Cycle%201%20:%20Fluid%20Mechanics

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Cycle 1 Fluid Mechanics

• P M V Subbarao
• Professor
• Mechanical Engineering Department

Mass and Momentum based Measurements
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Theoretical and Rigorous Work of French

• Daniel Bernoulli (1700 1789) Hydrodynamique
  (Hydrodynamica), published in 1738
• Bernoulli and Leonhard Euler.
• 1750Euler offered a memoir containing analysis
  and equations for hydraulic turbines.
• 1754 An idealized theoretical application of
  Newtons Law to centrifugal impellers.
• Known as Euler Equation.
• Did much to help the development of hydraulic
  machinery.
• 1767 Relation between Torque and Change in
  moment of momentum of the fluid as it passed
  through the machine.

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Leonhard Euler

• Leonhard Euler (1707-1783) was arguably the
  greatest mathematician of the eighteenth century.
• One of the most prolific writer of all time his
  publication list of 886 papers and books fill
  about 90 volumes.
• Remarkably, much of this output dates from the
  last two decades of his life, when he was totally
  blind.
• Euler's prolific output caused a tremendous
  problem of backlog the St. Petersburg Academy
  continued publishing his work posthumously for
  more than 30 years.

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Interaction of Particles with Solid Wall

• Maxwell is considered by many physicists to be
  the 19th-century scientist who had the greatest
  influence on 20th-century physics.
• His contributions to the science are considered
  by many to be of the same magnitude as those of
  Isaac Newton and Albert

James Clerk Maxwell ( 1831 1879)
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Bernoulli to Prandtl
Ideal to Real
1738
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Viscous flows A Huge Elephant
External Flows
Creeping Flows
Turbulent Flows
Wall Shear Flows
Free Shear Flows
Internal Flows
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More Innovations due to More confusionList of
Experiments

• Study of Creeping Flow.
• Study of developing flow through a pipe.
• Study of boundary layer growth on a smooth and
  rough flat plates.
• Measurement of drag on a cylinder and an
  aerofoil.
• Study of Mixing Layers.

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Creeping flow

• Prof. George Gabriel Stokes, (1819 1903)
  worked most of his life describing fluid
  properties.
• His most significant accomplishment was the work
  describing the motion of a sphere in a viscous
  fluid.
• This work lead to the development of Stokes Law,
  a mathematical description of the force required
  to move a sphere through a quiescent, viscous
  fluid at specific velocity.

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Applications
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The Stokes Law
Fd CµVd
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Oseens Approximation
Equivalent sphere for irregular solids
for a cylinder is
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Developing Flow Through Pipe
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Boundary Layer Theory
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Study of Mixing Layers
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Measurement of Drag on Cylinder Aerofoil