Kinematics of Fluid Flow - Introduction

• Study of motion of fluid particles with respect to coordinates fixed at a point is called Eulerian

method of study.

• Study of motion of fluid particles w.r.t. coordinates fixed on a moving boat is known as Lagrangian

method of study.

• In Eulerian method

v = f (x, y, z, t)

p = f (x, y, z, t)

r = f (x, y, z, t).

• In case of steady flow velocity, pressure, acceleration and density, etc., do not change with time.

• In case of unsteady flow above variable at a point may change with time.

• If the velocity vector at all points in the flow is same at any instant of time, the flow is known as

uniform. The flow is known as non-uniform if the velocity vector varies from point to point at any

instant of time.

• Depending upon the existence of flow characters the flow may be classified as one, two-and three-

dimensional flow.

• In laminar flow, the fluid particles move along, regular paths which can be predicted well in

advance. It is also known as streamline flow.

In turbulent flow, the fluid particles are characterized by random and erratic movement resulting into

formation of eddies.

• A streamline is an imaginary line drawn in a flow field such that a tangent drawn at any point on this

line represents the direction of velocity vector.

• A pathline is the locus of a fluid particle as it moves along.

• A streakline connects all particles passing through a given point. It can be traced by injecting a dye

in the liquid.

• The position of a streamline at a given instant of time is known as instantaneous streamline. In case

of time-dependent flow, it may keep on changing.

• For incompressible fluid, the continuity equation is

Q = A1 V1 = A2 V2

• For compressible fluid, the continuity equation is

Q = r1 A1V1 = r2 A2V2

• The continuity equation for three-dimensional steady flow of incompressible fluid is

= 0

i.e., = 0

where f is the velocity potential.

• The flownet is graphical representation of two-dimensional irrotational flow and consists of a

family of streamlines intersecting orthogonally a family of equipotential lines.

• Uses of flownet are

1. For a given boundary of flow, the velocity and pressure distribution can be determined, if

velocity distribution and pressure at any reference section are known.

2. Uplift pressure on the underside of the dam can be calculated.

3. Outlets can be designed for their streamlining.

4. Loss of flow due to seepage in earth dams and unlined canals can be evaluated.

• Fluid motion in which the streamlines are concentric circles is known as the vortex.

• It there is no-rotation of fluid particles about their respective mass centre, the vortex is irrotational

or free vortex. If the fluid particles undergo rotation about their mass centres, the resulting vortex

is known as the forced vortex.