## FLUID KINEMATICS

**Introduction: **The fluid kinematics deals with description of the motion of the fluids without reference to the force causing the motion. Thus it is emphasized to know how fluid flows and how to describe fluid motion. This concept helps us to simplify the complex nature of a real fluid flow.

When a fluid is in motion, individual particles in the fluid move at different velocities. Moreover at different instants fluid particles change their positions. In order to analyze the flow behavior, a function of space and time, we follow one of the following approaches:

1. Lagarangian approach

2. Eularian approach

**FLUID KINEMATICS: **In the Lagarangian approach a fluid particle of fixed mass is selected. We follow the fluid particle during the course of motion with time (fig).

The fluid particles may change their shape, size and state as they move. As mass of fluid particles remains constant throughout the motion, the basic laws of mechanics can be applied to them at all times. The task of following large number of fluid particles is quite difficult. Therefore this approach is limited to some special applications for example re-entry of a spaceship into the earth's atmosphere and flow measurement system based on particle imagery.

In the Eularian method a finite region through which fluid flows in and out is used. Here we do not keep track position and velocity of fluid particles of definite mass. But, within the region, the field variables which are continuous functions of space dimensions ( x , y , z ) and time ( t ), are defined to describe the flow. These field variables may be scalar field variables, vector field variables and tensor quantities. For example, pressure is one of the scalar fields. Sometimes this finite region is referred as control volume or flow domain.

For example the pressure field 'P' is a scalar field variable and defined as

Velocity field, a vector field, is defined as

Similarly shear stress is a tensor field variable and defined as

Note that we have defined the fluid flow as a three dimensional flow in a Cartesian co-ordinates system.

**Types of Fluid Flow: **Uniform and Non-uniform flow: If the velocity at given instant is the same in both magnitude and direction throughout the flow domain, the flow is described as uniform.

Mathematically the velocity field is defined as

Independent to space dimensions ( x , y , z ).

When the velocity changes from point to point it is said to be non-uniform flow. Fig.() shows uniform flow in test section of a well-designed wind tunnel and ( ) describing non uniform velocity region at the entrance.

Steady and unsteady flows:

The flow in which the field variables don't vary with time is said to be steady flow. For Steady flow,

Or

It means that the field variables are independent of time. This assumption simplifies the fluid problem to a great extent. Generally, many engineering flow devices and systems are designed to operate them during a peak steady flow condition.

If the field variables in a fluid region vary with time the flow is said to be unsteady flow.