Fluid Mechanics Chapter 2 Part I

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Fluid Mechanics Chapter 2

• Fundamental Concepts

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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

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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

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Some basics

• Specific weight of a substance is weight per unit
  volume

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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
  field.
• 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

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Basics

• 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

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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

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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

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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

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Uniform flow field

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

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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
  time

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Timelines , pathlines, streaklines and streamlines
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Conclusions

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

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Mathematically deriving streamlines and pathlines

• Streamlines
• Pathline A simulataneous solution of following
  equations give path line in

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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