Manipal Institute of Technology
A constituent college of Manipal University
Dept. of Aeronautical Engineering
AAE 201
Mechanics of Fluids
Mr. Shiva
Assistant Professor
Department of Aeronautical & Automobile Engineering
By Shiva U Asst. Prof.
Manipal Institute of Technology
A constituent college of Manipal University
Dept. of Aeronautical Engineering
Chapter 3
Kinematics
of Fluids
By Shiva U Asst. Prof.
Manipal Institute of Technology
A constituent college of Manipal University
Dept. of Aeronautical Engineering
Syllabus
Fluid Kinematics: Stream line, path line, streak line, stream
tube, classification of flows, steady, unsteady, uniform, nonuniform, laminar, turbulent, rotational, irrotational flows, one,
two and three dimensional flows, Continuity equation in 3D
flow, stream function, velocity potential function.
By Shiva U Asst. Prof.
Manipal Institute of Technology
A constituent college of Manipal University
Dept. of Aeronautical Engineering
Fluid Kinematics
What is fluid kinematics?
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.
By Shiva U Asst. Prof.
Manipal Institute of Technology
A constituent college of Manipal University
Dept. of Aeronautical Engineering
By Shiva U Asst. Prof.
Manipal Institute of Technology
A constituent college of Manipal University
Dept. of Aeronautical Engineering
Methods of Describing the Fluid Flow
The fluid motion is described by two methods.
1. Lagrangian Method
2. Eulerian Method
By Shiva U Asst. Prof.
Manipal Institute of Technology
A constituent college of Manipal University
Dept. of Aeronautical Engineering
Eularian and Lagrangian approaches
Eularian and Lagrangian approaches are of the two methods to
study fluid motion. The Eularian approach concentrates on
fluid properties at a point P (x,y,z,t). Thus it is a field
approach.
In the Lagrangian approach one identifies a particle or a group
of particles and follows them with time. This is bound to be a
cumbersome method. But there may be situations where it is
unavoidable. One such is the two phase flow involving
particles.
By Shiva U Asst. Prof.
Manipal Institute of Technology
A constituent college of Manipal University
Dept. of Aeronautical Engineering
Descriptions of Fluid Motion
streamline
Defined instantaneously
has the direction of the velocity vector at each point
no flow across the streamline
steady flow streamlines are fixed in space
unsteady flow streamlines move
pathline
Defined as particle moves (over time)
path of a particle
same as streamline for steady flow
streakline
Streamlines
tracer injected continuously into a flow
same as pathline and streamline for steady flow
By Shiva U Asst. Prof.
Manipal Institute of Technology
A constituent college of Manipal University
Dept. of Aeronautical Engineering
Streamlines
Streamline definition
A streamline is one that drawn is
tangential to the velocity vector at
every point in the flow at a given
instant and forms a powerful tool in
understanding flows.
By Shiva U Asst. Prof.
Manipal Institute of Technology
A constituent college of Manipal University
Dept. of Aeronautical Engineering
Stream-tube
The definition of streamline is the
fact that there cannot be a flow
across it; i.e. there is no flow
normal to it. Sometimes, as shown
in Fig. we pull out a bundle of
streamlines from inside of a general
flow for analysis. Such a bundle is
called stream tube and is very
useful in analyzing flows. If one
aligns a coordinate along the stream
tube then the flow through it is onedimensional.
By Shiva U Asst. Prof.
10
Manipal Institute of Technology
A constituent college of Manipal University
Dept. of Aeronautical Engineering
Stream-tube
Is the surface formed instantaneously by all the streamlines
that pass through a given closed curve in the fluid.
By Shiva U Asst. Prof.
11
Manipal Institute of Technology
A constituent college of Manipal University
Dept. of Aeronautical Engineering
Pathlines
Pathline is the line traced by a given particle. This is generated
by injecting a dye into the fluid and following its path by
photography or other means (Fig.)
By Shiva U Asst. Prof.
12
Manipal Institute of Technology
A constituent college of Manipal University
Dept. of Aeronautical Engineering
Streakline
Streakline concentrates on
fluid particles that have gone
through a fixed station or
point. At some instant of time
the position of all these
particles are marked and a line
is drawn through them. Such a
line is called a streakline (Fig.).
By Shiva U Asst. Prof.
13
Manipal Institute of Technology
A constituent college of Manipal University
Dept. of Aeronautical Engineering
Timeline
Timeline is generated by drawing a line through adjacent
particles in flow at any instant of time.
In a steady flow the streamline, pathline and streakline all
coincide. In an unsteady flow they can be different.
Streamlines are easily generated mathematically while
pathline and streaklines are obtained through experiments.
By Shiva U Asst. Prof.
14
Manipal Institute of Technology
A constituent college of Manipal University
Dept. of Aeronautical Engineering
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