governing equations of fluid mechanics

... have been studied extensively for Navier-Stokes equations and some of nonlinear parab equations However, the onding re-sultsforother ofequationsinfluid andparab systems are still small There are ... Voight) equations insmooth bounded domains with homogeneous Trang 4In the last few years, questions related to 3DNavier-Stokes-Voigt equations have the attention of a of solutions in terms of of to ... Library of Ha Noi P University 2 Trang 31 MOTIVATION AND HISTORY OF THE PROBLEMPartial differential evolution equations appear frequently in the of ph and pro h as heat transfer and diffusion, pro of

Ngày tải lên: 10/01/2020, 17:13

... have been studied extensively for Navier-Stokes equations and some of nonlinear parab equations However, the onding re-sultsforother ofequationsinfluid andparab systems are still small There are ... Voight) equations insmooth bounded domains with homogeneous Trang 4In the last few years, questions related to 3DNavier-Stokes-Voigt equations have the attention of a of solutions in terms of of to ... Library of Ha Noi P University 2 Trang 31 MOTIVATION AND HISTORY OF THE PROBLEMPartial differential evolution equations appear frequently in the of ph and pro h as heat transfer and diffusion, pro of

Ngày tải lên: 17/01/2020, 17:34

... implied warranties of merchantability or fitness for a particular purpose Trang 33 SCOPE OF FLUID MECHANICS Knowledge and understanding of the basic principles and concepts of fluid mechanics are ... design The collapse of the Tacoma Narrows Bridge in 1940 is evidence of the possible consequences of neglecting the basic principles fluid mechanics The design of all types of fluid machinery including ... knowledge of basic principles fluid mechanics Other applications include design of lubricating systems, heating and ventilating of private homes, large office buildings, shopping malls and design of

Ngày tải lên: 01/06/2018, 15:01

... Trang 1Fluid Mechanics and the Theory of Flight Download free books at Trang 2R.S Johnson Fluid Mechanics and the Theory of Flight Trang 3Fluid Mechanics and the Theory of Flight © 2012 ... ************** Trang 38 A concept that permeates much of fluid theory is the notion of vorticity It is an important property of a fluid flow, both in terms of what is observed in real flows and the rôle ... introduce a suitable, general description of a fluid, and then to develop an appropriate (mathematical) representation of it This involves regarding the body of fluid on the large (macroscopic) scale

Ngày tải lên: 21/01/2021, 09:58

... Trang 1Fluid statics Fluid statics is concerned with the balance of forces which stabilise fluids at rest In the case of a liquid, as the pressure largely changes ... Characteristics of pressure The pressure has the following three characteristics 1 The pressure of a fluid always acts perpendicular to the wall in contact with the fluid 2 The values of the pressure ... the principle of the hydraulic press 3.1.4 Pressure of fluid at rest In general, in a fluid at rest the pressure varies according to the depth Consider a minute column in the fluid as shown

Ngày tải lên: 22/10/2012, 10:59

... was the derivation of the momentum equation of viscous fluid for turbulent flow and the theory of oil-film lubrication as oil in a hydraulic machine Similarly, even in the case of a gas, the compressibility ... a narrowing channel Trang 8Fig 4.9 Deformation of elementary rectangle of fluid Now, assume that, as shown in Fig 4.9, an elementary rectangle of fluid ABCD with sides dx, dy, which is located ... with in my first three years at Owens was Professor Osborne Reynolds, the Professor of Engineering He was one of the most original and independent of men and never did anything or expressed himself

Ngày tải lên: 22/10/2012, 10:59

... pupil of Johann Bernoulli and a close friend of Daniel Bernoulli Contributed enormously to the mathe- matical development of Newtonian mechanics, while formulating the equations of motion of a ... conservation of energy applied to a fluid Trang 3Fig 5.2 Movement of roller-coaster Fig 5.3 Conservation of fluid energy A streamline (a line which follows the direction of the fluid velocity) is chosen ... theorem (5.21) Coeficient of contraction Ratio C, of area a, of the smallest section of the discharging flow to area a of the small hole is called the coefficient of contraction, which is approximately

Ngày tải lên: 22/10/2012, 10:59

... 1Flow of viscous fluid All fluids are viscous In the case where the viscous effect is minimal, the flow can be treated as an ideal fluid, otherwise the fluid must be treated as a viscous fluid ... between the velocity, pressure, etc., in the flow of a two-dimensional incompressible viscous fluid Consider the elementary rectangle of fluid of side dx, side dy and thickness b as shown in Fig ... the x Fig 6.1 Flow balance in a fluid element Trang 2The mass of fluid element (pbdxdy) ought to increase by a(pbdxdy/at) in unit time by virtue of this stored fluid Therefore, the following equation

Ngày tải lên: 22/10/2012, 10:59

... pipe In the case of a smooth pipe, the following equations have been developed: equation of Blasius: A = 0.3164Re-’I4 (Re = 3 x lo3 - 1 x lo’) equation of Nikuradse: equation of K6rmin-Nikuradse: ... / 2 g ) expresses the frictional loss of head (the lost energy of fluid per unit weight) [(u2/2g) expresses the pressure reduction equivalent to the sum of the velocity stored when the velocity ... flow velocity) Since the velocity of a viscous fluid is zero on the wall, the fluid near the wall is decelerated The range subject to deceleration extends as the fluid flows further downstream,

Ngày tải lên: 22/10/2012, 10:59

... travelling velocity a of a long wave in a water channel of small depth h is a The ratio of the flow velocity to the wave velocity is called the Froude number The Froude number of a tranquil flow ... 137 Fig 8.2 Open channel velocity D in an open channel of constant section and inclination angle 8 of the bottom face Now examine the balance of forces on water between the two sections a distance ... the direction of the flow is that component of water weight Since the flow is not accelerating this force must equal the frictional force due to the wall If the cross-sectional area of the open

Ngày tải lên: 22/10/2012, 10:59

... 9.2 Ideal fluid Let us theoretically study (neglecting the viscosity of fluid) a cylinder placed in a flow The flow around a cylinder placed at right angles to the flow U of an ideal fluid is ... length of a flat plate Now, assume the distribution of u to be given by 1.46 c, = - %m Trang 12The drag of a body 159 Fig 9.13 Friction drag coefficients of a flat plate The above equations ... whole body surface of the component in the direction of the flow velocity U of this force p dA, is called form drag or pressure drag The drag D/ is the similar integration of zdA and is called

Ngày tải lên: 22/10/2012, 10:59

... D of a boat is determined by the velocity u of the boat, the density p of fluid and the acceleration of gravity g, derive the relationship between them by dimensional analysis 5 When fluid of ... development of surface tension waves and to a poured liquid Mach number When a fluid flows at high velocity, or when a solid moves at high velocity in a fluid at rest, the compressibility of the fluid ... applied to other fluids such as air or oil, and also used irrespective of the size of the sphere Furthermore, the form of eqn (10.9) is always applicable, not only to the case of the sphere but

Ngày tải lên: 22/10/2012, 10:59

... measurement of flow velocity and flow rate Fluid includes both gas and liquid According to the type and condition of the fluid, or if it flows in a pipe line or open channel, various methods of measurement ... the flow outlet pressure p 2 of fluid, the vertically set gear (Fig 11.1 l(a)) turns in the direction of the arrow Thus, every complete revolution sends out fluid of volume 4 V 11.2.5 Turbine ... form of measuring chamber of constant volume It is then possible to obtain the integrated volume by counting the number of times the volume is filled, and the flow rate by measuring the number of

Ngày tải lên: 22/10/2012, 10:59

... acting on the small element of fluid in Fig 12.1 Since the fluid is an ideal fluid, no force due to viscosity acts Therefore, by Newton’s second law of motion, the sum of all forces acting on the ... force, the equation of motion for this case can be obtained This is the case where the 198 Flow of an ideal fluid Fig 12.1 Balance of pressures on fluid element viscous term of eqn (6.12) is omitted ... exist, the following equations result from ,t eqns (12.3) and (12.12): 202 Flow of an ideal fluid ( 12.1 7) These equations are called the Cauchy-Riemann equations in the theory of complex variables

Ngày tải lên: 22/10/2012, 10:59

... downstream one after another The envelope of these wavefronts forms a Mach cone The propagation of sound is limited to the inside of the cone only If the included angle of this Mach cone is 201, then5 ... Trang 2Thermodynamical characteristics 2 19 or is called a perfect gas Equations (13.2) and (13.3) are called its equations of state Here R is the gas constant, and where R, is the universal gas ... (13.4) (13.5) L: P Here According to the first law of thermodynamics, when a quantity of heat dq is supplied to a system, the internal energy of the system increases by de, and work p dv is done

Ngày tải lên: 22/10/2012, 10:59

... valve at the end of the pipe is suddenly closed, the velocity of the fluid will abruptly decrease causing a mechanical impulse to the pipe due to a sudden increase in pressure of the fluid Such a ... Flow 3 Oil of viscosity v = 3 x lo-' m2/s extends over a 3 m length of a tube of diameter 2.5cm, as shown in Fig 14.8 Air pressure in one arm of the U- tube, which produces 40 cm of liquid column ... closed, the flow velocity u of the fluid in the pipe, and therefore also its momentum, becomes zero Therefore, the pressure increases by dp Since the following portions of fluid are also stopped one

Ngày tải lên: 22/10/2012, 10:59

... Trang 1Computational fluid dynamics For the flow of an incompressible fluid, if the Navier-Stokes equations of motion and the continuity equation are solved simultaneously ... methods Of late, with the progress of computers, it has become popular to solve flow problems numerically By such means it is now possible to follow a kaleidoscopic change of flow This field of engineering ... to &)lay of the first term of left side but the upwind difference to atlax, then the following equations are obtained and ( 1 5.1 2) (1 5.1 3 ) Equation (1 5.13) is still only of first order

Ngày tải lên: 22/10/2012, 10:59

... Review of Thermodynamics 2.1 Basic Definitions 47 47 Review of Mechanics 3.1 Kinematics of of Point Body 3.2 Center of Mass 3.2.1 Actual Center of Mass ... Aproximate Center of Area 3.3 Moment of Inertia 3.3.1 Moment of Inertia for Mass 3.3.2 Moment of Inertia for Area 3.3.3 Examples of Moment of Inertia 3.3.4 Product of Inertia ... xlv xlvi xlvi liii liii Introduction to Fluid Mechanics 1.1 What is Fluid Mechanics? 1.2 Brief History 1.3 Kinds of Fluids 1.4 Shear Stress 1.5...

Ngày tải lên: 16/02/2014, 23:20

... the result of a workshop, “Partial Differential Equations and Fluid Mechanics , which took place in the Mathematics Institute at the University of Warwick, May 21st–23rd, 2007 Several of the speakers ... an estimate of the time-averaged energy dissipation rate and a Lieb–Thirring-like inequality The precision and physical soundness of an estimate of the number of degrees of freedom of a given ... flow of a fluid through porous media The original equation due to Darcy can be shown to be an approximation of the equations governing the flow of a fluid through a porous solid within the context of...

Ngày tải lên: 14/03/2014, 10:20

... Essentials of Fluid Mechanics is targeted to science and engineering students who, having had some basic exposure to fluid mechanics, wish to attain an overview of the different branches of fluid mechanics ... on Fundamental Equations of Fluid Mechanics and Aerodynamics, enlarges the material in the original, and forms the basis for the treatment of different branches of fluid mechanics that appear in ... Str¨mungslehre, or Essentials o u o of Fluid Mechanics, is an indication of Prandtl’s intentions to guide the reader on a carefully thought-out path through the different areas of fluid mechanics On his way,...

Ngày tải lên: 17/03/2014, 14:00