Theory in Fluid Mechanics

1. Cycle 1 : FluidMechanics
P M V Subbarao
Professor
Mechanical Engineering Department
Mass and Momentum based
Measurements…

2. 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.

3. 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.

4. 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. 5
Bernoulli to Prandtl
1904
Ideal to Real
1822
1860
1738

6. Viscous flows – A Huge Elephant
Creeping Flows
Turbulent Flows
External Flows
Internal Flows
Free Shear Flows
Wall Shear Flows

7. More Innovations due to More confusion
List 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.

8. 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.

9. Applications

10. The Stokes Law
Fd = CµVd

11. Oseen’s Approximation
Equivalent sphere for irregular solids
for a cylinder is

12. Developing Flow Through Pipe

13. Boundary Layer Theory

14. Study of Mixing Layers

15. Measurement of Drag on Cylinder & Aerofoil