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Module 3 : INVISCID INCOMPRESSIBLE FLOW
Lecture 1 : Fundamental Aspects
In general, fluids have a well-known tendency to move or flow. The slight change in shear stress or
appropriate imbalance in normal stresses will cause fluid motion.
Fluid kinematics
deals with various
aspects of fluid motion without concerning the actual force that causes the fluid motion. In this
particular section, we shall consider the ‘field' concept to define velocity/ acceleration of fluid by
virtue of its motion. In the later part, some ‘visualization' concepts are introduced to define the
motion of the fluid qualitatively as well as quantitatively.
There are two general approaches in analyzing the fluid motion. In the first method (Lagrangian
approach), the individual fluid particles are considered and their properties are studied as a function
of time. In the second method (Eulerian approach), the ‘field' concept is introduced and the
properties are completely prescribed as the functions of space and time. In other words, the
attention is focused at fixed points in space as the fluid passes those points.
Velocity and Acceleration Field
Since the ‘continuum' assumption holds well for fluids, the description of any fluid property (such as
density, pressure, velocity, acceleration etc.) can be expressed as a function of location. These
representation as a function of spatial coordinates is called as “field representation” of the flow.
One of the most important fluid variables is the velocity field. It is a vector function of position and
time with components u, v and w as scalar variables i.e.
(3.1.1)
The magnitude of the velocity vector i.e. , is the speed of fluid. The total time
derivative of the velocity vector is the acceleration vector field of the flow which is given as,
(3.1.2)