Short Answer:

Uniform and non-uniform flow are two types of fluid motion based on how the velocity of the fluid changes with respect to space. In uniform flow, the velocity of the fluid remains the same at every point in the flow field at a given instant of time.

In non-uniform flow, the velocity of the fluid changes from one point to another at a given instant. Simply, if velocity is constant across the entire section, the flow is uniform; but if it varies with location, it is non-uniform. These types of flow help in understanding how fluids move in different geometries and conditions.

Detailed Explanation:

Uniform and Non-Uniform Flow

In fluid mechanics, the motion of a fluid can be described by observing how its properties such as velocity, pressure, and density vary from one point to another within the flow field. Based on the change in velocity with respect to position (space), fluid motion is classified into uniform flow and non-uniform flow.

These two types of flow are very important for understanding real-life fluid behaviors in pipelines, channels, and around objects. They help engineers to analyze the distribution of velocity, predict pressure loss, and design efficient systems.

Uniform Flow

Definition:
A flow is said to be uniform when the velocity of the fluid at every point in the flow field is the same at a given instant of time. In such flow, the speed and direction of the fluid particles remain constant with respect to space.

Mathematically, for uniform flow:

This means that the velocity does not change from one position to another along the direction of flow.

Example:

Flow of water through a straight pipe of constant diameter under constant discharge.
Flow of air through a long straight duct with smooth walls.

In these cases, the velocity remains uniform across the length of the flow region.

Characteristics of Uniform Flow:

Velocity remains constant at every point in the flow field at any given time.
Streamlines are parallel and evenly spaced.
The direction and magnitude of the velocity vector do not vary with position.
It usually occurs in ideal conditions where geometry and boundary conditions are constant.

In simple words, a uniform flow means every particle in the fluid moves with the same speed and in the same direction at any instant of time.

Non-Uniform Flow

Definition:
A flow is said to be non-uniform when the velocity of the fluid changes from one point to another at a given instant of time. The velocity may vary due to changes in cross-sectional area, obstructions, or flow path curvature.

Mathematically, for non-uniform flow:

This means that the velocity of the fluid changes with position along the direction of motion.

Example:

Flow through a pipe with varying diameter (nozzle or diffuser).
Flow of river water where the depth and width of the channel change continuously.

In these examples, the velocity varies because the cross-sectional area of the flow region changes along its length.

Characteristics of Non-Uniform Flow:

Velocity varies from one point to another in space.
Streamlines are not parallel; they converge or diverge depending on flow conditions.
The magnitude or direction of velocity changes with position.
Non-uniform flow is more common in real-world systems because most geometries are not constant.

Hence, in non-uniform flow, fluid particles move with different speeds or directions at different locations at the same instant.

Examples of Uniform and Non-Uniform Flow

Uniform Flow Examples:

Water flowing steadily through a straight pipeline with constant cross-section.
Air moving through a wind tunnel section of fixed area at constant velocity.

Non-Uniform Flow Examples:

Flow through a converging or diverging nozzle where velocity changes as the area changes.
Flow of liquid in an open channel with a changing slope or width.
Airflow over an aircraft wing, where the flow speed and direction vary around the surface.

These examples help visualize how geometry and boundary conditions affect the nature of the flow.

Importance in Fluid Mechanics

The study of uniform and non-uniform flow is essential because most practical engineering systems involve changes in geometry or conditions that affect fluid velocity. Some key points of importance are:

Design and Analysis: Engineers must know whether the flow is uniform or non-uniform to properly design components like pipes, ducts, and nozzles.
Calculation of Pressure Losses: In uniform flow, pressure loss is simpler to calculate; in non-uniform flow, more complex equations are required.
Energy Distribution: Non-uniform flow leads to variations in energy and momentum, affecting system performance.
Flow Control: Knowing the flow type helps in controlling flow distribution, especially in cooling systems and fluid networks.
Prediction of Flow Behavior: It helps in predicting how fluid speed and direction change with geometry, which is vital for stability and efficiency.

Thus, identifying uniform and non-uniform flow is a fundamental step in solving any fluid mechanics problem.

Flow Visualization for Uniform and Non-Uniform Flow

Flow visualization techniques such as dye injection or smoke trails help to identify whether a flow is uniform or non-uniform.

In uniform flow, the streamlines are parallel and evenly spaced, indicating that the velocity is constant throughout the flow field.
In non-uniform flow, the streamlines either converge (indicating acceleration) or diverge (indicating deceleration).

For instance, in a nozzle, streamlines get closer, showing that the flow is accelerating (non-uniform), while in a diffuser, they spread apart, showing decelerating flow.

Practical Applications

Uniform Flow: Used in laboratory testing and calibration processes, such as wind tunnel testing, where constant flow velocity is required.
Non-Uniform Flow: Found in most industrial applications, like turbines, pumps, and airfoils, where velocity distribution is not constant due to changes in geometry or operating conditions.

Hence, both types of flow are significant, depending on the design and purpose of the system.

Conclusion

In conclusion, uniform flow is the type of flow where the velocity remains constant at every point in the flow field at a given instant, while non-uniform flow occurs when the velocity varies from point to point. Uniform flow is generally idealized and used for simple analyses, whereas non-uniform flow represents real-life conditions found in engineering systems. Understanding these two types of flow helps engineers analyze and design efficient fluid systems by predicting how the velocity changes in different parts of the flow field.