The Reynolds Experiment
In 1883 Reynolds performed his classical experiment on pipe flow. A schematic
of the apparatus is shown underneath. It consisted from a water tank, a pipe with
a bell-mouth entrance immersed into the water tank, an assembly to inje

1
Dr. Georgios H. Vatistas, November 2000
Chapter I
Fundamental Concepts of
Fluid Mechanics
"For we do not think that we know a thing until
we acquainted with its primary conditions or first
principles and have carried our analysis as far as
its simplest

Types of Fluid Element Motions and Deformations
Fluid elements can undergo two types of motion as a whole (without any structural
change): solid body translation (i) and rotation (ii).
The two other motions involve structural change (deformation) of the f

Conservation Equations
in Differential Form
The fundamental laws governing fluid behavior are:
(i)
The law of conservation of mass: "mass can not be created not destroyed"
(ii)
Newton's second law of motion: "the total force external the system is equal t

September 2006
Ancient Wisdom
and the Laws of Nature
Georgios H. Vatistas
Department of Mechanical and Industrial Engineering
Concordia University
Montreal Canada
Summary. The laws of nature as we see them are the foundations of science and technology. Th

Governing Equations
[Adapted from: Yuan, S.W. (1967) Foundations of Fluid Mechanics. Prentice-Hall Inc.,
Englewood Cliffs.]
Using the relationships of the Orthogonal Curvilinear Coordinates lecture, we can
transform the derived governing equations in Cart

FRAMES OF REFERENCE
Newtonian (or classical) mechanics presupposes that all the observations are performed within an inertial
(or Galilean) frame of reference. Since the foundation of fluid mechanics is Newtonian mechanics, fluids in
motion should also be

Taylors Series Expansion
F (x, y)
FF( xx,o+yox,
) yo )
y
y
x
y o = constant
x
In 2-Dimensions
F x o + x, y o + y = F x o , y o
+ x
f
f
+ y
x x o, yo
y x o, yo
2 f
2 f
+ 1 x 2
+ y 2
2!
x 2 x o, yo
y 2 x o, yo
+ 2 xy
2 f
x y x o, yo
+ .
If y = constant
y =

Nature of Stresses Acting on a Fluid Element
Two types of forces are known to act on a fluid element.
i.
External, or body forces (gravitational and electromagnetic). These forces are distributed over the
volume of the medium and are usually expressed per