Chapter 3 Classification of Flow .doc

Classification of flow

1. Flow Classification 1





Chapter “3”

2. Flow Classification 2

3. Flow Classification 3


Flow Classification

Flow can be classified in a number of ways. The system generally
adopted is to consider the flow as being characterized by two
parameters: time and distance. The first major subdivision is based on
consideration of the time scale. This categorizes all flows as either
steady or unsteady.

Steady Flow: The flow is steady if the parameters describing that flow do
not vary with time (,0t/V t/V =0,0t/p ). Typical
parameters of a flow are: velocity, discharge, pressure or depth.
Conversely, a flow is Unsteady if these parameters vary with time.

The second subdivision relates to the scale of distance. This classifies
flows as being uniform or non-uniform.

Uniform Flow: A flow is uniform if the parameters describing the flow do
not vary with distance along the flow pass (0sV  ). Conversely,
for a non-uniform flow, the magnitude of the parameters varies from
point to point (0sV  ≠) along the path flow.

Some flows exhibit changes with respect to both time and distance,
while others change with respect to time or distance only. However, the
majority of flows will fall into one of the classifications list below.

4. Flow Classification 4

Steady uniform Flow: For such a flow the discharge is constant with time,
and the cross-section through which the flow passes is of constant
area.
Steady non-uniform Flow: The discharge is constant with time, and the
cross-sectional area varies with distance (the cross-section varies from
point to point).
Unsteady uniform Flow: The cross-section through the flow is constant,
but the discharge varies with time.
Unsteady non-uniform Flow: In which the cross-section and the discharge
vary with both time and distance.

One, Two and Three Dimensional Flow
One dimensional flow: It is that type of flow in which the flow
parameter such as velocity is a function of time and
one space co-ordinate only  0w ,0V ),x(fu 
.
where w and V ,U are velocity components in z ,y ,x directions
respectively.

Two dimensional flow: The flow in which the velocity is a function of
time and two rectangular space co-ordinates. Flow
parameter such as velocity is a function of time and
one space co-ordinate only.  0w ,y ,xfV ),y ,x(fu
21 
.

5. Flow Classification 5

Three dimensional flow: It is that type of flow in which the velocity is
a function of time and three mutually perpendicular
directions.   z ,y,xfw ),z ,y,x(fV ),z ,y,x(fu
321 
.

Rotational and Irrotational Flows
Rotational flow: The fluid particles while moving in the direction of
flow rotate about their mass centers (motion of
liquid in a rotating tank).

Irrotational flow: The fluid particles while moving in the direction of
flow do not rotate about their mass centers (flow
above a drain hole of a stationary tank or a wash
basin).

Laminar and Turbulent Flows
To classify flow as either laminar or turbulent, an index called the
Reynolds number is used. It is computed as follows: 
D V
R
e

where: 
eR Reynolds number (unit less), V
= Average velocity, (s/m ors/ft ), 
= kinematic viscosity (s/ft or s/m
22 ).

6. Flow Classification 6

Laminar flow: Laminar flows is one in which paths taken by the
individual particles do not cross one another and
move along well defined paths, 2000R
e for flow in
pipes.
(Flow through a capillarity tube, flow of blood in veins
and arteries, ground water flow).

Turbulent flow: A turbulent flow is that flow in which fluid particles
move in a zig zag way4000R
e , for flow in pipes.

(for4000R2000
e ), flow in pipes may be laminar or turbulent
"transition")


Compressible and Incompressible Flows
Compressible flow: It is that type of flow in which the density " " of
the fluid changes from point (i.e. the density is not
constant for the fluid,  = constant).

Incompressible flow: It is that type of flow in which the density ( ) of
the fluid is constant for the fluid flow. Liquid are
generally considered flowing incompressible. ( =
constant).

Types of Flow Lines

7. Flow Classification 7

Path line: A path line is the path followed by a fluid particle in
motion. A path line shows the direction of particular
particle as it moves ahead.

Streamline: A streamline is constructed by drawing a line which is
tangential to the velocity vectors of a connected
series of fluid particles. The streamline is thus a line
representing the direction of flow of the series of
particles at a given instant. Equation of streamline in
three-dimensional flow is given as: w
dz
V
dy
u
dx



Stream tube: A set of streamlines may be arranged to form an
imaginary pipe or tube. This is known as "stream
tube". Under certain circumstance, stream tubes can
actually be identified.

Streak lines: Since, it is difficult to construct a streamline for a real
flow; a simple method of obtaining approximate
information regarding streamline patters is to inject a
dye into the flow. The dye will trace out a path known
as a "streak line" which may be photographed.
(The path taken by smoke coming out of chimney)

8. Flow Classification 8

Note:
 A streamline cannot intersect itself nor can two streamlines
cross.
 There is no flow cross a streamline.
 Whereas a path line gives the path of one particular particle
at successive instant of time, a streamline indicates the
direction of a number of particles at the same instant.
 The series of streamlines represent the flow pattern at
instant.

9. Flow Classification 9

















(a) Experiment to illustrate Types of Flow , (b) Typical Dye Streak

10. Flow Classification 10


Streamline

A Path line is Formed by following the
Actual Path of a Fluid Particle.












A Stream tube Consists of a Bundle of Individual Streamlines













A Streak line is Formed by Continuous Introduction of
Day or Smoke from a Point in the Flow.

11. Flow Classification 11