NAME
ENROLLMENT NO.
ROLL NO.
Mayursinh Chudasama
130030106070
08
Parth Mungra
130030106071
09
Shyamal Nandani
Maulik dudhatra
130030106072
130030106069
10
07

The study of fluid in motion without considering the
causes of the forces is called

Fluid kinematics is the study on fluid motion in space
and time without considering the force which causes
the fluid motion.

According to the continuum hypothesis the local
velocity of fluid is the velocity of an infinitesimally
small fluid particle/element at a given instant t. It is
generally a continuous function in space and time

The following terms are considered to
describe the flow of motion of fluid.
1) Path Line
2) Streak Line
3) Stream Line
4) Stream tube
The path traced by a single fluid
particles in motion over a period of time is
called its path line. The path line shows the
direction of velocity of the particle.
It is an instantaneous picture of the
position of all the fluid particles in the flow
which have passed through a given fixed
point.
A stream line is an imaginary line
drawn through the flow field in such a
way that the velocity vector of the fluid
at each and every point on the
streamline is tangent to the streamline at
that instant.
=
=
It may be defined as a tubular
space formed by the collection of
stream line passing through the
perimeter of a closed curve.
It is defined as that type of flow in which
the fluid in which the fluid characteristics like
pressure, velocity, density etc. at a point do
not change with respect to time.
( dV/dt)x0,y0,z0
Unsteady flow is defined as the flow in
which the fluid characteristics like pressure,
velocity, density etc. at a point do not
change with respect to time.
It is defined as that type of flow in which
the flow parameters like pressure, velocity,
density etc. at given time do not change
with respect to space.
It is the flow in which the flow
parameters like pressure, velocity, density
etc. at given time change with respect to
space.

A laminar flow is one in which the
fluid particles move in layers or lamina
with one layer sliding over the other.
Reynolds's number is less than 2000 for
laminar flow.

It is that type of flow in which the fluid
particles move in zigzag way.
Reynolds's number is greater than 4000 for
turbulent flow.
A rotational flow exists when the fluid
particles rotate their own axis while
moving along a streamline.
The flow is irrotational when the fluid
particles do not rotate about their own
axis while moving along a stream line.
In general,
fluid flows  a net motion of molecules from one point in space to
another point as a function of time.
We employ th e continuum hypothesis and consider fluids to be made up
of fluid particles that interact with each other and with th eir surroundin gs.
Each particle contains numerous molecules.
 We can describe the flow of a fluid in terms of motion of fluid particles
rather th an individual molecules.
This motion can be described in terms of the velocity & accelerati on of
the fluid particles.
At a given instant in time,
descriptio n of any fluid property (such as ρ , p , V , a  T)
= f ( fluid' s location ) = f ( spatial coordinate s)

field representa tion of flow.
For example,
T = T (x, y, z, t)
One of the most important fluid variable s is the velocity field




V (x, y, z, t ) = u(x, y, z, t ) i + v(x, y, z, t) j + w(x, y, z, t) k




V (x, y, z, t) = u i + v j + w k =< u, v, w >



d rA
VA =
where r = position v ector
dt
 direction

V
 speed

2
2
2
magntude  V  V  u  v  w

dV
dt

 a  accleratio n
Two general approaches in analyzing fluid mechanics problems
(1) Eulerian method - - - uses the field concept introduced above
- - the fluid motion is given by completely prescribin g the necessary properties
(p,  , v, etc.)  f(space, time)
- - obtain informatio n about the flow in terms of what happens at fixed points in
space as the fluid flows past thos e points
(2) Lagrangian method
- - The fluid particles are " tagged " or identified , and their properties determined as
the y move.
- - involves following individual fluid particles as they move about and determined how the
fluid properties associated with th ese particles change as a function of time.
In fluid mechanics

Eulerian method
use
Lagrangian informatio n 
 Eulerian data
(data)

(informati on)

For a steady flow the stream-tube
formed by a closed curved fixed in
space is also fixed in space, and no fluid
can penetrate through the stream-tube
surface, like a duct wall.
Considering a stream tube of cylindrical cross
sections A1 and A2 with velocities v1 and v2
perpendicular to the cross sections A1 and A2
and densities ƍ1 and ƍ2 at the respective cross
section. Assume the velocities and density are
constant across section, a fluid mass closed
between cross section 1 and 2 at an instant t
will be moved after a time interval dt by v1 dt
and v2 dt
to the cross section 1’ & 2’
respectively.
 Because the closed mass between 1 and 2
must be the same between 1’ and 2’, and the
mass between 1’ and 2 for a steady flow can
not change from t and t+dt, the mass
between 1 and 1’ moved in dt, ƍ A v dt must


Therefore the continuity equation of
steady flow :
1 A1 v1  2 A2 v2
Interpretation : The mass flow ratem   A u  const.
For incompressible fluid with   
1
2
A1 v1  A2 v2
Interpretation : The volume flow rate
V  A u  const.
From
the
continuity
equation
for
incompressible fluid :
,for a stream-tube.
v1 A2

v2
A1
A grid obtained by a drawing a series of
streamlines and equipotential lines is
known as a flow net.
 The flow nets provides a simple graphical
technique for studying 2-D irrotational
flows specially in the cases where
mathematically relations for stream
functions and velocity potential functions
are either not available or rather difficult
to solve.


The stream lines show the direction of
flow where as equipotential lines joining
the points of equal velocity potential.

Circulation is defined as the line integral
of the tangential velocity around a
closed contour in the flow field.

Sink flow is
opposite to the
source flow in
which moves
radially inwards
towards a point
where it
disappears at a
constant rate.
The flow coming
from a point and
moving out radially
in all directions of a
plane at uniform
rate is known as
source flow.
 This flow represents a
singular point source
of spontaneous mass
creation.
