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    fluid mechanics //مجموعة مشاركات(( لعلم الموائع)) !!يمكنك الاضافة والمشاركة

    الاخوة الاعزاء هذه مجموعة مشاركات لغرض تقديم معلومات وروابط تخص علم الموائع fluid mechanics لتسهيل البحث لاعضاء الملتقى مع كل الود والاحترام والتقدير **لكل الاخوة

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    http://www.fluidmechsolns.com/
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    http://www.fluidmech.net/
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    Fluid Mechanics: OverviewAbout Us | Directory | Career | News | Chat | InfoStore | Industrial | Ask an Expert





    Search AllMaterialsDesign CenterProcessesUnits and ConstantsFormulasMathematics for HomeMembershipPalm StoreForumSearch MemberCalculators
    Materials
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    Pipe Flow Calculations Software
    Pressure drop & fluid flow rate calculationsPipe Flow Rates & Pressure Drops
    Download a free trial of Pipe Flow ExpertFluid PreliminariesBy definition, a fluid is a material continuum that is unable to withstand a static shear stress. Unlike an elastic solid which responds to a shear stress with a recoverable deformation, a fluid responds with an irrecoverable flow. Variables needed to define a fluid and its environment are:
    QuantitySymbolObjectUnitspressure pscalarN/m2velocity vvectorm/sdensity rscalarkg/m3viscosity mscalarkg/m-sbody forcebvectorN/kgtime tscalarsExamples of fluids include gases and liquids. Typically, liquids are considered to be incompressible, whereas gases are considered to be compressible. However, there are exceptions in everyday engineering applications. Types of Flow; Reynolds NumberFluid flow can be either laminar or turbulent. The factor that determines which type of flow is present is the ratio of inertia forces to viscous forces within the fluid, expressed by the nondimensional Reynolds Number, where V and D are a fluid characteristic velocity and distance. For example, for fluid flowing in a pipe, V could be the average fluid velocity, and D would be the pipe diameter. Typically, viscous stresses within a fluid tend to stabilize and organize the flow, whereas excessive fluid inertia tends to disrupt organized flow leading to chaotic turbulent behavior. Fluid flows are laminar for Reynolds Numbers up to 2000. Beyond a Reynolds Number of 4000, the flow is completely turbulent. Between 2000 and 4000, the flow is in transition between laminar and turbulent, and it is possible to find subregions of both flow types within a given flow field.
    Governing EquationsLaminar fluid flow is described by the Navier-Stokes equations. For cases of inviscid flow, the Bernoulli equation can be used to describe the flow. When the flow is zero (i.e. statics), the fluid is governed by the laws of fluid statics. Flow & Pressure Drop in a pipe
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    Navier-Stokes equations

    Main article: Navier-Stokes equations
    The Navier-Stokes equations (named after Claude-Louis Navier and George Gabriel Stokes) are the set of equations that describe the motion of fluid substances such as liquids and gases. These equations state that changes in momentum (acceleration) of fluid particles depend only on the external pressure and internal viscous forces (similar to friction) acting on the fluid. Thus, the Navier-Stokes equations describe the balance of forces acting at any given region of the fluid.
    The Navier-Stokes equations are differential equations which describe the motion of a fluid. Such equations establish relations among the rates of change the variables of interest. For example, the Navier-Stokes equations for an ideal fluid with zero viscosity states that acceleration (the rate of change of velocity) is proportional to the derivative of internal pressure.
    This means that solutions of the Navier-Stokes equations for a given physical problem must be sought with the help of calculus. In practical terms only the simplest cases can be solved exactly in this way. These cases generally involve non-turbulent, steady flow (flow does not change with time) in which the Reynolds number is small.
    For more complex situations, such as global weather systems like El Niño or lift in a wing, solutions of the Navier-Stokes equations can currently only be found with the help of computers. This is a field of sciences by its own called computational fluid dynamics.

    General form of the equation

    The general form of the Navier-Stokes equations for the conservation of momentum is:
    [IMG]http://*******.answers.com/main/*******/wp/en/math/9/e/0/9e06e49b9eb143aa160e635ecdd0e0ca.png[/IMG] where
    • ρ is the fluid density,
    [IMG]http://*******.answers.com/main/*******/wp/en/math/6/7/c/67c18a3922c20fbb1e4dac36b565b181.png[/IMG] is the substantive derivative (also called the material derivative)
    • [IMG]http://*******.answers.com/main/*******/wp/en/math/0/a/a/0aa3ec374bdc0d6a17aecbb6bcda6a89.png[/IMG] is the velocity vector,
    • [IMG]http://*******.answers.com/main/*******/wp/en/math/8/5/7/857ee5b2a5c8944ed663d065acf9069e.png[/IMG] is the body force vector, and
    • [IMG]http://*******.answers.com/main/*******/wp/en/math/6/2/3/623709596363008e89cf20b6caba4df7.png[/IMG] is a tensor that represents the surface forces applied on a fluid particle (the comoving stress tensor).
    Unless the fluid is made up of spinning degrees of freedom like vortices, [IMG]http://*******.answers.com/main/*******/wp/en/math/6/2/3/623709596363008e89cf20b6caba4df7.png[/IMG] is a symmetric tensor. In general, (in three dimensions) [IMG]http://*******.answers.com/main/*******/wp/en/math/6/2/3/623709596363008e89cf20b6caba4df7.png[/IMG] has the form:
    [IMG]http://*******.answers.com/main/*******/wp/en/math/2/5/3/253e203d2af5d9fa011687c922c15336.png[/IMG] where
    • σ are normal stresses, and
    • τ are tangential stresses (shear stresses).
    The above is actually a set of three equations, one per dimension. By themselves, these aren't sufficient to produce a solution. However, adding conservation of mass and appropriate boundary conditions to the system of equations produces a solvable set of equations.

    Newtonian vs. non-Newtonian fluids

    A Newtonian fluid (named after Isaac Newton) is defined to be a fluid whose shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. This definition means regardless of the forces acting on a fluid, it continues to flow. For example, water is a Newtonian fluid, because it continues to display fluid properties no matter how much it is stirred or mixed. A slightly less rigorous definition is that the drag of a small object being moved through the fluid is proportional to the force applied to the object. (Compare friction).
    By contrast, stirring a non-Newtonian fluid can leave a "hole" behind. This will gradually fill up over time - this behaviour is seen in materials such as pudding, oobleck, or sand (although sand isn't strictly a fluid). Alternativley, stirring a non-Newtonian fluid can cause the viscosity to decrease, so the fluid appears "thinner" (this is seen in non-drip paints). There are many types of non-Newtonian fluids, as they are defined to be something that fails to obey a particular property.

    Equations for a Newtonian fluid

    Main article: Newtonian fluid
    The constant of proportionality between the shear stress and the velocity gradient is known as the viscosity. A simple equation to describe Newtonian fluid behaviour is
    [IMG]http://*******.answers.com/main/*******/wp/en/math/5/1/8/518de83f2b10251f344d35fae5df63a0.png[/IMG] where
    τ is the shear stress exerted by the fluid ("drag") μ is the fluid viscosity - a constant of proportionality [IMG]http://*******.answers.com/main/*******/wp/en/math/5/d/5/5d5f6df9523292d6aa38007fa3bae316.png[/IMG] is the velocity gradient perpendicular to the direction of shear For a Newtonian fluid, the viscosity, by definition, depends only on temperature and pressure, not on the forces acting upon it. If the fluid is incompressible and viscosity is constant across the fluid, the equation governing the shear stress (in Cartesian coordinates) is
    [IMG]http://*******.answers.com/main/*******/wp/en/math/5/d/e/5ded50d8b5af19e6f00d284bf156b5bb.png[/IMG] where
    τij is the shear stress on the ith face of a fluid element in the jth direction vi is the velocity in the ith direction xj is the jth direction coordinate If a fluid does not obey this relation, it is termed a non-Newtonian fluid, of which there are several types.

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    الروابط فعالة بامكانك اختيار الموضوع واتباع الرابط

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    Selected Sites (see also All Sites in this category)
    1. Engineering Formulas - eFunda
      Formulas, derivations, diagrams, and online calculators. Fluid mechanics topics include the Navier-Stokes equation, the Bernoulli equation, Reynold's number, pipe friction, manometer, and Venturi flowrate. Mechanics and materials topics: stress/strain, Mohr's circle, Hooke's law, Young's modulus, Rosette strain gage, and principal stress calculation. Vibrations topics: undamped vibration, damped vibration, forced vibration, multiple degree-of-freedom (DOF) system, accelerometer, and spring-mass calculation. Heat transfer topics: conduction, insulation, R-value, free convection, forced convection, and radiation. Failure criteria topics: maximum shear criterion, von Mises criterion, maximum stress criterion, ductile yield calculation, and brittle failure calculation. Finance topics: annual percentage rate, money factor, loan calculator, and lease calculator. Beam mechanics topics: Euler beam theory, cantilevers, simply supported beams, mixed supported beams, and beam cross sections (all, w-type, s-type, channels). Column buckling topics: elastic buckling, inelastic buckling, critical loads, eccentric loading, and buckling calculation. Access the site free for a limited time during any browser session; register and pay for unlimited access. more>>
    2. Fluid Mechanics, Chaos and Mixing - Julio M. Ottino, Chemical Engineering Dept., Northwestern University
      Research Interests of the Chaos and Mixing Group include: Granular Flows and Solid-Solid Mixing; Competition Between Chaos and Order; Liquid-Liquid Mixing; Mixing in 3-D Flows; Mixing in Cell Culture Systems; Solid-Liquid Mixing; and Geometric Aspects of Fluid Mixing. Links to papers (in PDF format) and related sites. more>>
    3. Fluid Mechanics - Dave Rusin; The Mathematical Atlas
      A short article designed to provide an introduction to fluid mechanics, which studies air, water, and other fluids in motion: compression, turbulence, diffusion, wave propagation, and so on. Mathematically this includes study of solutions of differential equations, including large-scale numerical methods (e.g the finite-element method). History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites

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    Problem Solutions in
    Transport Phenomena :
    Fluid Mechanics Problems





    For theory relevant to the fluid mechanics and momentum transfer problems below, please refer to the following books:
    Bird, R. B., Stewart, W. E., and Lightfoot, E. N., "Transport Phenomena", 2nd edition, John Wiley, New York (2002). Note that BSL is an abbreviation often used for this classic textbook based on the initials of its authors.
    Geankoplis, C. J., "Transport Processes and Unit Operations", 3rd edition, Prentice-Hall, Englewood Cliffs, New Jersey (1993).
    The solutions below will also help you solve some of the problems in the books by BSL and Geankoplis.



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    حسن هادي
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    Click here for Problem Solutions in Transport Phenomena : HEAT TRANSFER PROBLEMS Click here for Problem

    لاعتقادي بكونها مفيدة لذلك كررتها لاسهل عليكم البحث مع التقدير

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    International Journal of Fluid Mechanics Research

    الرابط التالي
    http://www.begellhouse.com/journals/...a5b40f8f8.html

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