INTRODUCTION to FLUID MECHANICS

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INTRODUCTION toFLUID MECHANICS
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CONTENTS

• Introduction
• Fundamental Concepts of Fluid Mechanics
• Fluid Statics
• Fluid Dynamics
• Conclusion

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Introduction

• The first study about fluids from Archimedes(BC
  285-212).He developed some calculating methods
  using buoyancy of water, but real development is
  in Renaissance.
• In fluid mechanics,Leonardo daVinci(1452-1519)
  made important development.He found continuum
  equation,nozzle flows
• In frictionless flow,the most important
  developers are Daniel Bernoulli(1700-1782),
  Leonar Euler(1707-1783),Joseph-Louis
  Lagrange(1736-1813), and Pier Simon
  Laplace(1749-1827).
• Obsorne Reynolds(1842-1912) improved of the
  experiment classical tube (1883) so he found
  pure numbers,its most important for fluid
  mechanics.

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• Henri Navier(1785-1836) George
  Stokes(1819-1903) are add to frictionless terms
  to the Newtonian flows, so all flows analyze
  application to be succesfull and also they found
  momentum equations,today it is known Navier
  Stokes Equation.

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Fundamental Concepts of Fluid Mechanics

• Fluid mechanics is the study of how fluids move
  and the forces on them. (Fluids include liquids
  and gases.) Fluid mechanics can be divided into
  fluid statics, the study of fluids at rest, and
  fluid dynamics, the study of fluids in motion. It
  is a branch of continuum mechanics, a subject
  which models matter without using the information
  that it is made out of atoms. Fluid mechanics,
  especially fluid dynamics, is an active field of
  research with many unsolved or partly solved
  problems. Fluid mechanics can be mathematically
  complex. Sometimes it can best be solved by
  numerical methods, typically using computers.

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• A modern discipline, called Computational Fluid
  Dynamics (CFD), is devoted to this approach to
  solving fluid mechanics problems. Also taking
  advantage of the highly visual nature of fluid
  flow is Particle Image Velocimetry, an
  experimental method for visualizing and analyzing
  fluid flow. Fluid mechanics is the branch of
  physics which deals with the properties of
  fluids, namely liquids and gases, and their
  interaction with forces.

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Fluid Statics

• All fluid and gas conditions one of the
  fluids.Fluid statics is examine to stable fluids
  pressure and force.Stable fluids to be exposed
  just pressure and gravity force.
• The pressure at any arbitrary point P a distance
  h below the upper surface of the liquid.
• Pressure Which force is effect to perpendicular
  the unit surface,called Pressure.
• Mathematically P F / A or P dF / dA

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• Density The density of a material is defined as
  its mass per unit volume. The symbol of density
  is ? (the Greek letter rho).
• Mathematically ? m / v
• Different materials usually have different
  densities, so density is an important concept
  regarding buoyancy, metal purity and packaging.

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• Compressible Flow It changes, depends on
  density (?),pressure and temperature.Such as
  gases
• Incompressible Flow Density (?) is
  constant.Such as fluids
• When all the time derivatives of a flow field
  vanish, the flow is considered to be a Steady
  flow. Otherwise, it is called Unsteady. Whether a
  particular flow is steady or unsteady, can depend
  on the chosen frame of reference.

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Reynolds Transport Theorem

• In order to convert a system analysis into a
  control-volume analysis we must convert our
  mathematics to apply to a specific region rather
  than to individual masses. The conversion, called
  the Reynolds transport theorem
• The Fixed control volume encloses a stationary
  region of interest to a nozzle designer. The
  control surface is an abstract concept and does
  not hinder the flow in any way. It slices through
  the jet leaving the nozzle, circles around
  through the surrounding atmosphere,and slices
  through the flange bolts and the fluid within the
  nozzle.

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• Deforming control volume varying relative motion
  at the boundaries becomes a factor, and the rate
  of change of shape of the control volume enters
  the analysis.

• Moving control volume here the ship is of
  interest, not the ocean, so that the control
  surface chases the ship at ship speed V.

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Conservation of Mass

• Mass can neither be created nor destryod. The
  inflows, outflows and change in storage of mass
  in a system must be in balance.

• This states that in steady flow the mass fluxes
  entering and leaving the control volume must
  balance exactly. If, further, the inlets and
  outlets are one-dimensional, we have for steady
  flow

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• In general, the steady-flow-mass-conservation
  relation can be written as

• If the inlets and outlets are not
  one-dimensional, one has to compute by
  integration

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Conservation of Linear Momentum

• In Newtons law, the property being
  differentiated is the linear momentum mV.
  Therefore our variable is B mV and dB/dm
  V and application of the Reynolds transport
  theorem gives the linear-momentum relation for a
  deformable control volume

• If we want only, say, the x-component, the
  equation reduces to

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The Bernoulli Equation

• A widely used relation between pressure,velocity
  and elevation. All properties p, V, p, and A
  gradually change in the streamwise direction s.
  The streamtube is slanted at some arbitrary angle
  ,so that the elevation change between sections
  is dz ds sin

• This is Bernoullis equation for unsteady
  frictionless flow along a streamline.It is in
  differential form and can be integrated between
  any two points 1 and 2 on the streamline

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Thermodynamic Laws

• First Law If heat dQ is added to the system or
  work dW is done by the system,the system energy
  dE must change according to first law.

• Second Law Relates entropy change dS to heat
  added dQ and absolute temperature T.

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The Energy Equation

• We will use Reynolds transport theorem to the
  first law thermodynamics.Variable B becomes
  energy(E),and the energy per unit mass is

• Recall that positive Q denotes heat added to the
  system and positive W denotes work done by the
  system. The system energy per unit mass e may be
  of several types

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Differential Equation of Mass Conservation

• All the basic differential equations can be
  derived by considering either an elemental
  control volume or an elemental system.Here we
  choose an infinitesimal fixed control volume( dx
  , dy , dz) and use our basic control-volume
  relations .The flow through each side of the
  element is approximately one-dimensional, and so
  appropriate mass-conservation relation to use
  here is

• The element volume cancels out of all terms,
  leaving a pure differential equation involving
  the partial derivatives of density and velocity

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• Elemental cartesian fixed control volume showing
  the inletoutlet mass fluxes on the x faces.

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The Differential Equation of Linear Momentum

• We use the same elemental control volume as for
  which the appropriate form or the linear-momentum
  relation is

• The sum of hydrostatic pressure plus viscous
  stresses which arise from motion with
  velocity gradients

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• Notation for stresses

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• Elemental cartesian fixed control volume showing
  the surface forces in the x direction

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• Newtonian Fluid Navier Stokes Equation The
  viscous stresses are proportional to the element
  strain rates and the coefficient of viscosity.
  For incompressible flow, to three-dimensional
  viscous flow.

• Where is the viscosity coefficent.The diff.
  Equation for a Newtonian fluid with a constant
  density and viscosity.

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Conclusion

• In this project, first looking just about Physic
  but when studied my subject, as we saw this
  presentation, mathematical terms are so
  necessary.
• For this subject Mathematic information must be
  know cause some parts make a partial
  differentation and also integration knowledge is
  also useful.
• It is also enjoyable because learned something to
  be curious about in my daily life. Such as
  watching F1 racing, but how to cars acceleration
  was improved, their aerodynamics structure how to
  be better or airplanes how to flight or why the
  ships doesnt sink
• So in this project analyzed Mathematical
  structure and so many things is about
  engineering. One of the Mathematic foundation
  wants to solve some problems Physical terms,

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• If somebody solve this, they give 1.000.000.It
  wants big Mathematical calculations and need
  powerful computers to solve the problem.

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References

• Frank M.White, Fluid Mechanics, McGraw-Hill Inc.,
  1979
• Robert Ressnick David Halliday, Physics , John
  Wiley and Sons Inc., 1996
• Shames , Mechanics of Fluids , Mc Graw-Hill Inc.
  , 1962
• http//en.wikipedia.org/wiki/Fluidmechanics