Fluid Mechanics Chapter 2 Part I - PowerPoint PPT Presentation

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Fluid Mechanics Chapter 2 Part I


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Title: Fluid Mechanics Chapter 2 Part I

Fluid Mechanics Chapter 2
  • Fundamental Concepts

Fluid as a Continuum
  • The region of space in which a fluid properties
    such as density could be treated as continuous is
    called continuum.
  • In a continuum each fluid property is expected to
    have a definite value at every point in space
  • So fluid properties of density, temperature and
    velocity and so on are considered continuous
    function of time in a continuum

Some basics
  • So in a continuum, density of a fluid will be
  • Specific gravity is a measure of how dense a
    fluid is with reference to water
  • So Mercury is 13.6 times denser than water with a
    specific gravity of 13.0
  • Specific gravity decreases with increase in TEMP

Some basics
  • Specific weight of a substance is weight per unit

Velocity Field
  • A very important property defined by a field is
    the velocity field, given by
  • Velocity is a vector quantity, requiring a
    magnitude and direction for a complete
    description, so the velocity field is a vector
  • velocity vector, also can be written in terms of
    its three scalar components
  • Velocity field means it is the velocity of a
    fluid passing through a point in space with
    coordinates X,Y,Z at time instant t.
  • U,V,W are the components of velocity in X , Y and
    Z directions

  • Steady Flow If properties at any point in a
    fluid flow donot change with time, it is called a
    steady flow. Mathematically for any property
  • So it could be

Steady Flow
  • In a steady flow the fluid properties may vary
    from point to point in the field but would remain
    constant at that point with respect to time

One-, Two-, and Three-Dimensional Flows
  • A flow is classified as one-, two-, or
    three-dimensional depending on the number of
    space coordinates required to specify the
    velocity field
  • velocity field may be a function of three space
    coordinates and time.
  • Such a flow field is termed three-dimensional

Uniform Flow
  • A Flow in which Velocity is constant at any cross
    section of flow is called a uniform flow
  • Under this assumption a 2 dimensional flow is
    modeled as one dimensional for analysis.
  • The density and pressure may also be assumed
    constant in the cross section of a uniform flow

Uniform flow field
  • A flow field in which velocity is constant and
    independent of all space coordinates in the
    entire flow field

Timelines , pathlines, streaklines and streamlines
  • Pathline It is the path or trajectory of a
    moving fluid particle. To identify this a dye
    /colour may be added to the fluid and photographs
    taken for the particle throughout its motion.
  • Streakline If we focus our attention on a fixed
    location. And identify All the particles which
    passed through this location at different draw a
    line joining all these particles, the line so
    drawn will be called streakline
  • StreamlinesLines drawn in a flow field so that
    at a given instant they are tangent to the flow
    direction are called streamlines
  • Timelines A line marked in a flow and
    visualising it how it changes over a period of

Timelines , pathlines, streaklines and streamlines
  • Steady Flow Streamlines, streaklines and path
    lines are the same(identical).
  • Unsteady flow All these lines are different

Mathematically deriving streamlines and pathlines
  • Streamlines
  • Pathline A simulataneous solution of following
    equations give path line in

Mathematically deriving streamlines and pathlines
  • Streaklines First derive the path lines and the
    apply following formulas

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End of Part I of the Chapter
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