Cycle 1 : Fluid Mechanics

P M V SubbaraoProfessor

Mechanical Engineering Department

Mass and Momentum based Measurements…

Theoretical and Rigorous Work of French

• Daniel Bernoulli (1700– 1789): Hydrodynamique (Hydrodynamica), published in 1738

• Bernoulli and Leonhard Euler.

• 1750:Euler offered a memoir containing analysis and equations for hydraulic turbines.

• 1754: An idealized theoretical application of Newton’s 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.

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.

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)

5

Bernoulli to Prandtl

1904

Ideal to Real1822

1860

1738

Viscous flows – A Huge Elephant

Creeping FlowsTurbulent Flows

External Flows

Internal Flows

Free Shear Flows

Wall Shear Flows

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.

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.

Applications

The Stokes Law

Fd = CµVd

Oseen’s Approximation

Equivalent sphere for irregular solids

for a cylinder is

Developing Flow Through Pipe

Boundary Layer Theory

Study of Mixing Layers

Measurement of Drag on Cylinder & Aerofoil