Fluid Mechanics: Non-Uniform Flow

Study Notes

Flow Types and Characteristics

Non-uniform flow features varying velocities of liquid particles across different sections of a pipe or channel.
Steady flow maintains a constant quantity of fluid per unit time, while unsteady flow has a fluctuating fluid quantity.
Laminar flow occurs when individual fluid particle paths do not intersect, indicated by a Reynolds number less than 2000.
Turbulent flow involves crossing particle paths and lacks defined trajectories; this occurs with a Reynolds number exceeding 4000.
One-dimensional flow is represented as a straight line; two-dimensional flow appears as a curve.

Fluid Motion and Mechanics

Fluid motion can be categorized into translation, rotation, and distortion, with distortion split into angular and volume types.
Viscosity is a temperature-dependent property of fluids, remaining relatively unaffected by pressure.
Energy conservation in fluid flow is governed by Newton's second law, the continuity equation, and energy conservation principles, aligned with thermodynamic laws.

Key Fluid Dynamics Equations

The continuity equation applies to ideal fluid flows, affirming mass conservation and energy constancy along the flow path.
Reynolds number formula: ( Re = \frac{PDV}{\mu} ), where ( P ) is fluid density, ( D ) is pipe diameter, ( V ) is mean fluid velocity, and ( \mu ) is dynamic viscosity.
Bernoulli's equation states total energy remains constant in steady flow of a frictionless, incompressible fluid.

Fluid Properties and Measurement

Cohesion refers to the attraction between a fluid's own molecules; adhesion indicates volumetric changes due to resistance.
Density relates to viscosity through the formula: ( \text{Density} = \frac{\text{Dynamic Viscosity}}{\text{Kinematic Viscosity}} ).
The ideal fluid is characterized as both frictionless and incompressible, significantly simplifying fluid dynamic analysis.

Important Instruments and Laws

Hydrometers measure the specific gravity of liquids, while Pitot tubes assess fluid velocity within pipes.
Pascal's law highlights the uniformity of pressure in confined liquids, acting at right angles to containing surfaces.
Fluid definitions include gases, liquids, and fluidized solids, which continuously deform under shear forces.

Flow Lines and Concepts

Path line denotes the trajectory of moving fluid particles.
Streamlines indicate flow direction at any given point, while streak lines show the instant position of fluid particles passing a point.
Uniform flow preserves equal velocities across all sections of a channel or pipe, used frequently in channel flow analysis.

Description

This quiz focuses on the concepts of non-uniform flow in fluid mechanics, exploring the velocity variations of liquid particles in pipes and channels. It covers the categories of fluid motion, including translation, rotation, and distortion, as well as fundamental principles such as Newton's second law, the continuity equation, and energy conservation. Test your knowledge of fluid behaviors and energy equations in this engaging quiz.