Explain Fluid kinematics || Fluid mechanics UNIT-2 definition, types, explain B-tech

Fluid kinematics

Fluid kinematics is a branch of fluid mechanics that deals with the study of motion and deformation of fluids without considering the forces that cause the motion. In other words, fluid kinematics focuses on describing the movement of fluids in terms of their geometrical and physical properties, such as velocity, acceleration, and displacement. 

Langragian and

 Eularian method

Langragian method :

The Lagrangian method follows the motion of individual particles of the fluid as they move through space and time. In this method, the position and velocity of each particle are tracked as they move through the fluid, allowing for a detailed analysis of the behavior of the fluid at the particle level. The Lagrangian approach is useful for studying problems where individual particles are important, such as in the study of turbulent flow.

Eulerian method:

The Eulerian method, on the other hand, focuses on the properties of the fluid at a fixed point in space. In this method, a fixed grid is used to represent the fluid, and the properties of the fluid at each point on the grid are analyzed as the fluid flows past. This approach is useful for studying problems where the overall behavior of the fluid is more important than the behavior of individual particles, such as in the study of fluid flow around objects.

Both methods have their strengths and weaknesses, and the choice of which method to use depends on the specific problem being studied. In general, the Lagrangian method is more computationally intensive but provides a more detailed picture of the fluid behavior, while the Eulerian method is less computationally intensive but provides a more global view of the fluid.

Description of Fluid flow 

Fluid flow refers to the movement of a liquid or gas through a physical system or environment. It can be described by various parameters, such as velocity, pressure, viscosity, density, and temperature.

In fluid dynamics, the behavior of a fluid is studied under different conditions, including laminar flow (smooth and orderly flow), turbulent flow (irregular and chaotic flow), and transitional flow (a mixture of both laminar and turbulent flow).

The flow of fluids is affected by many factors, including the shape and size of the container or conduit through which it flows, the velocity and pressure of the fluid, and the properties of the fluid itself, such as its viscosity, compressibility, and temperature.

Fluid flow has many practical applications in engineering, physics, and biology, including the design of aircraft and automobiles, the study of ocean currents and weather patterns, and the understanding of blood flow in the human body.

Description of stream 

line in fluid kinematics 

In fluid kinematics, a streamline is a path that a small, fluid element follows as it moves through a fluid flow.

Streamlines are imaginary lines that are tangent to the velocity vector at any given point in the flow. This means that the direction of a streamline at any point in the flow corresponds to the direction of the fluid velocity at that point.

In other words, a streamline is a line that shows the path of a fluid particle as it moves through the flow. Each streamline is unique and does not intersect with any other streamline.

Streamlines can be used to visualize the flow field of a fluid and to study properties such as velocity, acceleration, and pressure at different points in the flow. They are also useful for predicting the behavior of fluids in various applications, such as in the design of aerodynamic shapes or the analysis of blood flow in the human body.

Streamline of fluids 

Streamlines are imaginary lines that are used to visualize the flow of a fluid. They represent the path of a fluid particle as it moves through the fluid. In a steady flow, streamlines can be used to describe the velocity field at any point in the fluid.

The properties of streamlines include:

1.Streamlines are always tangent to the velocity vector of the flow at each point.

2.Streamlines never cross each other. If they did, it would mean that two fluid particles would occupy the same point in space at the same time, which is physically impossible.

3.Streamlines are continuous, meaning that they form a smooth and uninterrupted path through the fluid.

4.Streamlines are closer together in regions of higher velocity, and farther apart in regions of lower velocity.

5.The density of streamlines represents the volume flow rate of the fluid through a given cross-sectional area.

Pathline & Streakline

 Explanation 

In fluid dynamics, a pathline and a streakline are two concepts that describe the movement of fluid particles in a flow field.

pathline

A pathline is the path traced out by a single fluid particle as it moves through the flow field over a period of time. This pathline is a curve in space that represents the particle's trajectory, and it is determined by the velocity field of the flow.

streakline

A streakline, on the other hand, is a line that is formed by fluid particles that have previously passed through a fixed point in the flow field. These particles will have different pathlines, but they will all have passed through the same fixed point, resulting in a continuous line in space.

To visualize the difference between a pathline and a streakline, imagine a river with a bridge over it. If you drop a dye packet into the water and track its movement over time, you are tracing out the pathline. However, if you observe the dye packet from the bridge and see a line of dye passing by, you are seeing the streakline.

Both pathlines and streaklines can be useful for understanding fluid flow, and they can be visualized using various techniques such as particle tracing or computational fluid dynamics simulations.

Types of flow:

There are several types of flow, including:

1. Laminar flow

2. Turbulent flow

3. Transitional flow

4. Steady flow

5. Unsteady flow

6. Compressible flow

7. Incompressible flow

8. Viscous flow

9. Non-viscous flow

10. Open-channel flow

11. Closed-channel flow

12. Subsonic flow

13. Supersonic flow

14. Transonic flow

1. Laminar flow: A smooth, orderly flow where fluid particles move in parallel layers without mixing.

Laminar flow 

2. Turbulent flow: A chaotic, unpredictable flow where fluid particles mix in a random manner, causing eddies, swirls, and fluctuations in pressure and velocity.

Turbulent flow 

3. Transitional flow: A flow that exhibits both laminar and turbulent characteristics.

4. Steady flow: A flow where the fluid properties at a point do not change over time.

Study flow 

5. Unsteady flow: A flow where the fluid properties at a point change over time.

6. Compressible flow: A flow where the density of the fluid changes due to changes in pressure and temperature.

7. Incompressible flow: A flow where the density of the fluid remains constant.

8. Viscous flow: A flow where the fluid experiences internal friction due to viscosity.

9. Non-viscous flow: A flow where the fluid does not experience internal friction.

10. Open-channel flow: A flow where the fluid is partially or completely exposed to the atmosphere.

11. Closed-channel flow: A flow where the fluid is confined within a closed conduit or channel.

12. Subsonic flow: A flow where the fluid velocity is less than the speed of sound.

13. Supersonic flow: A flow where the fluid velocity is greater than the speed of sound.

14. Transonic flow: A flow where the fluid velocity varies between subsonic and supersonic speeds.

Types of motion:

In fluid mechanics, there are three main types of motion that a fluid can:

1. Translation motion.

2. Rotational motion.

3. Vortical motion.

1. Translation motion: This type of motion occurs when the entire fluid moves as a single body from one location to another. Examples include the flow of water in a river or the movement of air in a wind tunnel.

2. Rotational motion: This type of motion occurs when the fluid particles rotate about a fixed axis. Examples include a spinning top or a tornado.

3. Vortical motion: This type of motion occurs when there is a combination of translation and rotational motion, resulting in the formation of a vortex or whirlpool. Examples include eddies in a river or the vortex created behind a moving object in a fluid, such as an airplane wing.

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