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Recap
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- Kinematics of fluid deals with the geometry of fluid motion. It characterizes
the different types of motion and associated deformation rates
of fluid element.
- The fluid motion is described by two methods, namely, Lagrangian
method and Eulerian method. In the Lagrangian view, the velocity and
other hydrodynamic parameters are specified for particles or elements
of given identities, while, in the Eulerian view, these parameters are
expressed as functions of location and time. The Lagrangian version of
a flow field can be obtained from the integration of the set of equations
describing the flow in the Eulerian version.
- A flow is defined to be steady when the hydrodynamic parameters
and fluid properties at any point do not change with time. Flow in
which any of these parameters changes with time is termed as unsteady.
A flow may appear steady or unsteady depending upon the choice of
coordinate axes. A flow is said to be uniform when no hydrodynamic
parameter changes from point to point at any instant of time, or else
the flow is non-uniform.
- The total derivative of velocity with respect to time is known as material
or substantial acceleration, while the partial derivative of velocity
with respect to time for a fixed location is known as temporal acceleration.
Material acceleration = temporal acceleration + convective
acceleration.
- A streamline at any instant of time is an imaginary curve or line in the flow field so that the tangent to the curve at any point represents the
direction of the instantaneous velocity at that point. A path line is the
trajectory of a fluid particle of a given identity. A streak line at any
instant of time is the locus of temporary locations of all particles that
have passed through a fixed point in the flow. In a steady flow, the
streamlines, path lines and streak lines are identical.
- Flow parameters, in general, become functions of time and space coordinates.
A one dimensional flow is that in which the flow parameters
are functions of time and one space coordinate only.
- A fluid motion consists of translation, rotation and continuous deformation.
In an uniform flow, the fluid elements are simply translated
without any deformation or rotation. The deformation and rotation
of fluid elements are caused by the variations in velocity components
with the space coordinates. The linear deformation or strain rate is
defined as the rate of change of length of a linear fluid element per unit
original length. The rate of angular deformation at a point is defined as
the rate of change of angle between two linear elements at that point
which were initially perpendicular to each other. The rotation at a
point is defined as the arithmetic mean of the angular velocities of two
perpendicular linear segments meeting at that point. The rotation of
a fluid element in absence of any deformation is known as pure or rigid
body rotation. When the components of rotation at all points in a flow
become zero, the flow is said to be irrotational.
- The vorticity is actually an antisymmetric tensor but it is defined as a
vector that equals to two times the rotation vector. Vorticity is zero
for an irrotational flow.
- The existence of a physically possible flow field is verified from the
principle of conservation of mass.
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Congratulations! you
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