the heat transfer in natural convection induced by a constant wall heat flux. This dimensionless parameter depends on the Prandtl number, Pr, and the modified Rayleigh number, Ra ∗ , as Π Q∼Ra ∗/(1+Pr −1) . The development of Π Q is based on physical arguments and allows the use of a single heat transfer correlation over the entire Prandtl number range. Dimensional arguments in terms of the laminar boundary layer and turbulent microscale concepts lead to a Nu∼ Π Q 1/5 and Nu∼ Π Q 1/4 dependence for the laminar and turbulent heat transfer, respectively. Comparison of these correlations with existing published data shows a good agreement.

Engineering Fluid Mechanics

9R37. Engineering Fluid Mechanics. - WP Graebel (Dept of Mech Eng and Appl Mech, Univ of Michigan, Ann Arbor MI). Taylor &amp; Francis Publ, New York NY. 2001. 676 pp. ISBN 1-560-32711-1. $89.95.Reviewed by AS Paintal (Eng Dept, Metropolitan Water Reclamation District, 100 E Erie St, Chicago IL 60611).This is a text for an introductory course in engineering fluid mechanics. Fluid mechanics is one of the basic courses required for an undergraduate degree in engineering. The purpose of the book is to provide basic theory as well as to develop analytical skills in the engineering students. The book helps the students to get a feel for flow patterns; pressure variations; and continuity, energy, and momentum principles. The book is organized into 12 chapters and seven appendices. The chapters provide orderly development of the subject. Chapter 1 gives a brief introduction of the subject. Fluid properties are defined and procedures for solving engineering problems are suggested. Chapter 2 deals with hydrostatics and pressure variations and distributions in fluids subjected to rigid body accelerations. Chapter 3 is devoted to fluid dynamics. The ideas of control volume and control surface are introduced, and concepts of incompressibility and discharge are defined. The fundamental equations of fluid mechanics in one dimension are formulated using the concepts of conservation of mass, linear momentum, angular momentum, and energy. Application of these equations for problem solving is emphasized. In Chapter 4, the differential equations using the continuity, energy, and momentum concepts are derived in two- and three-dimensions. The concepts of potential flow are also introduced. Chapter 5 deals with the dimensional analysis and model-prototype relationships. Chapters 6 and 7 concern laminar and turbulent flows. The equation for laminar flows between parallel plates and circular tubes are formulated, and the concept of boundary layer is introduced in Chapter 6. The concept is further developed for turbulent boundary layers in Chapter 7. Turbulent flow in pipes is thoroughly analyzed. The chapter also covers drag and lift forces. Chapter 8 considers the hydraulics of open channel, and the effect of gravity on flow is analyzed. Chapter 9 deals with the compressible flow problems and the effect of Mach Number on the flow. In Chapter 10, various flow, pressure, and velocity measurement techniques are evaluated. Chapter 11 is devoted to hydraulic machines. In Chapter 12, suggestions are made for additional study of various engineering disciplines involving the principles of fluid mechanics. There are a number of solved problems included in every chapter to explain the principles involved. At the end of each chapter, a set of unsolved problems is provided for practice. The answers to even-numbered problems are given at the end of the book. There are seven appendices. Appendix A deals with conversion of units and gives useful constants. Appendix B summarizes the fluid properties of water air and other common fluids in British (US) and SI units. Appendix C covers mathematical aids used for solving fluid mechanics problems. Appendix D provides compressible flow tables for air k=1.4. A brief history of fluid mechanics is given in Appendix E. Appendix F’s focus is on the design of a pump system. The purpose is to demonstrate how the design and other broader issues are considered in the design. Engineering Fluid Mechanics provides a balanced treatment of engineering fluid mechanics. The theory as well as problem solving skills are emphasized. The book should be considered for adoption as a text for an introductory undergraduate course in fluid mechanics. It will be useful for engineers working in the area of fluid mechanics or preparing for the examination leading to a professional engineer license.