##### Fluid Kinematics

#### Fluid Kinematics

Fluid Kinematics is the branch of fluid mechanics which deals with response of fluids in motion without considering forces and energies in them. The geometry of motion refers to the study of kinematics .

#### Types of Fluid flow

- Ideal and Real flow
- Compressible and incompressible flow
- Laminar and turbulent flow
- Steady and Unsteady flow
- Uniform and non uniform flow
- Rotational and irrotational flow

#### Flow Patterns

**Stream line**– Tracing of motion of different fluid particles**Streak line**– It is the line traced by series of fluid particles passing through a fixed point**Path line**– It is the actual path traced by a fluid particle over a period of time**Equipotential line**– Location of equal piezometric head

Flow patterns has following trajectory shapes:

- Streamline – PR
- Streak line – PQ
- Path line – PS
- Equipotential line – PT

**Vorticity **and** stream function** parameters exist both in rotational flow and irrotational flow but for irrotational flow its value is zero.

**Velocity potential** function exists only in ideal flow and irrotational flow.

#### Free vortex motion

A free vortex motion is that in which the fluid may rotate without any external force being applied on it. A free vortex flow is also called irrotational flow in order to emphasis the irrotationality of flow at all points except at the singular points.

Therefore, *The flow of water in a wash hand basin is being emptied through a central opening, is an example of free vortex motion.* In a central region of free vortex motion, the viscous effects becomes quite predominant due to which the fluid tends to rotate like a solid body with velocity proportional to the radius.

The motion of the particle is circular i.e. *tangential*.

Therefore,* vortex flow is free vortex motion*.

However, In it *no external torque* rotates the fluid mass.

#### Forced vortex motion

A motion in which the fluid rotates by the means of some external source of power is a forced vortex motion .

Its surface is parabolic (i.e. the rise of liquid level at ends and fall of liquid at the axis of rotation).

Therefore, **Rotational **vortex is a*forced vortex motion.*

However, In it *some external torque* or force rotates the fluid mass.

#### Rankine vortex motion

Rankine vortex motion is a combination of Free vortex motion and as well as Forced vortex motion.

*The movement of air mass in the case of Tornado* *is an example of Rankine vortex motion*. In other words, it is a Forced vortex motion at the core and Free vortex motion outside.

#### BERNOULLI’S Equation applicable for

- along a streamline
- for steady flow
- for incompressible flow
- when the effect of viscosity is neglected

#### EULER’S Equation is based on

EULER’S Equation is based on momentum conservation but not mass conservation. Thus, integration of differential form of euler’s equation of motion yields to bernoulli’s equation.